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Rheology and stability of magnetite dense media Klein, Bernard 1992

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RHEOLOGY AND STABILITY OF MAGNETITE DENSE MEDIAbyBERNHARD KLEINB.A.Sc, The University of British Columbia, 1985A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDepartment of Mining and Mineral Process EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSiTY OF BRITISH COLUMBIAMay 1992© Bernhard Klein, 1992National Libraryof CanadaCanadian Theses ServiceNOTICETHE QUALITY OF THIS MICROFICHEIS HEAVILY DEPENDENT UPON THEQUALITY OF THE THESIS SUBMITTEDFOR MICROFILMING.UNFORTUNATELY THE COLOUREDILLUSTRATIONS OF THIS THESISCAN ONLY YIELD DIFFERENT TONESOF GREY.Bibliothègue nationaledu CanadaService des thses canadiennesAVISLA QUALITE DE CETTE MICROFICHEDEPEND GRANDEMENT DE LA QUALITE DE LATHESE SOUMISE AU MICROFILMAGE.MALHEUREUSEMENT, LES DIFFERENTESILLUSTRATIONS EN COULEURS DE CETTETHESE NE PEUVENT DONNER QUE DESTEINTES DE GRIS.In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.___________________________Department of Mining & Mineral Process EngineeringThe University of British ColumbiaVancouver, CanadaDate May 6, 1992DE-6 (2/88)ABSTRACTThe efficiency of the dense medium separation process is known to depend on therheology and stability of the medium. In particular, the medium should exhibit a low viscosityand a high settling stability. Despite this knowledge, little information existed on these mediumproperties. The lack of information stems partially from the difficulties associated withmeasuring the rheological properties of unstable suspensions. In order to measure theseproperties, it was necessary to design a rheometer for settling suspensions. Once this wasachieved, the rheology and stability of magnetite suspensions were characterized and theinfluences of various medium parameters on these properties were investigated.Settling experiments revealed that magnetite dense media exhibit bulk zone settlingproperties that are characterized by the presence of (from top to bottom): a supernatant, atransition zone, a constant density zone and a sediment. The constant density zone was foundto have a solids content that was the same as that of the initial suspension. Test results indicatedthat the suspension mudline settled at approximately the same rate as the constant density zoneand should therefore provide a good indication of the media stability.Based on knowledge of the settling properties of magnetite suspensions, a rheometerfixture was designed that could be used to measure the rheological properties of suchsuspensions. The fixture is an elongated double gap concentric cylinder cup and bob arrangementthat positions the bob in the constant density zone of the settling suspension duringmeasurements.11Rheological measurements revealed that magnetite dense media exhibits yield shearthinning and thixotropic flow properties. The Casson flow curve model was found to fit therheological flow curves for these suspensions better than other well known models.Investigations into the effects of various parameters on medium rheology and stabilityrevealed that solids content, magnetite particle size and, in the presence of clays, pH are the mostimportant suspension variables. Other parameters that significantly affect the suspensionproperties include magnetization, dispersing agents and the presence of clay and fine coalcontaminants. Several of these parameters significantly affected the Casson yield stress, whileonly a few parameters affected the Casson viscosity, indicating that the yield stress is the mostcontrollable rheological parameter. In addition, over the tested shear rate range, the yield stressterm contributed much more to the apparent viscosity of the suspensions than the Cassonviscosity term, and is therefore the most important rheological property. It was also found thatthe yield stress is inversely related to the mudline settling rate such that when the yield stress ishigh the settling rate is low and vice versa.Investigations into the effect of particle size distribution on the properties of magnetitedense media revealed that media properties can be improved by using bimodal particle sizedistributions. In particular, at low medium densities, where stability is of concern, the size ratioof the two particle fractions and the proportion of fine magnetite particles were found to havea large effect on the settling rate. At high medium densities, where the media can be excessivelyviscous, optimum size ratios and proportions of fine particles can be selected to reduce thesuspension Casson yield stress.111TABLE OF CONTENTSABSTRACT iiTABLE OF CONTENTS ivLIST OF TABLES xLIST OF FIGURES xiiTABLE OF SYMBOLS xixACKNOWLEDGEMENTS xxiiCHAPTER 1: INTRODUCTION 1CHAPTER 2: OBJECTWES 2CHAPTER 3: SCOPE AND IMPORTANCE 3A: LITERATURE REVIEW 4CHAPTER 4: DENSE MEDIUM SEPARATION 44.1 Applications and Importance 44.2 Principle of Separation 64.3 Process Flowsheets 124.4 Factors Affecting Separation Performance 154.5 Effect of Medium Properties on Separation Performance 164.5.1 Static Separators 174.5.2 Dynamic Separators 20CHAPTER 5: MAGNETITE CHARACTERIZATION 265.1 Introduction 265.2 Mineralogy and Geological Deposition 265.3 Craigmont Magnetite Production 285.4 Physical and Chemical Properties 28CHAPTER 6: RHEOLOGICAL MEASUREMENTS 346.1 Rheological Measuring Devices 346.2 Concentric Cylinder Rheometry 366.2.1 Flow Geometry 366.2.2 Measurement Errors 416.2.2.1 Effect of Particle Settling 41iv6.2.2.2 Other Errors.6.3 Yield Stress MeasurementsRHEOLOGY OF SUSPENSIONSIntroductionTime Independent Flow7.2.1 Characterization of Flow Behaviour7.2.2 Flow Curve Modelling7.2.2.1 Newton’s Viscosity Law7.2.2.2 The Power-Law Model7.2.2.3 The Cross Model7.2.2.4 The Carreau Model7.2.2.5 The Bingham Plastic Model7.2.2.6 The Herschel Buildey Model7.2.2.7 The Casson ModelTime Dependent FlowVisco-elasticityCONTROL OF RHEOLOGICAL PROPERTIESRHEOLOGY OF MAGNE’IIl’E DENSE MEDIAIntroductionCharacterizationControl of Medium Properties9.3.1 Physico-Mechanical Parameters9.3.1.1 Solids Content9.3.1.2 Particle Size9.3.1.3 Particle Size Distribution9.3.1.4 Particle Roughness and Shape44475151525255575859616263646568CHAPTER 7:7.17.27.37.4CHAPTER 8:8.18.28.38.4CHAPTER 9:9.19.29.369Introduction 69Micro-rheology 698.2.1 Hydrodynamic Effects 708.2.2 Granuloviscous Effects 738.2.3 Electroviscous Effects 738.2.4 Aggregation Effects 74Physico-mechanical Parameters 788.3.1 Solids Content 788.3.2 Particle Density 838.3.3 Particle Shape 858.3.4 Particle Size 878.3.5 Particle Size Distribution 90Physico-chemical Parameters 948.4.1 pH and Dissolved Ions 948.4.2 Dispersing Agents 9698989899100100101103103VCHAPTER 10:10.110.210.310.49.3.2 Physico-Chemical Parameters9.3.2.1 pH and Dissolved Ions9.3.2.2 Dispersing Agents9.3.2.3 Magnetization9.3.3 Contamination110110110114115CHAPTER 11: SUMMARY OF LITERATURE REVIEWSECTION B: EXPERIMENTAL PROGRAM12.112.212.312.412.5117120120120120121122123CHAPTER 13: SAMPLE PREPARATION ANT)MATERIALSIntroductionMagnetite Characterization Procedures13.2.1 Density Determination13.2.2 Size Analyses13.2.3 Magnetics Content13.2.4 Electrophoretic Mobility13.2.5 Chemical Composition13.2.6 Magnetic PropertiesMagnetite Sample13.3.1 Preparation of Magnetite Sample .13.3.2 Characterization of Upgraded Magnetite13.3.2.1 Magnetite Density13.3.2.2 Particle Size Distribution13.3.2.3 Electrophoretic Mobility13.3.2.4 Magnetics Content13.3.2.5 Elemental Analyses13.2.2.6 Magnetic Properties13.3.3 Preparation of Size Fractions13.3.4 Characterization of Size Ranges104104105106108STABILITY OF MAGNETITE DENSE MEDIAIntroductionSettling in SuspensionsMeasurement of StabilitySettling Properties of Magnetite Dense MediaCHAPTER 12: EXPERIMENTAL PLANIntroductionMeasuring Rheological Properties of Settling SuspensionsRheology and Stability of Magnetite Dense MediaEffect of Parameters on Medium PropertiesEffect of Particle Size Distribution on Medium Properties13.113.213.3CHARACTERIZATIONSample .OF125125125125126128128129129130130132132135139142142146148150vi14.314.415.1 Introduction15.215.315.415.515.6151151151155155157157157162162162163163165165165165166169169170174175175177182183185187191203203205206209RHEOLOGICAL PROPERTIES OF MAGNETITE DENSE MEDIAIntroductionFlow Behaviour of Magnetite Dense MediaFlow Curve Modelling16.3.1 Model Fitting16.3.2 Model Discrimination13.4CHAPTER 14:14.114.213.3.4.1 Size Analysis of Size Fractions13.3.4.2 Density of Size Fractions13.3.4.3 Elemental Composition of the Size Fractions13.3.5 Preparation of Narrow Size Fractions13.3.6 Characterization of Narrow Size Fractions13.3.6.1 Size Analyses of the Narrow Size Fractions13.3.6.2 Densities of Narrow Size Fractions13.3.6.3 Elemental Composition of Size FractionsChemical Reagents and Medium Contaminants13.4.1 pH Modifiers13.4.2 Organic Dispersants13.4.3 Inorganic Dispersants13.4.4 Medium ContaminantsSE1TLING PROPERTIES OF MAGNETITE DENSE MEDIAIntroductionMudline Falling Rate14.2.1 Procedure for Mudline Falling Rate Determinations14.2.2 Results of Interface Settling TestsSolids Concentration Profile14.3.1 Procedure for Solids Concentration Profile Determinations14.3.2 Solids Concentration Profile ResultsConclusionsRHEOMETER FIXTURE FOR SETTLING SUSPENSIONSCHAPTER 15:Details of the Fixmre DesignFixture DimensionsCalibration of the FixtureFixture Evaluation15.5.1 Effect of Shaft and Spokes on Measured Stresses15.5.2 Particle Settling in the Elongated FixtureThe Rheological Measurement Procedures15.6.1 Measurement Time Periods15.6.2 Shear Rate Measurement Range15.6.3 Non-Newtonian Shear Rate CorrectionsConclusions15.7CHAPTER 16:16.116.216.3210210210211214221vii16.4 Time Dependent Flow Properties 22416.5 Conclusions 228CHAPTER 17: EFFECT OF PHYSICO-MECHANICAL AND PHYSICO-CHEMICALPARAMETERS ON MEDIUM PROPERTIES 22917.1 Introduction 22917.2 Determination of Parameter Levels 22917.3 Experimental Design 24017.4 Sample Preparation 24417.5 Characterization of Medium Properties 24717.6 Evaluation of the Effects on Medium Properties 25117.7 Results of Experimental Program 25217.7.1 Analyses of Measured Responses 25417.7.2 Effects of Suspension Parameters on Medium Properties 25817.7.2.1 Effect of Solids Concentration 25917.7.2.2 Effect of Particle Size 26017.7.2.3 Effect of Suspension pH 26217.7.2.4 Effect of Magnetization 26417.8 Conclusions 264CHAPTER 18: EFFECT OF PARTICLE SIZE DISTRIBUTION ON MEDIUMPROPERTIES 26618.1 Introduction 26618.2 Experimental Design 26618.3 Experimental Procedure 27018.4 Modelling the Effects of Particle Size Distribution 27118.5 Analyses of Regression Models 27418.5.1 Effect of Particle Size Distribution on the Casson YieldStress 27818.5.2 Effect of Particle Size Distribution on the CassonViscosity 28318.5.3 Effect of Particle Size Distribution on the Settling Rate. 28618.5.4 Optimization of Medium Properties 29018.6 Conclusions 291CHAPTER 19: CONCLUSIONS AND RECOMMENDATIONS FOR FURTHERWORK 29319.1 Conclusions 29319.2 Recommendations For Further Work 299REFERENCES 302APPENDIX I Publications Related to this Thesis 322viiiAPPENDIX II Program For Shear Rate Corrections 324APPENDIX Ill Simplex Optimization Program for Modelling RheologicalFlow Curve Data 332APPENDIX IV Model Discrimination Program to Compare Fits ofRheological Flow Curve Models 345APPENDiX V Settling Curves and Modelled Rheological Flow Curves forInvestigations into the Effects of Various Parameters onMedia Properties 351APPENDIX VI Settling Curves and Modelled Rheological Flow Curves forInvestigations into the Effects of Particle SizeDistribution on Media Properties 412APPENDIX VII Statistical Analyses of Modelled Media Properties 429ixLIST OF TABLESTable 5.1 Recommended specifications for magnetite used in dense media(Osborne, 1988). 30Table 8.1 Models describing relative viscosity as a function of solids content andmaximum packing fraction. 81Table 13.1 Magnetite samples considered for use in test work. 131Table 13.2 Comparison of density measurement results for upgraded magnetiteusing wet pycnometer, air pycnometer and volumetric flask methods. 134Table 13.3 Size analysis results for upgraded magnetite, determined using HoribaPSA, Elzone PSA and Cyclosizer. 137Table 13.4 Elemental analyses of upgraded magnetite sample. 145Table 13.5 Magnetic properties of the -400 mesh upgraded magnetite sample. 147Table 13.6 Size analyses of -45 pm, -30 pm and -15 pm size fractions determinedusing the Horiba Particle Size Analyzer. 152Table 13.7 Densities of the -45 pm, -30 pm and -15 pm size fractions determinedusing air pycnometer. 154Table 13.8 Elemental analyses of the -45 pm, -30 pm and -15 pm size fractions. 156Table 13.9 Size analyses of narrow size fractions determined using Elzone PSAand RRB size and distribution moduli. 158Table 13.10 Densities of narrow size fractions determined using air pycnometer. 160Table 13.11 Elemental analyses of the narrow size fractions. 161Table 16.1 Rheological flow curve equations used to model flow curve data formagnetite suspensions. 215Table 16.2 Coefficients of fitted rheological flow curve equations and R2 values. 216Table 16.3 Results of model discrimination procedure to determine which flowcurve equation best fit the rheological data. 223Table 17.1 Levels of -325 mesh (45 pm) contaminants in dense media. 239Table 17.2 Alias structure for fractional factorial design showing the confoundedmain effects, two factor interaction effects and three factor interactioneffects. 243Table 17.3 Coded levels for 295w fractional factorial experimental design used toinvestigate the effects of suspension variables on rheology andstability. 245Table 17.4 Variable levels corresponding to coded levels. 246Table 17.5 Responses of rheological properties and settling properties for each ofthe experimental runs. 249Table 17.6 Multiple index of determination values for each of the rheologicalequations fit to the measured flow curve data from the experimentalprogram. 250Table 17.7 Estimated effects of each variable for each of the determinedresponses. 253Table 17.8 Statistically significant estimates of the effects in order of magnitude. 255Table 18.1 Coded variable levels for central composite experimental design. 269xTable 18.2 Variable levels corresponding to coded levels. 269Table 18.3 Settling rate, Casson yield stress and Casson viscosity responses forexperimental program. 272Table 18.4 Casson yield stress, Casson viscosity and settling rate coefficients forfitted second order models. 273Table VII.1 Statistical analysis of the model for the Casson yield stress as afunction of particle size distribution parameters. 430Table VII.2 Statistical analysis of the model for the Casson viscosity as a functionof particle size distribution parameters. 431Table VII.3 Statistical analysis of the model for settling velocity as a function ofparticle size distribution parameters. 432xiLIST OF FIGURESFigure 4.1 Typical coal preparation process flowsheet using dense mediaseparation. 13Figure 4.2 Typical magnetite dense media recovery circuit (Osborne, 1988). 14Figure 6.1 Geometry of a conventional cup and bob rheometer fixture. 37Figure 6.2 Schematic showing settling of particles in a cup and bob rheometerfixture. 43Figure 7.1 Schematic showing various types of flow behaviours a) Newtonian, b)Bingham plastic, c) shear thinning, d) yield shear thinning, e) dilatant,and f) yield dilatant. 54Figure 7.2 Plot of two different flow curves that could be characterized by thesame apparent viscosity. 56Figure 8.1 Typical potential energy curve at the surface of a mineral particle. 76Figure 13.1 Process flow sheet showing the procedure that was used to upgrade themagnethe sample. 133Figure 13.2 RRB particle size distribution of upgraded magnetite sample measuredusing a) Horiba PSA, b) Elzone PSA and c) Cyclosizer. 138Figure 13.3 Electrophoretic mobility of -10pm magnetite sample showing an iso-electric point in the pH range of 2.3. 141Figure 13.4a Scanning electron micrograph of magnetite particles. 143Figure 13.4b Energy dispersive x-ray analyzer spectrum for magnetite particlesshowing an iron peak and a distinct silica peak. 144Figure 13.6 Scanning electron micrographs of a) magnetized (-75pm + 38jim)magnetite particles and b) magnetized -75pm magnetite particles. 149Figure 13.7 RRB particle size distributions of -45pm, -3Opm and -l5pm magnetitesamples determined using the Horiba PSA. 153Figure 13.8 RRB particle size distributions for narrow size fractions of magnetiteparticles from Elzone PSA data. 159Figure 14.1 Settling suspension of magnetite particles with a solids volume fractionof 15%. The photograph shows that the magnetite settles with a sharpsupernatantl suspension interface. 167Figure 14.2 Magnetite suspension mudline interface height versus settling timeshowing three sets of data (solids volume fraction = 0.15, pH = 8.24,temperature = 25°C). 168Figure 14.3 Volume solids fraction versus height in column of settling magnetiteparticles for settling times of zero minutes to ten minutes (solidsvolume fraction = 0.15, pH = 8.52, temperature = 25°C). 172Figure 14.4 Magnetite volume solids content as a function of height and settlingtime showing settling zones (solids volume fraction - 0.15, pH = 8.52,temp.= 25°C). 173Figure 15.1 Rheologic laboratory facility showing a) the Haake RV2O controller, b)the M5 viscometer, c) the PC and d) the temperature controller. 176Figure 15.2 Rheometer fixture for settling suspensions showing the bob positionedxiiin the constant density zone of a settling suspension. 178Figure 15.3 Plan view of a double concentric cylinder viscometer fixture. 181Figure 15.4 Rheometer fixture for measuring rheological properties of settlingsuspensions showing a) the bob, b) the inner cylinder, and c) the cup. 184Figure 15.5 Flow curves produced with the developed rheometer fixture, for 9.5mPa.s and 50 mPa.s standard viscosity oils. Three sets of data wereplotted for each oil. 186Figure 15.6a Photographs of the rheometer components: a) entire fixture, and b)shaft, spokes and cylindrical ring. 188Figure 15.6b Photographs of the rheometer components: c) shaft and spokes, and d)shaft. 189Figure 15.7 Flow curves produced for 10 mPa.s standard viscosity oil using a) theentire bob, b) the shaft, spokes and cylindrical ring, c) the shaft andspokes, and d) the shaft. 190Figure 15.8 Rheometer fixture for settling suspensions showing sampling points forsolids content determinations during rheological measurements. 192Figure 15.9 Constructed rheometer fixture for solids content determinations duringrheological measurements. 193Figure 15.lOa Solids concentration profile in the rheometer fixture at a settling timeof 2 minutes determined while the bob was not rotating. 195Figure 15.lOb Solids concentration profile in the rheometer fixture at a settling timeof 4 minutes determined while the bob was not rotating. 196Figure 15.lOc Solids concentration profile in the rheometer fixture at a settling timeof 6 minutes determined while the bob was not rotating. 197Figure 15.lOd Solids concentration profile in the rheometer fixture at a settling timeof 8 minutes determined while the bob was not rotating. 198Figure 15.lla Solids concentration profile in the rheometer fixture at a settling timeof 2 minutes determined while the bob was rotating at a shear rate of500 s1. 199Figure 15.llb Solids concentration profile in the rheometer fixture at a settling timeof 4 minutes determined while the bob was rotating at a shear rate of500 s_I. 200Figure 15.llc Solids concentration profile in the rheometer fixture at a settling timeof 6 minutes determined while the bob was rotating at a shear rate of500 s1. 201Figure 15.lld Solids concentration profile in the rheometer fixture at a settling timeof 8 minutes determined while the bob was rotating at a shear rate of500 s1. 202Figure 15.12 Measurement of shear stress at shear rate equal to 500 s’ versus timefor a magnetite suspension with a solids volume fraction of 0.15. 204Figure 15.13 Rheological flow curve for a magnetite suspension with 15% solids byvolume showing apparent dilatant flow behaviour at shear rates greaterthan approximately 40 s. 207Figure 15.14 Flow curve for magnetite suspension (solids volume fraction = 0.15)xiiiwith uncorrected shear rate data (AB8), and corrected shear rate data(RAB8). 208Figure 16.la Flow curve for magnetite suspension with a solids volume fraction of0.15 showing a band of data points produced from three consecutivemeasurements on the same suspension. 212Figure 16.lb Apparent viscosity versus shear rate for a magnetite suspension with asolids volume fraction of 0.15 showing data points for three consecutivemeasurements on the same suspension. 213Figure 16.2a Rheological flow curve for a magnetite suspension with a solids volumefraction of 0.15 and fitted Casson model. 217Figure 16.2b Rheological flow curve for a magnetite suspension with a solids volumefraction of 0.15 and fitted Herschel Buildey model. 218Figure 16.2c Rheological flow curve for a magnetite suspension with a solids volumefraction of 0.15 and fitted Carreau model. 219Figure 16.2d Rheological flow curve for a magnetite suspension with a solids volumefraction of 0.15 and fitted Cross model. 220Figure 16.3 Flow curve hysteresis for demagnetized magnetite suspension with asolids volume fraction of 0.15. 225Figure 16.4 Flow curve hysteresis for a suspension of magnetized magnetiteparticles (volume solids fraction = 0.15). 227Figure 17.1 Effect of magnetite solids content on the settling rate. 231Figure 17.2 Effect of particle size on settling rate of magnetite suspensions (volumesolids fraction = 0.15). 232Figure 17.3 Supernatant/slurry interface height as a function of time for magnetizedand demagnetized magnetite suspensions with a solids volume fractionof 0.15. 233Figure 17.4 The effect of pH on the settling rates of magnetite suspensions (volumesolids fraction = 0.15). 235Figure 17.5 Effect of carboxylmethyl cellulose and dextran on the settling rates ofmagnetite suspensions (volume solids fraction = 0.15). 236Figure 17.6 Effect of sodium hexametaphosphate and sodium silicate on the settlingrates of magnetite suspensions (volume solids fraction = 0.15). 237Figure 17.7 Effect of coal fines, kaolinite and bentonite content on the settling rateof magnetite suspensions with a volume solids fraction of 0.15. 241Figure 17.8 Relationship between the Casson yield stress and the settling rate. 257Figure 18.1 Predicted versus estimated Casson yield stress responses. 275Figure 18.2 Predicted versus estimated Casson viscosity responses. 276Figure 18.3 Predicted versus estimated settling rate responses. 277Figure 18.4 Response contours of the Casson yield stress as a function of size ratioand fine fraction (magnetite volume solids content = 0.15). 279Figure 18.5 Response contours of the Casson yield stress as a function of size ratioon fine fraction (magnetite volume solids content = 0.25). 280Figure 18.6 Response contours of the Casson viscosity as a function of size ratioand volume solids fraction. 284xivFigure 18.7 Response contours of the settling rate as a function of size ratio andfine fraction (magnetite volume solids fraction = 0.125). 287Figure 18.8 Response contours of the settling rate as a function of size ratio andfine fraction(magnetite volume solids fraction = 0.175). 288Figure 18.9 Relationship between the Casson yield stress and the settling rate. 289Figure AV.1 Settling curve interface height as a function of time for experimentalRun #1. 352Figure AV.2 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #1. 353Figure AV.3 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #1. 354Figure AV.4 Settling curve interface height as a function of time for experimentalRun #2. 355Figure AV.5 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #2. 356Figure AV.6 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #2. 357Figure AV.7 Settling curve interface height as a function of time for experimentalRun #3. 358Figure AV.8 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #3. 359Figure AV.9 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #3. 360Figure AV.1O Settling curve interface height as a function of time for experimentalRun #4. 361Figure AV.11 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #4. 362Figure AV.12 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #4. 363Figure AV.13 Settling curve interface height as a function of time for experimentalRun #5. 364Figure AV.14 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #5. 365Figure AV.15 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #5. 366Figure AV.16 Settling curve interface height as a function of time for experimentalRun #6. 367Figure AV.17 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #6. 368Figure AV.18 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #6. 369Figure AV.19 Settling curve interface height as a function of time for experimentalRun #7. 370Figure AV.20 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonxvmodels for experimental Run #7. 371Figure AV.21 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #7. 372Figure AV.22 Settling curve interface height as a function of time for experimentalRun #8. 373Figure AV.23 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #8. 374Figure AV.24 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #8. 375Figure AV.25 Settling curve interface height as a function of time for experimentalRun #9. 376Figure AV.26 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #9. 377Figure AV.27 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #9. 378Figure AV.28 Settling curve interface height as a function of time for experimentalRun #10. 379Figure AV.29 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #10. 380Figure AV.30 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #10. 381Figure AV.31 Settling curve interface height as a function of time for experimentalRun #11. 382Figure AV.32 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #11. 383Figure AV.33 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #11. 384Figure AV.34 Settling curve interface height as a function of time for experimentalRun #12. 385Figure AV.34 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #12. 386Figure AV.36 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #12. 387Figure AV.37 Settling curve interface height as a function of time for experimentalRun #13. 388Figure AV.38 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #13. 389Figure AV.39 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #13. 390Figure AV.40 Settling curve interface height as a function of time for experimentalRun #14. 391Figure AV.41 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #14. 392Figure AV.42 Rheological flow curve with fitted a) Carreau and b) Cross models forxviexperimental Run #14. 393Figure AV.43 Settling curve interface height as a function of time for experimentalRun #15. 394Figure AV.44 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #15. 395Figure AV.45 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #15. 396Figure AV.46 Settling curve interface height as a function of time for experimentalRun #16. 397Figure AV.47 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #16. 398Figure AV.48 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #16. 399Figure AV.49 Settling curve interface height as a function of time for experimentalRun #17. 400Figure AV.50 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #18. 401Figure AV.51 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #17. 402Figure AV.52 Settling curve interface height as a function of time for experimentalRun #18. 403Figure AV.53 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #18. 404Figure AV.54 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #18. 405Figure AV.55 Settling curve interface height as a function of time for experimentalRun #19. 406Figure AV.56 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #19. 407Figure AV.57 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #19. 408Figure AV.58 Settling curve interface height as a function of time for experimentalRun #20. 409Figure AV.59 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #20. 410Figure AV.60 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #20. 411Figure AVL1 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #1 (Ø=O.25, 4=0.40, d.Jd1=0.39, pH=8.08). 413Figure AVI.2 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #2 (p=0.25, =0.40, dJd1=0.13, pH=8.33). 414Figure AVI.3 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #3 (Ø=0.25, Ø=0.25, dJd1=0.39, pH=8.38). 415Figure AVI.4 a) Settling curve and b) fitted (Casson model) flow curve forxviiexperimental Run #4 (=0.25, p=0.25, cLJd1=0.13, pH=8.21). 416Figure AVI.5 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #5 (Ø=O.15, 4=O.40, dJd1=0.39, pH=8.17). 417Figure AVI.6 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #6 (=0.15, Ø=0.40, dJd1=O.13, pH=8.78). 418Figure AVL7 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #7 (Ø=O.15, =0.25, cLJd1=0.39, pH=8.42). 419Figure AVI.8 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #8 (=0.15, d=0.25, dJd1=0.13, pH=8.85). 420Figure AVI.9 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #9 (Ø=0.20, =0.325,d/d1=0.67, pH=8.25). 421Figure AVI.1O a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #10 (Ø=0.20, 4=O.325, dJd1=0.09, pH=8.63). 422Figure AVI.11 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #11 (p=O.2O, Ø=O.451, dJd=0.22, pH=8.35). 423Figure AVI.12 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #12 (Ø=0.20, Ø=O. 199, cLJd1=0.22, pH=8.29). 424Figure AVL13 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #13 (Ø=0.284, =0.325, dJd1=0.22, pH=8.27). 425Figure AVI.14 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #14 (p=0.116, Ø=O.325, dJd1=0.22, pH=8.41). 426Figure AVL15 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #15 (Ø=0.20, =O.325, dJd1=0.22, pH=8.42). 427Figure AVI.16 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #16 (=0.20, =0.325, dJd1=0.22, pH=8.94). 428xviiiTABLE OF SYMBOLSa,b,c,d,e,f model coefficientsA shear stress factorA1 model coefficientCD particle drag coefficientd particle diameterd, mean diameter of small particle fractiond1 mean diameter of large particle fractionD convective diffusion coefficientDr rotational diffusion coefficienttranslational diffusion coefficientFa accelerating forceFb buoyant forceFd drag forceF(d) cumulative per cent passing size dd632 size modulusd1 large particle diametersmall particle diameterE probable errorg gravitational accelerationm distribution modulusM shear rate factorh, hb bob heightH column heightH induced magnetic fieldHb height from cup bottom to bob topk,n power law model coefficientskf,lç rate constant of structure formation and rupture, respectivelyk0,k1 rate constants for rupture of linkages due to Brownian motion and shearingi is the estimated values of the effect,0 is the mean effect,L. value of effectm massm polydispersity material constantxixM intensity of magnetizationN,IT Krieger’s parameters for shear rate calculationp Nguyen’s parameter for shear rate calculationPer rotational Peclet numberPe translational Peclet numberr radiusr1 inner radius of inner gapr2 outer radius of inner gapr3 inner radius of outer gapr4 outer radius of outer gapr* shearing radiusRb bob radiusR0 cup radiusRe average particle Reynolds numbercritical Reynolds number for turbulence between cup and bobbob radiusR2 cup radiusR2 coefficient of multiple determinationS measured particle surface areacalculated surface area based on sizet timet-statisticT torquev velocityv settling rate transition zone/constant density zone interfacesettling rate constant density zone/sediment interfacev tangential velocityyr radial velocityVT terminal velocityV (7) variance of the estimated effectsVb bob peripheral velocityVSb bob slip velocitycup slip velocityX magnetic susceptibilityXl level of variable ixxY observed valueY1 measured response value for run iY1,Y2 predicted values from model one and two, respectivelyZ model discrimination variablematerial constantseparation densityE errorTI viscosity1lap apparent Newtonian viscosityshear rateTIc Casson viscosityTIN Newtonian coefficient of viscosityplastic viscosityrelative viscosityviscosity at zero shear rateviscosity at infinite shear ratestructural factorpf feed medium densityPi liquid densityparticle densityunderflow medium densityfine fraction of total solidsvolume solids fractionøeff effective volume solids fractionmaximum packing volume solids fractionshear stresstBy Bingham yield stressCasson yield stressHerschel Bulkley yield stressangular velocityxxiACKNOWLEDGEMENTSThe experiences gained during the time spent as a graduate student have been rewarding,interesting and enjoyable. The greatest reward was to become acquainted with the people thatI have met and worked with. There is no doubt that without the support and assistance of thesepeople, this document would never have been completed.I am deeply indebted to Professor Janusz Laskowski whose guidance, drive and supportwere critical to the completion of this thesis. I would like to express sincere thanks to ProfessorAndrew Mular for his guidance with the statistical aspects of the experimental program. I wouldalso like to thank Professor Ken Pinder for his useful comments and discussions regarding thesubject of rheology and Professor George Poling whose comment “keep it short” sticks in mymind as I prepare to submit this volume.I will miss the times spent working with Dr. Susan Partridge whose knowledge and inputcomplemented by her personality made performing this work an enjoyable experience. For thesereasons I am deeply indebted to her.I would also like to thank: Mr. Frank Schmidiger for the precision in which heconstructed the viscometer fixture; Mrs. Sally Finora for her technical assistance and for makingsure I drank enough coffee; my class mates Andrew Burkert and Richard Senior who knew littleabout my subject which allowed us to talk about something else for a change; Miss Cindy Thomwho proofread several sections of this document and who helped to prepare the figures; Mr. ReiniKlein, my brother, who prepared the photographs for me; Dr. W. Gordon Bacon for allowing meto use the BDA facilities to write up the thesis; and Mary Gelinas, Tali Afgin and Dave Clarkxxiiwho made time during the Christmas rush to assist in typing and assembling this document.I would like to express my appreciation to the Natural Sciences and Engineering ResearchCouncil of Canada for providing the research grant and equipment grant that were necessary forthis research program. I would also like to express my gratitude to Mr. W. Murray of the M7group for providing the magnetite samples for the test work.Finally, I would like to express appreciation to my wife, parents and siblings for their loveand support. I dedicate this thesis to my wife, Maren Klein, without whom I would have not hada cause to work for.xxiiiCHAPTER 1: INTRODUCTIONSuspensions of fine magnetite in water are used in dense medium separation processes.These suspensions behave like dense liquids to relatively coarse mineral particles which,depending on their density, either float or sink. The properties of dense media, however, differfrom those of a true liquid; they exhibit non-Newtonian rheology and the magnetite particles tendto settle producing non-homogeneous conditions.Media rheology and sedimentation stability are known to influence separation performanceof both static and dynamic separators. The rheology describes the resistance that a solid particleexperiences as it moves towards the appropriate separator outlet; a greater resistance results ina lower separation efficiency. The stability describes the degree of stratification of magnetiteparticles in the separator. Particle settling causes the formation of density gradients and zonesof varying medium density which can impair a sharp separation and thereby reduces theseparation efficiency. It is therefore desirable to control both of these media properties so thatthe process performance can be optimized.The rheology and stability of magnetite dense medium are affected by physico-mechanicaland physico-chemical parameters, and the presence of contaminants. While physico-mechanicalparameters describe the physical components of the system, the physico-chemical parametersdescribe the conditions that influence the inter-particle forces of attraction and repulsion.Contaminants, such as coal fines or clays, have a significant effect on the medium properties andmust therefore also be considered. It is important to note that the rheology and stability can becontrolled by manipulating the parameters, however, manipulating parameters to improve one of1the medium properties usually has an adverse effect on the other. It is therefore necessary toconsider the effects of these parameters on both the rheology and stability.While it is simple to measure and characterize settling properties, it is more difficult tomeasure the rheological properties of unstable suspensions. The stability can be characterizedby the settling rate of the supernatant-slurry interface; a high stability corresponds to a lowsettling rate and vice versa. However, since particle settling leads to the formation of a solidsconcentration gradient in the measuring region of standard cup and bob rotational viscometers,it affects rheological measurements.Since the overall objective of the dense medium related projects in the Department ofMining and Mineral Process Engineering included studies of the effect of media rheology ondense medium separation performance, improved methods of measuring dense media rheologyand a better understanding of this subject were needed.CHAPTER 2: OBJECTIVES1. To develop a method to measure the rheology of settling suspensions.2. To model and characterize the rheology of magnetite dense medium suspensions.3. To characterize the stability of magnetite dense medium suspensions.4. To study the relative significance of important controllable parameters that influencethe dense medium rheology and stability.5. To investigate the influence of particle size distribution on the dense medium rheologyand stability.2CHAPTER 3: SCOPE AN]) IMPORTANCEThe research objectives, as outlined above, are to provide basic information that is neededto study further the relationship between magnetite suspension properties and dense mediumseparation performance. Specifically, a full and accurate characterization of the rheologicalproperties of dense media will assist in determining their effect on process performance. Oncethe effects of these properties are understood, knowledge of how they can be manipulated willassist in optimizing the process efficiency. The ability to optimize separation efficiency throughthe control of media properties should benefit the processing of difficult-to-treat and fine coals.The development of a method to measure accurately the rheological properties of settlingsuspensions may also significantly aid processing and handling of many industrially importantdisperse systems such as coal water slurries, flotation concentrates and tailings, and cyanidationpuips.3A: LITERATURE REVIEWCHAPTER 4: DENSE MEDIUM SEPARATION4.1 Applications and ImportanceDue to the high efficiency and capacity of dense medium separation, it has become oneof the most important processes for cleaning coal and concentrating mineral ores. In particular,the process has the capacity to produce sharp separations even in cases when the densitydifference between the products is small and when the ore contains large amounts of near densitymaterial (Osborne, 1988). In addition, dense medium separation is used to process efficientlya wide range of particle sizes. The ore feed size typically ranges from 0.5 mm to 12 mm fordynamic separators and from 12 mm to 75 mm for static ones (Burt, 1984). It has been shownthat dynamic separators can be used efficiently to clean coal particles as fine as 75 pm (King andJuckes, 1984) and efforts to clean coal as fine as 15 pm have proven to be successful.In addition to its application in coal preparation, dense medium separation is also usedto process iron, diamond, potash, industrial mineral and sulphide and oxide base metal ores (Burt,1984). For many of these applications, the process is used as a pre-concentration step (Burt,1984, Aplan, 1989).It was reported (Osborne, 1988) that in 1980, over 35% of all coal cleaned in Canada andthe United States was processed using dense medium separation. In the United States, theapplication of the process for cleaning coal increased from 27.2% in 1975 to 39.0% in 19884(Aplan, 1989). This trend is expected to continue because of the ability of the process to dealwith fine coals at high separation efficiencies. The use of the process has increased worldwideas a result of the mining of more difficult-to-clean coals and the need to produce cleaner coal(Osborne, 1988).The medium density is determined by the total mass of fine solids and water divided bytheir total volume. Magnetite (density = 4800 kg m3 to 5200 kg m3) is typically used formedium with densities up to 2500 kg m3. At higher densities the medium becomes excessivelyviscous due to the high magnetite solids content. In this case higher density ferrosilicon ( density6700 kg m3 to 6900 kg m3) is used to produce medium with densities up to 4000 kg m3Mixtures of magnetite and ferrosilicon have also been used to produce a medium with suitableviscous properties while minimizing costs; ferrosilicon is significantly more expensive thanmagnetite. For coal preparation, where medium densities range from 1300 kg m3 to 1900 kg m3,magnetite is typically used.There is considerable interest in using dense medium separation to process fine coal (-500jim) as a result of the need for an efficient process that can handle these fine sizes. This isparticularly important for upgrading more difficult-to-clean coals, the removal of liberated pyrite,the deeper cleaning of coal to be used as coal/water slurries and coal/oil mixture fuels and theupgrading of oxidized coal fines. In addition, mechanized mining methods produce more finecoal than traditional methods resulting in an increased yield of fine material to be processed(Fourie et al, 1980, Killmeyer, 1982, Lathioor and Osborne, 1984, King and Juckes, 1984, 1988).Several plants have demonstrated the successful application of the cleaning to zero”concept using dense medium separation (Lathioor and Osborne, 1984, Burch and Stone, 1985).5The efficiency is, however, very dependent on the properties of the medium (Ferrara and Schena,1988). Stoessner (1987) showed that cleaning the -500 im fraction separately from the +500 jamfraction has many advantages with respect to separation efficiency because the medium propertiescould be better controlled for the specific size ranges.The second largest application of the dense medium separation process is in concentratingiron ore. The high capacity of the process and its ability to make separations at high densitiesmake it suitable for this application (Burt, 1984). In addition, the very high recovery efficiencyof the process has resulted in its extensive use for diamond concentration in South Africa(Chaston and Napier-Munn, 1976). As mentioned, DMS has found specific applications for theprocessing of sulphide and oxide base metal ores and industrial mineral ores. Recently, there hasbeen an increased interest to use dense medium separation to process potash ores (White andLittman, 1987). It was suggested that most new potash processing plants would install a densemedium circuit to produce a coarse grade product. The medium used for this application is asuspension of magnetite in brine.4.2 Principle of SeparationIt has long been known that suspensions of fme particles in water exhibit many propertiesthat are similar to those of a dense liquid. In particular, such a suspension has the ability toallow particles with a lower density than the medium to float and those with a higher density tosink (DeVaney, Shelton, 1940). The first commercial application of this concept was the Chanceprocess developed in 1918 (Chance, 1924). The process was advanced considerably with the6introduction of the Dutch State Mines dense medium cyclone in 1945 (Dreissen and Jennekens,1982) that introduced centrifugal forces to the separation process. Dreissen and Jennekens(1982), Burt (1984) and Osborne (1988) provide a summary of chronological developments inthe dense medium separation processes.The forces responsible for the movement of particles in the medium are the acceleratingforce, the buoyancy force and the viscous drag force. The predominant accelerating force instatic separators is due to gravity and in dynamic separators it is the result of centrifugal flow.From Newton’s second law, the force balance on a solid particle in a dense suspension can bedescribed by Equation 4.1.m=F +F +F (4.1)b a dwhere, b is the buoyant force,Fa is the accelerating force,Fd is the drag force,m is the mass of the particle, andis the particle acceleration.dtThe buoyant and gravitational forces acting on a particle can be calculated from itsvolume and density. The drag force is described by the Navier-Stokes equation. However,because of the complexity of determining a rigorous solution to this equation, drag coefficientsare used to describe these forces. Assuming the particle is spherical, the force balance in agravitational field can be rewritten as in Equation 4.2.7rn-4-!= td3g(p-p1)- CDP1V2A (4.2)dt 6 2where d is the particle diameter,g is the acceleration due to gravity,p, and Pi are the particle and liquid density,CD is the drag coefficient,v is the particle velocity,A is the surface area.The terminal velocity, v-i-, can be calculated from Equation 4.2 by setting the accelerationterm to zero.=- p,)gd (43)where, CD = 24/Re for Re < 0.1CD = 18.5/Re315 for 0.1 <Re < 1000CD = 0.445 for Re> 1000 and,Re = pdv/, average particle Reynolds number (Schlichting, 1979).For dynamic separators the predominant accelerating forces are due to centrifugal flow.The force balance for particles in these separators can be written as follows (Yopps et al 1987):rn! = td3v(p -- C pv2A (4.4)dt 6r Dir8where, r is radial position in the cyclone,Vr is the radial velocity, andv is the tangential velocity.In dynamic separators, the particle radial velocity determines whether the particle reportsto the overflow or to the underfiow products. The terminal radial velocity can be determined bysetting the acceleration term in equation (4.4) to zero (dv/dt 0) (Equation 4.5).- Pl)dV2) (4.5)3pl DrThese equations of motion describe the ideal movement of particles in a separator. Thedrag coefficient for an accelerating particle is, however, greater than that for a particle movingat steady terminal velocity (Schlichting, 1979). Since the time required to reach the terminalvelocity is small, the velocity equation will adequately describe the movement of the particles.Based on appropriate estimates of the parameters, the equations can be used to estimate theReynolds numbers for ore particles in dense media separators. Such an exercise reveals that inboth static and dynamic separators the Reynolds numbers for small and near density particles arein the intermediate range (0.1<Re<1000) where viscosity is important to particle movement(Napier-Munn, 1990). Calculations also indicate that large particles with densities significantlygreater than the medium experience turbulent flow. Napier-Munn (1990) fit of the form ofStokes equation to performance criteria (probable error and separation density). He found thatthe values of the fitted exponents for the viscosity and particle size terms were between valuesthat represent laminar and turbulent flow regimes. These results therefore support the conclusion9that most particles move in the intermediate flow regime where viscosity is important.The medium in both static and dynamic separators is constantly moving and flowing. Asa result eddy flows are produced which affect the motion of coal/ore particles in the separator.The above equations do not account for this type of movement in the medium and thereforerepresent an ideal situation which may be quite different to that in separators.In addition, the above equations have been derived for spherical particles moving in aNewtonian fluid. However, coal/ore particles are not spherical and dense media exhibitsnon-Newtonian properties. The correction for the non-spherical shape can be determined usinga volume equivalent diameter and shape factor. The settling of a particle through anon-Newtonian fluid is a more complicated subject; the drag coefficient is a function of theapparent viscosity which changes with shear rate. The effective shear rate experienced by aspherical particle moving through a Newtonian fluid at low Reynolds numbers can be shown toequal 2vT/d. Based on this expression, the effective shear rates for small and near densityparticles (in static and dynamic separators) are in the range (<100 s’) where the apparentviscosity is very dependent on shear rate.Du Plessis and Ansley (1967) determined the relation between the drag coefficient andBingham equation parameters (Equation 4.6). The relationship implies that the yield stressaffects particle movement through its contribution to the apparent viscosity of the medium.(4.6)where, r the plastic viscosity, and10tBY is the Bingham yield stress according to the Bingham equation,t=ty + (43)where, t is the shear stress and ‘ is the shear rate.Lockyer et al (1980) determined the drag force as a function of the coefficients (k andn) for a power law fluid.t kj’ (4.8)Fd = 127cM2(4)fln) (4.9)These expressions emphasize the need to relate separator performance to the completerheological properties rather than to some estimate of a suitable apparent viscosity.The magnitude of the forces on particles depends on the design of the separator and theoperating conditions. Various static separators have been developed including the dense mediumdrum, vessel and bath in which the separating forces on the particles are due to gravitationalacceleration. In dynamic separators, the centrifugal forces depend on the geometry of theseparator. The main types of dynamic separators are the Dutch State Mines (DSM) cyclone, theDynawhirlpool, the Tri-Flo, the Larcodem and the Vorsyl. A description of these separators canbe found in Burt (1986) and Osborne (1988).114.3 Process FlowsheetsBoth static and dynamic dense medium separators are used in coal preparation plants.The static separators are applied to upgrade the coarse coal and dynamic separators have foundapplications in treating the intermediate size coal. The flowsheet for a typical coal preparationplant using both types of separators is shown in Figure 4.1. The flowsheet shows that the rawcoal is classified into size fractions before feeding the separators. The coarse fraction +12 mmis fed to static separators, the 0.5 mm x 12 mm material is fed to dynamic separators and thefines (-0.5 mm) are upgraded using other processes such as water-only cyclones and flotation.It is important to de-slime the feed to the dense medium separators since fine material, such asclays, can adversely affect separation performance. Following upgrading, the products must bede-watered prior to shipping.The dense medium is recovered for re-use in a dense media recovery circuit (Figure 4.2)The magnetite is recovered for re-use in correct medium and dilute medium circuits. Themedium is drained from the separator products on screens and then flows to the medium sump.Medium not recovered at this stage is rinsed from the product with water through a second setof screens. This diluted medium is then upgraded and de-watered with the use of magneticseparators and densifying cyclones. The concentrated magnetite product is then added to themedium sump. The medium density is controlled at the outlet of the medium sump, where wateris added as required. A feedback controller is used to manipulate this water flow based on asignal from a nuclear density gauge.12RAWCOALWET—75mm+12mmSTATIC]FLOATS]DRAIN’51—75mm+12mmIDM5RINSE-DEWATERNC________SCREENNALSCREENS____________COALPRODUCTSINKSMEDIAIIDRAINAND]RINSEI_____________________________________________TAILINGSSCREENSDENSEMEDIAMEDIA_________MEDIAL.._1CI RCUITCOVER———RINSEI________—12mm÷0.5mmIDYNAMIC1IDRAINAND]LDE_WATERNG—12mm±0.5mmDESLIMEIDMSJLSCRENSSCREENI________________________COALPRODUCTSINKSMEDIAIDRAINANDIRINSEI__________________________________TAILINGSCREENSDENSEMEDIAIMEDIAIMEDIAI—ICIRCUIT———RECOVERYFINE1—0,5mmCOALICOALPRODUCTCLEANINTAILINGSFigure4.1Typicalcoalpreparationprocessflowsheetusingdensemediaseparation.COALFEEDSPLITTERCLASSIFYINCCYCLONESPROCESSWATFRFigure4.2Typicalmagnetitedensemediarecoverycircuit(Osborne,1988).4.4 Factors Affecting Separation PerformanceThe performance of both static and dynamic dense medium separators depends on theproperties of the medium, the design of the separating device and the operating conditions. Thedesign features of importance are specific to each type of separator; these have been describedelsewhere (Hudy, 1968, Deurbrouck and Hudy, 1972, Burt, 1984, Napier-Munn, 1983, Osborne,1988). The operating conditions include throughput, medium to coal ratio, feed particle size andfor dynamic separators inlet pressure; the effects of which have been reviewed by severalresearchers (Chaston and Napier-Munn, 1974, Napier-Munn, 1983, Osborne, 1988).The medium properties of interest are the density and some measure of both the stabilityand the rheology. The density is set between the densities of the two products by controlling themagnetite content. The stability describes the degree of stratification that occurs as a result ofthe settling of the medium particles. This stratification results in the formation of zones ofvarying density which can affect the sharpness of separation. The rheology describes theresistance that a particle experiences as it moves towards a separator outlet. In general mediawith low stabilities have low viscosities and vice versa. Both properties depend on the levels ofphysico-mechanical parameters, physico-chemical parameters and the presence of contaminants.It is therefore desirable to control these parameters in order produce a medium exhibiting a lowviscosity and a high stability.The partition curve is conventionally used to characterize separation performance for mostgravity separation processes. The probable error, E, the cut density, S50. the amount of materialshort circuiting to the overflow and the amount of material short circuiting to the underfiow can15be determined from this curve (King and Juckes, 1988). For dense medium cyclones, Scott etal (1986) defined the pivot parameters which are the medium split to separator underfiow andthe medium density in the separation region of the cyclone. These parameters are obtained fromthe point of intersection of partition curves produced for particles in different size ranges.4.5 Effect of Medium Properties on Separation PerformanceThere is a difference of opinion concerning the importance of viscosity in dense mediumseparation. Many researchers (Schranz, 1954, Geer et al, 1957, Whitmore, 1958, Collins et al,1983, Napier-Munn, 1983, Scott et al, 1987, Davis, 1987, Ferrara and Schena, 1988) haveprovided evidence to show the viscosity of the medium is an important process variable. Otherresearchers (King and Juckes, 1988) believe that because of the turbulent conditions in separators,the viscosity has little effect. Although turbulent flow in the separator likely influences particlemovement, the flow regime of the particle relative to medium determines the role of viscosity.As presented in Section 4.2, estimated Reynolds numbers for small and near density particles arein an intermediate range between laminar and turbulent flow regimes in which viscosity isimportant.Several investigators (Govier et al, 1957, Whitmore, 1958, Berghofer, 1959) have shownthat magnetite dense media exhibit non-Newtonian rheological properties that can be modelledwith the Bingham plastic equation. These non-Newtonian properties make it difficult to estimatethe drag force that a particle experiences as it moves through the medium (see section 4.2).Specifically, the role and relative importance of the yield stress and plastic viscosity are not16known. In addition, the rheological properties influence the medium stability which in turnaffects separation performance (Napier-Munn, 1990).4.5.1 Static SeparatorsOne of the first investigations showing that media viscosity affects the performance ofdense medium separators was performed by Schranz (1954). He used a surfactant (wetting agentcoco-amino-acetate) to reduce the consistency (viscosity) of barite and calcite media. Thereduction in viscosity resulted in improved separation performance (lower E) when cleaning coalin a small scale dense medium vessel. The improved performance was more pronounced forsmall (1.0-0.5 mm) particles than for larger ones. The study also showed that the separationperformance was better when using a stable” barite medium with reduced viscosity than whenusing a low viscosity but unstable” magnetite medium.Geer et al (1957) cleaned four different coals in a pilot scale drum separator usingmagnetite dense medium with bentonite to control viscosity. Increasing the viscosity resulted inan increased E; however, the magnitude of the increase was very dependent on the characteristicsof the coal. In particular, the viscosity affected E most when the coal was fine or when the coalcontained a large amount of near density particles. In a related investigation Yancey et al (1958)characterized the rheological properties of the medium using the Bingham plastic model. It wasfound that the yield stress was positively correlated with the plastic viscosity which made itdifficult to determine the respective roles of the two properties. To attempt to determine whichproperty had the greater affect on separation performance (Er), critical viscosity and critical yield17stress values were estimated from force balances. The critical viscosity is the viscosity thatwould prevent particles from settling a sufficient amount for separation and the critical yieldstress is the yield value that would support particles and prevent them from settling. Based onthe calculations, it was found that the critical viscosities were much greater than the measuredplastic viscosities. The changes in E could therefore not be explained by the changes inviscosity. The calculated critical yield stress values were, however, within the range of themeasured values implying that it affected process performance.Whitmore (1958) modelled the rheological properties of various types of dense media(barite, flotation tailings, shale, magnetite, galena) with the Bingham plastic equation. Usingdense medium baths to clean coal, he found that the E was affected by the plastic viscosity butwas independent of the Bingham yield stress (Equation 4.10). As is indicated by Equation 4.10,the E also increased as particle size (d) decreased. The value of the exponent for the particlediameter term (0.5) implies that the flow around the particles is turbulent. According to NapierMunn (1990), however, the exponent value of 0.5 for the viscosity term indicates that the flowis in the intermediate flow regime.1/2E = k (J (4.10)where k is a proportionality constant.In a subsequent investigation, Valentik and Whitmore (1964) showed that the yield stressaffected particle settling and thereby influenced separation performance. It was demonstrated thatsmall and near density particles do not exert sufficient stress on the medium to overcome the18yield stress and therefore do not settle. As a result, particles of different sizes have differentseparation densities. For example, for a top fed separator, the separation density for smallparticles is greater than the separation density for large particles. It was also observed that largesinking particles drag small float particles in their wake. Once at the bottom of the separators,these small particles were trapped by the yield stress and therefore reported to the sinks. Theeffect of the yield stress was reduced by vibrating the settling vessel; the vibration was added tosimulate conditions in an industrial separator. As a result of this investigation, it wasrecommended that control medium parameters be controlled (magnetization, clay content, particlesize, etc.) in order to reduce the yield stress. It was also stated that any increase in plasticviscosity, resulting from changes in these parameters, would be small compared to the effect ofa yield stress.In order to develop a better understanding of the respective roles of the yield stress andplastic viscosity, Valentik and Whitmore (1965) developed a model for the settling of particlesthrough a Bingham plastic fluid. In their model they assumed that usual drag forces experiencedby a moving body in a Newtonian fluid are supplemented by an additional force (=1t2d’CBY/4)to overcome the yield stress.Scott et al (1987) used tracers to study the effect of medium viscosity on the processingof iron ore in a bottom fed Wemco drum separator. The apparent viscosity of the ferrosiliconmedium was monitored with a Debex on-line viscometer and was adjusted by increasing themedium density (solids content), by adding magnetite and by allowing contaminant levels toincrease. As the viscosity increased, the E increased and the separation density increased. Theeffect of viscosity was more pronounced for small particles than for large ones. It was also19observed that the separation density for small particles was lower than the separation density forlarge ones. If it can be assumed that the yield stress contributed more to the effective apparentviscosity than the plastic viscosity, these results support those predicted by Valentik andWhitmore (1964).Results indicate that not only is medium viscosity important to the performance of staticseparators, but more specifically the non-Newtonian properties are important. The roles andrelative importance of the yield stress and plastic viscosity are, however, not known. Valentikand Whitmore (1964) suggested that yield stress contributes an additional component to the dragforce such that once the yield stress is overcome the plastic viscosity determines the movementof the particle. As presented in Section 4.2, the view of Du Plessis and Ansley (1967) is that theyield stress contributes to the drag coefficient implying that it affects separation performancethrough its contribution to the apparent viscosity. In either case, the yield stress must beconsidered to be important to the movement of the particles.4.5.2 Dynamic SeparatorsBased on direct and indirect evidence from the literature, Napier-Munn (1983) concludedthat for dense medium cyclones, “the characteristics and behaviour of the medium are processdetermining”. The relationship between separation performance and the medium viscosity andstability are, however, complicated by the non-Newtonian properties of the medium. NapierMunn (1990) concluded that the viscosity effects separation performance by two mechanisms:1. it influences the motion of the coal/ore particles, and202. it controls medium behaviour (stability) which in turn influences separationperformance.Researchers (Fern, 1952, Chaston and Napier-Munn, 1974) have believed for a long timethat a high medium viscosity resists the motion of particles and thereby has a deleterious effecton separation performance. Several investigators (Lilge et al, 1957, Collins et al, 1974, NapierMunn, 1980, Collins et al, 1983, Napier-Munn, 1984, Stoessner, 1987, Davis, 1987, Scott, 1988)have provided evidence to support this belief. The investigations have shown that the separationof small and near density particles are most affected by the medium viscosity. In addition, theeffect is more significant for the high density (solids content) separation of minerals than it isfor the low density separation of coal (Napier-Munn, 1990). Very few investigations have beenperformed to study the importance of the non-Newtonian properties of the medium.It has been established that dense media exhibit non-Newtonian flow properties whichimplies that the apparent viscosity will change with shear rate. Lilge et al (1957) related thetangential velocities of the medium at different radii in a cyclone to the shear rates. Apparentviscosities were then determined for different radii from rheological flow curves and thecalculated shear rates. For magnetite dense medium, which exhibited pseudoplastic properties,the apparent viscosity was determined to be highest near the periphery of the cone and lowestnear the centre. It should be noted, however, that since particles (coal/ore) move with themedium, the calculated shear rates (and therefore apparent viscosities) do not necessarilyrepresent those experienced by the particles. Specifically, particles of different size and densitywill move at different velocities (shear rates) relative to the medium and therefore experiencedifferent apparent viscosities.21To investigate the importance of viscosity independently of stability, Napier-Munn (1980)used a medium containing fine quartz in a dense liquid. Since the liquid had a density equal tothat of the quartz, the viscosity could be controlled by varying the amount of quartz in thesuspension. It was shown that a high medium viscosity resulted in a low separation efficiency.When a yield stress existed, the partition curve became horizontal over a density range close tothe medium density. It was suggested that the stress exerted by near density particles on themedium did not exceed the yield stress and therefore no density separation occurred. Analternate explanation is that at low shear rates, such as would be experienced by near densityparticles, a yield stress produces a high apparent viscosity that in turn resists particle movement.This result opposes the belief of some investigators (Ferrara and Schena, 1988) that a yield stresswould not influence the performance of dynamic separators due to the high shear stresses.From classifying hydrocyclone models that are based on the equilibrium orbit theory(Bradley, 1965), it can be shown that the separation density should increase with mediumviscosity (Napier-Munn, 1980). This trend was confirmed by tests performed with a densemedium cyclone using a “stable” medium composed of a quartz in a dense liquid (Napier-Munn,1984). It was shown that the separation density increased with both the plastic viscosity and theBingham yield stress. Several investigators (Napier-Munn, 1983, Napier-Munn, 1984, Scott etal, 1987, Davis and Napier-Munn, 1987) have observed, however, that increasing the viscosityof “unstable” media results in a decrease in the separation density. The discrepancy wasattributed to the unstable nature of the medium.Collins et al (1983) related medium stability to separation performance in tests with DSMcyclones and Vorsyl separators. The media were composed of mixtures of ferrosilicon and22magnetite and the stability (density differential between cyclone overflow and underfiow) wascontrolled by varying the magnetite content. It was found that separation performance wasoptimum when the density differential was in the range of 200 kg m3 to 500 kg m3. Theoptimum differential was found to be slightly higher for the separation of fine particles and lowerfor the separation of coarse particles. As the medium viscosity was increased, the differentialdecreased such that a very stable medium (differential < 200 kg m3) had an excessively highviscosity which in turn reduced separation efficiency. At differentials below 800 kg m3, theseparation density was found to be approximately equal to the underfiow density, while, at higherdifferentials it dropped off sharply. Napier-Munn (1984) and Davis (1987) found that theseparation density was close to but slightly higher than the underfiow density.Scott et al (1986) believe that a low medium stability results in the formation of densityzones; a high density zone forming near the apex of the cyclone and a low density zone formingnear the vortex. As a result, near density particles remain trapped in the cyclone; they are notdense enough to penetrate the high density zone of the apex and are too dense to report to theoverflow. When a large amount of near density material is present in the feed, it builds up inthe cyclone overloading it and eventually causing it to surge. In addition, the build up of solidscauses particle crowding which may impede particle movement resulting in a loss in separationefficiency (Ferrara and Schena, 1987).The results and observations described above imply that the relationship betweenseparation density and viscosity can be explained as follows. For an unstable medium, increasingthe viscosity reduces the underfiow medium density. If it can be assumed that the underfiowdensity is approximately equal to the medium density in the zone near the cyclone apex, the23reduced underfiow density corresponds to a lower density in this zone. As observed by Collinset al (1983), Napier-Munn (1984) and Davis (1987), the separation density is close to theunderflow density implying that particles with lower densities cannot penetrate the zone aroundthe apex and are therefore forced to report to the overflow. Increasing the viscosity, thereforeresults in a lower medium density near the cyclone apex which in turn decreases the separationdensity.Collins et al (1983) and Napier-Munn (1984) consider that the bulk of the medium in theseparator is of constant density except when low viscosities and high differentials exist. Underthese conditions the cyclone acts as a size classifier for medium particles (Ferrara and Schena,1988). As viscosity increases, size classification effects are reduced revealing a positivecorrelation between viscosity and stability. Studies (Yopps et al, 1987) with hydrocyclones havealso shown that the sharpness of size classification decreases as suspension viscosity increases.This relationship implies that the same mechanisms that are responsible for an increase inviscosity are also responsible for an increase in stability (decrease in size classificationefficiency).Horsley and Allen (1987) studied the relationship between the non-Newtonian propertiesof suspensions and size classification in hydrocyclones. They showed that when the suspensionexhibited a yield stress, the size classification efficiency was low. Increasing the yield stressresulted in a higher cut size and a reduction in classification efficiency. The existence of a yieldstress was attributed to particle aggregation. It was explained that fine particles that were trappedin the aggregates reported to the cyclone underfiow which resulted in a lower sizing efficiency.Since dense media exhibit a yield stress, similar mechanisms may be responsible for media24stability in dense medium cyclones.Researchers have shown that medium properties are process determining. Specifically,trends in process performance have been related to the viscosity and stability of the medium.In order to understand the mechanisms that relate medium properties to separation performance,however, it is necessary to have knowledge of the complete rheology.25CHAPTER 5: MAGNETITE CHARACTERIZATION5.1 IntroductionDuring the development of the dense medium separation process, the importance of theproperties of the suspended solids became apparent. DeVaney and Shelton (1940) compared theproperties of various solids that could be used as the medium solids. The factors considered tobe important included cost, density, shape of particles, resistance to abrasion, resistance tocorrosion, chemical inertness, and physical and chemical properties that affect the recoverabilityfor re-use. Magnetite is readily available and its properties meet the requirements listed above.The greater understanding of the role of the medium rheology and stability on densemedium separation performance, warrants investigations into the magnetite properties thatinfluence these medium properties. The important properties of the magnetite depend largely onits mineralogical composition, but they can be controlled to some extent. Properties such asliberation size and chemical purity depend on the geological environment in which the magnetitewas formed. The grade and particle size distribution are, however, determined by how thematerial is processed. The suitability of a particular source of magnetite is therefore partlyinherent and partly controlled by how it is prepared.5.2 Mineralogy and Geological DepositionMagnetite, Fe304 is an iron oxide mineral that belongs to the spinel group having the26chemical formula [Fe2][Fe3920]4. It has a cubic structure with oxygen atoms forming thelattice in a cubic close packed arrangement. Octahedral and tetrahedral interstices are occupiedby the ferrous, Fe2, and ferric, Fe, cations (Cann, 1979).Impurities affect the important physical and chemical properties of magnetite. Theimpurities may be present in three forms:i. as a result of iso-morphous substitutions of metal ions for Fe2 and Fe;ii. as mineral inclusions formed by exsolution during cooling; andiii. as inclusions formed during crystallization.The conditions of mineralogical deposition are important for the substitution andexsolution processes. The exsolved minerals typically contain the elements Ti, V, Mn, Mg andCr. Substitution is dependent on temperature, pressure, composition of the environment andproperties of the ions. Substitution of Fe2 is commonly by Ca2, Mn2,Mg2,Ni2, Co2 andZn2, and substitution of Fe can be by Cr and V. In addition, at high temperatures, there maybe coupled substitution of Ti and Fe2 for 2Fe (Cann, 1979).Magnetite is commonly found in skam, differentiated magmatic, stratabound, ultramaficand placer deposits. In British Columbia, the largest and most common deposits are skarns.Many of these deposits have been mined for iron ore; examples include Texada Island IronMines, the Brynnor Mine at Kennedy Lake, and the Jedway and Wesfrob mines on SouthMoresby Island. Many other mines contained significant amounts of magnetite, although mostdid not produce it as a secondary product with the exception of the Craigmont Mine. The stockpiles from the Craigmont Mine are the main source of magnetite for western Canadian coalproducers.275.3 Craigmont Magnetite ProductionThe Craigmont mine produced magnetite as a secondary product from its copper ironskarn deposit. The mine is located 200 kilometres north east of Vancouver, B.C.. From thebeginning of the operation in 1961 to closing in 1982 the mine produced 426,000 tonnes ofcopper from 36,750,000 tonnes of ore with an average grade of 1.28 per cent copper (Shewchuck,1983). Production of magnetite began in 1969 due to the demand by Kaiser Resources whoneeded it for their dense medium separation process at their Femie coal mine (Shewchuk, 1983).It is presently the main source of magnetite for use in dense medium by coal preparation plantsthroughout British Columbia and Alberta. The ore-body had an average iron grade of 19.8 percent which is accounted for by its magnetite grade of 14 per cent and hematite grade of 12 percent. In total, approximately one million tonnes of magnetite was concentrated from the raw oreand the reprocessed tailings. Annual shipments of approximately 50,000 tonnes to coal mineswere reported in 1982 (Hancock, 1988). Presently 430,000 tonnes remain in stockpiles.Magnetite recovery, from tailings material, grading 15% magnetite, where a further 600,000tonnes may be recovered, should commence in 1991 to increase the stockpile at a production rateof 50,000 tonnes per year (Murray, 1990).5.4 Physical and Chemical PropertiesThe suitability of a particular source of magnetite depends on its physical and chemicalproperties. The most important properties include particle density, particle size and size28distribution, particle shape, magnetic characteristics, magnetics content, elemental composition,surface chemistry and moisture content (Osborne, 1988). To determine the suitability of aparticular supply of magnetite, standard measuring procedures and property levels have beenestablished (Jonker, 1984; Anon, 1985; Osborne, 1986, 1988).Various organizations have set specifications for magnetite used in dense mediumseparation. These specification (Table 5.1) are based on the original standards set by the Britishcoal mining industry (Jonker, 1984; Osborne, 1986, 1988) and since they are quite general, theyshould only be considered as guidelines.The magnetite density determines the solids volume concentration required to produce aspecified medium density which is the total mass of magnetite and water divided by their totalvolume. The higher the density of the magnetite, the lower is the medium solids volumeconcentration. The concentration of magnetite in suspension affects the medium rheology andstability; at high concentrations the medium becomes viscous while at low concentrations it hasa poor stability. The density of the magnetite is also an indicator of its chemical purity. Puremagnetite has a density of 5180 kg m3 (Hancock, 1988); densities lower than this indicate thepresence of some form of impurities.The magnetite particle size and size distribution depends on the natural grain size. If thegrain size is very small, fine grinding may be necessary to liberate the magnetite from otherminerals. Small magnetite particles (-10 rim) are difficult to recover for re-use and can producea viscous medium. If the liberation size is large, it is possible to produce particle sizes and sizedistributions that are easy to recover and that produce desirable media characteristics.29o‘CD .C.()CD0..Cd)-CDCD00 Cd)fQ -aD CD0‘‘dVCd)-Cd)Cl)‘a-.Cl)Cd)-.•a-.CD0Qcr(ThCd)—.0CCC0Cd)SSCD ICd)a-. 0 1•CJI CD 0 I 0 i I a-. CD Cd) IAVVVIA‘CIAIVIVCi’rji00CCD.CCbCC—aUiL1CC. 0 DParticle shape is largely determined by the fracture characteristics of the magnetite andby the type of comminution process used to reduce the particle size. Most magnetite is groundusing conventional rod and ball mills producing angular and irregularly shaped particles.Alternatively, magnetite particles from steel smelter fly-ash (Osborne, 1988) and from placerdeposits have more rounded particle shapes. It has been shown that rounded ferrosilicon particlesprovide superior medium properties, with respect to viscosity, particularly at high solids content(Collins et al, 1974).Magnetite is ferromagnetic and since it is recovered by magnetic separators and isrecycled, its magnetic properties are very important. The magnetic properties are characterizedby the magnetic susceptibility, the saturation moment, and the coercive force.The magnetic susceptibility and saturation moment are indicators of the force exerted ona particle in a magnetic field. A greater magnetic force results in an improved recovery inmagnetic separators. Mineralogical replacement of ferrous cations in the magnetite latticestructure by other ions results in an inferior susceptibility and saturation moment. Mineralinclusions, such as finely disseminated quartz, also reduce the magnetic strength of the material.The coercive force describes the state of magnetization of the particles. A high coerciveforce corresponds to a high remnant magnetism resulting in magnetic aggregation of the particlesin the medium. Aggregation has a negative influence on both the rheology and the stability ofthe medium. When the magnetite has a high coercive force or remnant magnetism,demagnetizing coils have been installed in dense medium recovery circuits to reduce the amountof magnetic aggregation (Hartig et al 1951; Osborne, 1986, 1988).Once the magnetite is introduced into a magnetic field, its magnetic domains align in the31direction of the applied field. By removing the magnetic field, the domains realign to a state oflowest energy where the net magnetic effects of the domains cancel one another. If the magnetiteexhibits remnant magnetic properties, the domains remain partially aligned which causes theparticles to behave like small magnets. The coercive force has been attributed to the replacementof iron ions in the lattice structure. For example, these properties are particularly high whentitanium, (Ti4), is present in the ore. The coupled substitution of titanium, (Ti4), and ferrousiron, (Fe2j, ions for two ferric ions, (2Fe), which have a similar ionic radius, can take placeduring crystallization (Cann, 1979). Under these conditions the titanium ions are not as mobileas the ferric ions which seems to inhibit the dis-alignment of the domains. Therefore, when themagnetic field is removed the particles have a net magnetic force (Graham et al, 1982).Titaniferrous magnetite is characterized by high remnant magnetism that usually makes itunsuitable for use in dense medium.The “magnetics content” is a measure of the amount of magnetic material that isrecoverable with a magnetic separator and it can be considered as a magnetite grade. Measuredvalues depend on the type of measuring equipment used (Davis Tube, Magnachute etc.) and, tosome extent, on the equipment operator; the results are, therefore, difficult to compare. Thenon-magnetic fraction is typically magnetite grains locked with other minerals, very smallmagnetite particles that are difficult to recover and non-magnetic minerals that were trappedbetween magnetite particles during recovery from the run-of-mine ore (Osborne, 1988).The elemental composition of a magnetite sample, as discussed above, describes its purityand determines the sample density, magnetic properties, magnetics content and surface chemistry.The elements of most interest are: ferric and ferrous iron; cations that typically replace the iron32ions in the lattice structure; and elements that may be present in associated minerals.Surface chemistry of magnetite has received little attention in the dense media relatedresearch. The surface chemistry, however, influences inter-particle forces of attraction andrepulsion that affect particle aggregation which is very important to the properties of the medium.The iso-electric point (i.e.p.) for iron oxide minerals is typically between pH 6.0 and 7.0 (Leja,1983). The exact value of the i.e.p. can vary and it depends on the types and quantities ofimpurities in the sample. To control the state of aggregation, dispersing agents can be used.Many of the properties of magnetite are interrelated. The suitability of a potential sourcemay therefore be detemiined from some basic mineralogical information. It should be noted thatso far little effort has been given to the tailoring of a magnetite supply to optimize the densemedium separation processes.33CHAPTER 6: RHEOLOGICAL MEASUREMENTS6.1 Rheological Measuring DevicesThe most widely used devices developed to measure rheological properties of fluids andsuspensions include rotational viscometers and capillary (tube) viscometers (Nguyen, 1983,Cheng, 1980). Van Wazer (1963) and Whorlow (1980) described many of the devices that havebeen developed.The function of each device is to produce data that describe the flow behaviour of fluidsor suspensions in terms of shear stress and shear rate. Usually, one of either shear stress or shearrate is controlled while the other parameter is measured. The most appropriate device for aspecific application depends on the rheological properties of interest such as viscosity, yieldstress, thixotropy and visco-elasticity. The rotational viscometers are the most versatile and canbe used to measure all of these properties. Based on a review of rheological measuring devices,Graham and Lamb (1982) recommended rotational viscometers for measuring the rheologicalproperties of magnetite dense medium.The tube viscometers have also been widely used to measure the rheology of suspensions(Nguyen, 1983). Van Wazer et al, (1963), Whorlow (1980), and Hanks (1981) have reviewedseveral of these instruments. The two main concerns in using these viscometers are that they cannot be used to measure time dependent flow properties (Whorlow, 1980, Nguyen, 1983) and thatfor suspensions, measurement errors are produced as a result of particle migration in the tube(Whitmore, 1957, Seshadri and Sutera, 1970, Whorlow, 1980, Graham and Lamb, 1982). Tube34viscometers are, however, relatively inexpensive in comparison to rotational viscometers and canprovide some useful information if the data are treated properly (Whorlow, 1980).There are two main types of rotational viscometers; these are referred to as controlledstress and controlled rate viscometers. As is implied, in a controlled stress rheometer, the shearstress is controlled and the corresponding shear rate is measured. The best known manufacturersof these devices are Rheometrics, Carri-Med and Bohlin. In the controlled rate viscometer, suchas the Haake Rotovisco, the shear rate is controlled and the corresponding shear stress ismeasured.Each instrument has some specific advantages over the other. Both use similar measuringfixtures, either concentric cylinders or cone and plate. For suspensions that settle, cone and platefixtures are impractical because the sample in the measuring area would sediment before anymeasurements could be taken. Particle settling in concentric cylinder devices also causesmeasurement errors.The two basic types of concentric cylinders are the Couette type in which the cup rotatesaround a stationary bob, and the Searle type where the bob rotates in a stationary cup. Couetteinstruments are better for high shear rate measurements because in the Searle instruments,turbulence forms at relatively low shear rates (Schlichting, 1968). Significant advances havebeen made in the measurement and control of shear stresses and rates making these instrumentsvery accurate for a wide variety of fluids and suspensions. Van Wazer et al (1963) and Whorlow(1980) have reviewed many of the instruments that have been developed.356.2 Concentric Cylinder RheometryThe flow behaviour of a fluid or suspension is described in terms of a rheological flowcurve. This is a relationship between the shear rate and shear stress for the sample. In aconcentric cylinder viscometer, one cylinder rotates relative to the other; the rate of shear beingproportional to the angular velocity. The shear stress is usually measured as a torque on one ofthe cylinders. Figure 6.1 shows the geometry of a conventional concentric cylinder arrangement.The main assumptions required to determine the shear stress and shear rate from the torque andangular velocity, respectively, are (Van Wazer, 1963):i. steady, laminar flow only in the direction of cylinder rotation;ii. no wall slippage;iii. no end effects; andiv. shear rate, ,is a function of shear stress, t, only (Equation 6.1).( =f(t) (6.1)6.2.1 Flow GeometryThe shear stress and the shear rate depend on the geometry of the fixture and therotational speed. Derivations of expressions that relate the shear stress to the shear rate can befound in Van Wazer (1963) and Whorlow (1980). For a simple cup and bob fixture the shearstress can be described by Equation 6.2.36SECTION ZZ’Figure 6.1 Geometry of a conventional cup and bob rheometer fixture.z z,37T (6.2)2trhwhere, T is the measured torque,r is the bob radius, andh is the bob heightThe shear rate can be described by Equation 6.3.O)= r__ (6.3)where, 0 is angular velocityThe shear rate can be related to the shear stress by Equation 6.4.= -2t!. = f(r) (6.4)For a Newtonian fluid, the relation between shear rate and shear stress is by definition:Tt 1NY= 2(6.5)2n hrwhere, iN is the Newtonian viscosity coefficient.In this case the shear rate can be calculated by Equation 6.6.2oR2(6.6)R-R138where, R1 is the radius of the bob, andR2 is the radius of the cup.Several methods have been developed to determine the relation between shear stress andshear rate for fluids with unknown flow properties. Krieger and Efrod (1951, 1952) developeda method of calculating the shear rate from measurements with a single fixture as compared toother methods requiring several fixture geometries. Krieger (1968a, 1968b) then modified therelations from his original work. The following expression describes the shear rate relation withrespect to shear stress and rotational velocity:‘ (t) = 2No +f(t)) (6.7)where,N öln(t) (6.8)Mn(o)(6.9)öln(w)and,fit) t2/12(1_+_. . .. ) (6.10)where,t = 21n(s) (6.11)and (see Figure 6.1),Rs = (6.12)R1If the suspension exhibits a yield stress, there may be a small error in the shear rates as39calculated by Krieger’s equations. At low shear rates, the stress at the cup surface may be toosmall to cause the suspension to shear as the suspension will only shear out to the radius wherethe shear stress exceeds the yield stress. Therefore, the gap is effectively smaller than thatdetermined by the geometry of the cup and the bob (Hone and Pinder, 1979).The shear stresses at the cup and bob surfaces are related to their radii by the equation:RI—1=_i (6.13)t2 R1JThe radius to which the suspension will be sheared can be calculated by:r* RiJ [] (6.14)The gap is, therefore, effectively reduced to the difference:Gap = r* - R1 (6.15)Nguyen (1983) proposed a different solution to the shear rate calculation for the casewhere the yield stress exceeds the stress at the cup surface (Equations 6.16 and 6.17).= (6.16)15 pwhere,öln(’r) (6.17)ö ln()40The error obtained by using Krieger’s method depends on the magnitude of the yieldstress. Nguyen (1983) showed for drilling fluid with a high yield stress, low shear rate values,calculated using Krieger’s method, were in error by less than 2%.6.2.2 Measurement ErrorsThere are several measurement errors that occur when making rheological measurementson non-Newtonian suspensions. These errors are the result of particle movement such as settlingand migration away from the device surfaces.6.2.2.1 Effect of Particle SettlingSettling of particles make measurements in concentric cylinder fixtures difficult. In atypical cup and bob, the particles settle during measurement. This settling results in theformation of a particle depleted zone in the upper annulus between concentric cylinders and asludge at the bottom of the cup. The particle depleted zone will have a lower resistance to flowthan a homogeneous suspension resulting in a low shear stress measurement. At the same time,the sludge build up at the bottom of the cup may contact the bob and impede its rotation (seeFigure 6.2). These problems are most severe for suspensions of fast settling large, high densityparticles at low solids content.Several devices have been developed to measure rheological properties of settlingsuspensions. In most, methods were developed to maintain a homogeneous suspension in the41annular gap. Overand et al (1984) used a cup with slots on its walls and an open bottom whichis placed in a mixing bowl containing the suspension. The mixed suspension flows into theannular gap through the slots in the cup wall and thereby maintains the composition of thesuspension in the annular gap. They showed, using Newtonian fluids, that at low agitation rateswithin the mixing bowl, results compared well to values obtained with no mixing. Clarke (1967)positioned a cup with an opened bottom in a stirred vessel. The impeller at the bottom of thevessel caused the mixed suspension to circulate up through baffles in the walls of the vessel intothe top of the cup and down through the annular gap between the cylinders. Purohit and Roy(1965) developed a similar arrangement using paddles.Haake developed a bob with a helical groove which, when rotated supplies a lift tosettling particles. Haake also developed an arrangement with a pump which forces thesuspension up through the annular gap at a rate greater than the settling rate of the fastest settlingparticles (Haake, 1988). Similarly, Valentyik (1971), Ferrini et al (1979), Reeves and Roy(1985, 1990) and Klemblowski et al (1988), supplied the suspension to the top of the cup,allowing it to flow through the annular gap and out through the bottom during the measurements.Each of these methods, however, introduced undefined components to the shear rate experiencedby the suspension. While these devices may have produced good results under some conditions,for non-Newtonian suspensions with possibly time-dependent properties the undefined shear ratelikely influences the measured values.42SupernatantCupBobSuspensionSedimentZoneFigure 6.2 Schematic showing settling of particles in a cup and bob rheometer fixture.436.2.2.2 Other ErrorsSeveral possible effects may increase overall errors in measurements with concentriccylinder fixtures. Possible sources of error include end effects, wall slip, turbulence andtemperature effects. These can be corrected or minimized by the adjustment of the data and theproper design of the fixture.The end effect is due to the shearing of the suspension by the bottom surface of the bobwhich contributes to the measured torque and is not accounted for. End effect errors can bereduced by:i. minimizing the sheared surface area of the bottom of the bob,ii. arranging the geometry, so that the shear rate is the same at the bottom of the bobas that between the cylindrical surfaces, andiii. adding an extra effective length to the bob in calculations to account for theadditional stress (Van Wazer et al 1963, Whorlow, 1980).In a double gap arrangement the area of the bottom of the bob is small, therefore the endeffects may be considered to be negligible (Moore and Davies, 1956).Wall slip occurs in suspensions when a layer of liquid forms at the surface of the bob dueto the migration of particles away from the surface (Whitmore, 1957; Horie and Pinder, 1979;Mannheimer 1982, 1985; Leighton and Acrivos 1987). Since the liquid has a lower resistancethan the suspension, much of the shearing may take place in this layer resulting in a low shearstress measurement. Particle migration may occur due to the centrifugal forces acting on themby the rotating flow. In addition, since it is physically not possible for particles to penetrate the44surface, they are displaced away from the wall, creating a layer with a lower particleconcentration (Whorlow, 1980). The effect may be more pronounced for non-Newtoniansuspensions and at high shear rates (Wein et al, 1988). These type of effects may produce flowresults that can be mistaken as thixotropy since the particle migration takes place with time(Leighton and Acrivos 1987).Oldroyd (1956) mathematically described the effect of wall slip on the rotational speed(Equation 6.18).= ... + .. + (6.18)R Rb 2 twhere, and VSb are slip velocities for the cup and bob surfaces respectively.Several methods have been developed to correct for wall slip (Oldroyd, 1956,Mannheimer, 1985, Schlegel, 1986, 1988, Hanks ,1988, Yoshimura and Prud’homme et al 1988).These methods rely on various assumptions about the flow of the suspension in the annular gapthat may or may not apply. Roughening of the wall surface has also been shown to minimizethe wall slip effect (Cheng, 1978, Nguyen, 1983, Cheng, 1984).Searle type concentric cylinder viscometers have a low limiting maximum shear ratebeyond which turbulent flow wifi prevail. The turbulence results from moving fluid near theinner rotating cylinder that tries to move outward due to momentum and centrifugal forces. Thisoutward flow causes the formation of Taylor vortices, which is an intermediate stage betweenlaminar and turbulent flow (Duty and Reid, 1964, Graebel, 1964, Purohit and Roy, 1965,45Schlichting, 1968, Sun, 1972, Whorlow, 1980, Cheng, 1988). These vortices can be observedvisually as horizontal bands in the annular gap (Purohit and Roy, 1965). The result is an increasein the measured shear stress at high shear rates which is often mistaken for dilatancy in thesuspension. Taylor (1923) determined that the formation of this type of flow is a function of thegeometry of the fixture and the viscosity of the fluid. The critical Reynolds number, forthe onset of the Taylor vortices formation can be determined from Equation 6.19 (Taylor, 1923).RRe. =V(R-R) >41.3 C (6.19)b c b R—Rc bwhere, Vb is the peripheral velocity of bob.The transition to turbulent flow has been studied in more detail by Harris and Reid(1964), Krueger et al (1966) and Hocquart et al (1988). In Couette flow, where the cup rotates,the centrifugal forces stabilize the flow allowing for measurements at much higher shear rateswhile maintaining a laminar flow regime.At high shear rates the temperature of the sample may increase significantly with time.This may lead to errors in measurements, particularly for fluids and solutions whose viscosityis strongly dependent on temperature. For suspensions, in which the rheology is more dependenton particle interactions than on the viscosity of the suspending fluid, temperature is lesssignificant (Van Wazer et a!, 1963, Whorlow, 1980). The temperature is commonly kept constantby surrounding the fixture with a temperature controlled water jacket.466.3 Yield Stress MeasurementsThe yield stress is defined as the threshold stress that must be applied before permanentdeformation occurs. Cheng (1985) described yield stress as a time dependent property that hasa static and dynamic value. The static yield stress is greater than the dynamic value and it ismeasured after the sample has had sufficient time to develop its structure fully. The dynamicyield stress is measured after the sample has been sheared at which time the structure is at someequilibrium value. According to Tung et al (1989) the static yield stress is measured at a highDeborah number and the dynamic yield stress at a low Deborah number, where the Deborahnumber is defined as the ratio of characteristic relaxation time to the time of observation. Thetype of yield stress measured depends on the technique used. Cheng (1985) suggested using anobservation time that best suits the characteristic time of the particular process. The existenceof a yield stress has been the subject of many debates (Mannheimer, 1988). It is argued thatgiven sufficient time, applying a small stress will cause a fluid with an apparent yield stress todeform.Several techniques and devices have been developed to measure the yield stress, manyof which have been summarized by Nguyen (1983), Nguyen and Boger (1983), Cheng (1985),and Tung et al (1988). These can be divided into two major groups, direct methods and indirectmethods (Nguyen, 1983). The most common direct methods include the stress relaxation, thevane and the applied shear stress techniques. Indirect methods involve extrapolating flow curvedata or fitting the data with an appropriate model to find the zero shear rate intercept of the shearstress axis. Mewis and Spaull (1976) refer to a yield value determined in this way as an apparent47yield stress.The controlled stress technique of making direct yield stress measurements involvesslowly increasing the stress in a sample until it begins to flow and reducing it until it ceases toflow. In this case, the yield stress is approached from both static and dynamic conditions. It wasfound that the time allowed to observe flow at a particular stress influences the determined yieldstress value. In particular, the longer the time allowed to observe flow, the lower is the yieldstress (Cheng 1985). A controlled stress rheometer must be used to make these measurements.The vane method of direct yield stress measurement uses a special fixture of bladesattached to a spindle with the blades set at equal angles around the spindle. This fixture ispositioned in a cup containing the suspension. At very low shear rates the torque measuredthrough the shaft will increase from zero as force is applied. When the sample begins to shear,a maximum torque will be measured which decays with time to an equilibrium value. It isassumed that the suspension is sheared along a cylindrical surface defined by the dimensions ofthe blades. The yield stress may then be determined from the maximum torque and the area ofthe sheared surface (Nguyen, 1983, Nguyen and Boger, 1983, Nguyen, 1985, Tung et al 1989).The stress relaxation technique for determining yield stress involves shearing a suspensionat a constant rate and reducing the rate to zero either suddenly or slowly. The remnant stressexerted by the sample on the bob, preventing it from returning to a position of zero stress, isconsidered to be the yield stress (Nguyen and Boger, 1983, Nguyen, 1983). Wall slip may allowthis stress to decay with time, resulting in a lower than actual yield stress measurement (Nguyen,1983).The accuracy of indirect yield stress determinations depends on the accuracy and number48of data points in the low shear rate range. The low shear rate data can be extrapolated to theshear stress axis with the shear stress axis intercept being the yield value. For visco-plasticfluids, the shear stress drops off very quickly at low shear rates. For some fluids it may be foundthat if measurements can be made at sufficiently low shear rates no yield stress is found at all(Cheng, 1985). Cheng (1985) recommended constructing an equilibrium flow curve bymeasuring the equilibrium stress with time at various shear rates and then extrapolatingequilibrium flow curve data. Using a model to fit such data provides a good approximation ofthe yield stress. The model chosen must, however, be suitable to describe the flow behaviourof the particular suspension at low shear rates. In this case, the estimate of yield stress isconsidered to be better than the value obtained by extrapolating the data (Nguyen, 1985).The yield values determined using different techniques are difficult to compare as widevariations in the results are often observed (Tung et al, 1985, 1986, 1986, 1989). It is known thatthese variations may be due to the type of yield stress being measured, the time of measurement,the history of the sample and any errors associated with the technique. Comparisons of thesemethods have been made by Nguyen (1983), who found a good correlation between the valuespredicted by the fitted models using nonlinear equations (such as the Casson andHerschel-Bulkley equations) and direct methods such as stress relaxation and the vane method.The Bingham Plastic model was found to estimate a high yield stress, particularly at highsuspension solids concentrations. Tung et al, (1986, 1989) found that yield stress values obtainedusing the vane method were twice as large as values obtained by the model fitting techniques.The results could be explained by the difference between static and dynamic yield stresses(Cheng, 1985). They also found that the stress relaxation method predicted values that were49much lower than values obtained by using other methods. These lower values were attributedto wall slip.In general, the more methods used to measure the yield stress, the more definite are theresults. However, because of time dependence, shear history and the differences between themeasuring techniques, the results may be difficult to compare. A method that best suits theapplication in which the suspension is used is the most appropriate (Cheng, 1985).50CHAPTER 7: RHEOLOGY OF SUSPENSIONS7.1 IntroductionSuspensions of fme magnetite in water have many of the same mechanical properties asa liquid. These mechanical properties are the responses to the application of stress and arereferred to as rheological properties (Harris, 1977, Hanks, 1981). When shear stress is appliedto a suspension, the suspension deforms irreversibly and begins to flow according to a shearstress-shear rate relationship (Equation 7.1).t =J(y) (7.1)This relationship can be graphically plotted as a flow curve, the most common of whichare shown in Figure 7.1. The shapes of the curves depend on the micro-rheology which describesthe types and magnitude of interactions between the components of a suspension (Goldsmith andMason, 1967). The interactions are often responsible for the formation of a structure that maycomplicate the flow behaviour by making it time dependent (Cheng, 1985). In this case, theshear stress depends on both the shear rate and on time (Equation 7.2).= g(j,t) (7.2)The influence of the interactions can be controlled by manipulating the physical and51chemical characteristics of the suspension (Tadros, 1980). Tn this way the rheological propertiesof suspensions can then be controlled.7.2 Time Independent FlowFlow curves are used to characterize the rheological properties of fluids and suspensions.In order to apply this information, it is important to describe these curves mathematically.Several flow curve models have been developed to characterize flow curve shapes. Thecoefficients from these models can then be used as dependent variables to represent therheological properties.7.2.1 Characterization of Flow BehaviourThe basic flow curve shapes (Figure 7.1) or combinations of them, can be used tocharacterize the rheology of most suspensions. These flow behaviours can be categorized intotwo groups;i. those exhibiting only viscous properties, andii. those exhibiting visco-plastic properties.In an ideal viscous fluid, any strain resulting from the application of stress results ininstantaneous flow. In visco-plastic fluids, a yield stress must be overcome before any strain isrelieved by flow.The simplest flow behaviour is exhibited by fluids that obey Newton’s Viscous Law; these52are referred to as Newtonian fluids and they are characterized by a shear stress that is directlyproportional to the time derivative of strain. This flow behaviour is shown as flow curve (a) inFigure 7.1 which is a straight line passing through the origin of the shear stress - shear rate plot.The slope of the line is the viscosity which fully characterizes the flow behaviour of these fluids.Many dilute suspensions exhibit these Newtonian properties (Boger et al, 1978, Tadros, 1980,Hanks, 1981).Fluids or suspensions characterized by flow curves that deviate from that of a Newtonianfluid are referred to as non-Newtonian. Curve (c) of Figure 7.1 represents shear thinning orpseudoplastic properties. These curves exhibit a higher differential viscosity at low shear ratesthan at high shear rates. The differential viscosity is merely the slope of a tangent to the curveat a specific shear rate. Coarse particle suspensions and suspensions with asymmetric particleshapes are often characterized by this behaviour (Horie and Pinder, 1979, Cheng 1980b).The second class of non-Newtonian viscous fluids are dilatant or shear thickening(presented as curve (e) in Figure 7.1). The most common example of a suspension exhibitingthese properties is quick sand (Hanks, 1981). Upon shearing, such a system becomes less fluid.This type of flow behaviour is less common than shear thinning. Griskey (1989) has summarizedwhat is known about suspensions exhibiting this type of flow behaviour. Dilatant behaviour hasalso been observed at high shear rates for suspensions that are shear thinning at low rates (Hanks,1981).The plastic properties exhibited by many suspensions have been explained in terms of theinteractions between particles. These interactions are responsible for the formation of a structurethat will, upon the application of stress, resist flow (Hunter and Firth, 1981; Hunter, 1985a). The53Cr)U)LiiCDHCDCDliiICDShHEAR RATE.’Figure 7.1 Schematic showing various types of flow behaviours a) Newtonian, b) Binghamplastic, c) shear thinning, d) yield shear thinning, e) dilatant, and 0 yield dilatant.dOFCaa54minimum stress required to initiate flow is referred to as the yield value. Upon furtherapplication of stress, visco-plastic fluids flow in the same manner as the viscous fluids alreadydescribed. Curves (b), (d) and (f) are examples of Bingham plastic, yield shear thinning andyield shear thickening flow curves, respectively. Concentrated suspensions of interacting particlesoften exhibit Bingham plastic or yield shear thinning properties (Nguyen, 1983, Nguyen andBoger, 1983, Renehan, 1988b).Apparent viscosity is often used to characterize the rheology of suspensions. The apparentviscosity represents the viscosity of a suspension at a particular shear rate (Van Wazer, 1963).Figure 7.2 shows two flow curves with the same apparent viscosity. Clearly, apparent viscositydoes not fully describe the flow behaviour of these fluids. In addition, it can be misleading asit characterizes both the flow behaviours as being the same when they are different.7.2.2 Flow Curve ModellingIn order to describe the flow curves mathematically, several rheological models have beendeveloped. Mechanistic approaches are, however, difficult to apply because of the diversity ofproperties responsible for the rheological behaviour. More commonly, empirical models havebeen used to describe the characteristics of the flow behaviour.Several empirical equations relating shear stress to shear rate have been developed tomodel the basic flow curve shapes. The criteria for the suitability of a model are:i. it should fit the data over a wide range of shear rates,ii. it should be simple with a minimum number of independent constants,55/(ncc)H(I-)E////I//I/ep =SHEAR RATE.’Figure 7.2 Plot of two different flow curves that could be characterized by the same apparentviscosity.56iii. its’ constants should be easily determined and,iv. the constants should have some physical significance.Regression methods may be used to fit the equations to the rheological data. The fit ofthese equations can then be compared using statistical methods. Many of the equations weredeveloped for specific systems for which their coefficients have physical significance. Inparticular, coefficients may describe various viscosities or yield stress values which help toexplain the types of interactions responsible for the rheological properties. Models with thesmallest number of coefficients are preferred because they are usually simple to use.The following describes some of the models commonly used to represent the rheologicalproperties of suspensions. Included are Newton’s Viscosity Law, three models that can be usedto characterize shear thinning properties and three models that describe plastic flow properties.The shear thinning properties are often characterized using the Power-Law Model, the CrossModel and the Carreau Model. Models that describe plastic flow properties must have a yieldstress term such as the Bingham Plastic Model, the Herschel Bulkley Model and the CassonModel.7.2.2.1 Newton’s Viscosity LawThe flow behaviour of Newtonian fluids can be described by Newton’s Law of Viscosity(Equation 7.3).(7.3)57where tN is the Newtonian coefficient of viscosity.According to Hanks (1981), this equation is not a law but rather an empirical rheologicalequation of state. It has been used to describe the rheology of dilute suspensions ofnon-interacting spheres in Newtonian liquids (Einstein, 1905, Harris, 1977, Boger, 1978, Tadros,1980, Hanks, 1981, Czaban, 1988). Above a critical solids concentration, suspensions exhibitnon-Newtonian properties (Nguyen and Boger, 1984, Czaban, 1988). The onset ofnon-Newtonian flow is believed to be due to the particle-particle interactions that becomesignificant with increasing solids concentrations (Smoluchowski, 1916, Tadros, 1980, 1985). Thecritical solids concentration, above which interactions cause the flow to become non-Newtonian,has been found to decrease with decreasing particle sizes and with increasing asymmetry ofparticle shapes.7.2.2.2 The Power-Law ModelThe power law model originated from empirical observations by Ostwald who noticed thatrheological data plotted a straight line on log-log plots (Hanks, 1981). The model (Equation 7.4)is also referred to as the Ostwald-De Waele model.7.4This equation can be used to model all three basic viscous flow behaviours. Thecoefficients k and n are referred to as the fluid consistency index and flow behaviour index,58respectively (Boger et al, 1978, Nguyen, 1983). A high k value implies that the suspension hasa high viscosity. The deviation of n from unity is a measure of the non-Newtonian behaviour.Clearly, at n equal to unity, the equation becomes Newton’s viscous law and k becomes 11N• Forn less than unity, the model describes pseudoplastic flow and, for n greater than one it describesdilatant flow.The model fails to fit the flow behaviours of many suspensions accurately at very low andvery high shear rates (Van Wazer, 1963, Boger et al, 1978, Hanks, 1981, Nguyen, 1983).Another criticism is that, based on dimensional analysis, the coefficients have little physicalsignificance (Van Wazer, 1963, Harris, 1977). Despite these misgivings, it is likely the mostwidely used model for describing pseudoplastic behaviour (Harris, 1977). It has been used tocharacterize coal-oil mixtures (Alessandrini et al, 1983), kaolinite suspensions (Czaban, 1988),quartz and feldspar slurries (Aarnio and Laapas, 1988) as well as other mineral slurries (Bogeret al, 1978).7.2.2.3 The Cross ModelThe Cross model (Equation 7.5) was developed based on the assumption thatpseudoplastic flow is due to the process of the formation and rupture of linkages in chains ofparticles. This process is believed to occur in aggregated systems where links between particlesresult in the formation of chain-like aggregates which rupture due to Brownian motion andshearing (Cross 1965, 1970).59-lap 1a + (7.5)(1 - ar)where 1lap is the apparent viscosity,T is the apparent viscosity at infinite shear rate,T is the apparent viscosity at zero shear rate,a is a material constant associated with rupture of linkages, andm is a parameter that depends on the polydispersity.The material constant a is defined as k1/k0 where k0 is the rate constant associated withrupture due to Brownian movement and k1 is the rate constant for ruptures resulting fromshearing.Studies with calcite mineral suspensions revealed that values of r, and a were very large.The high a value is attributed to the relative insignificance of the effect of Brownian movementon the linkage rupture as compared to the effect of shearing. Therefore the ratio of the respectiverate constants is very high. This could be expected for most coarse suspensions. In the caseof high initial viscosity, and relatively coarse particles, the Cross model can be simplified(Equation 7.6).= + ajr (7.6)A value of m equal to 2/3 was found to be suitable for many pseudoplastic systems whichreduces the number of coefficients in the equation to two (Cross, 1965). The Cross model hasbeen applied to suspensions that exhibit pseudoplastic behaviour (Mewis and Spaull, 1976).607.2.2.4 The Carreau ModelThe Carreau model (Equation 7.7) was developed to describe the pseudoplastic propertiesof polymer solutions and melts. It is based on molecular network theory which describes thenon-Newtonian flow with respect to the creation and loss of segments. The rate of the creationand loss of these segments is a function of shear rate and results in the non-Newtonian responseto shear. At a high deformation rate there is a simultaneous increase in rate of segmentformation due to increased contacts, and an increased rate of junction breakage due to shearing(Carreau 1972, 1979a, 1979b).= i(1 + (A’)2) (7.7)where, A is a time constant,11 is the zero shear rate viscosity, ands is associated with the power law behaviour.According to this equation, at high shear rates the viscosity approaches zero which is aflaw of the model. To correct this flaw, a high shear rate viscosity term, jL, can be added tothe equation as indicated in Equation 7.8.-= + (A)2 (7.8)- TL.)This equation has been successfully applied to numerous polymer solutions (Carreau,611972,1979; Tam, 1988). It is a flexible, meaningful and simple model that is an improvementover the power-law model (Carreau, 1979).7.2.2.5 The Bingham Plastic ModelThe Bingham Plastic model (Equation 7.9) describes the simplest type of visco-plasticflow. The model characterizes the ideal case in which a complete structure breakdown occursonce the yield stress has been exceeded. Once the yield stress is exceeded a linear relationshipexists between the shear stress and shear rate (Nguyen, 1983).=ty + (7.9)where, tBY is the Bingham yield stress, and‘q,1 is the plastic viscosity.For most real systems, once the yield stress has been exceeded, the suspensions exhibita non-linear flow behaviour. In this case the model may be adequate for fitting only the veryhigh shear rate data (Nguyen, 1983). However, using this equation to predict yield stress can bevery inaccurate. The lack of data at low shear rates often results in a high estimate of the trueyield stress if the Bingham model is used. The model can even predict a yield stress where noneexists (Nguyen, 1983 Nguyen and Boger, 1983). Therefore, the Bingham yield stress should beconsidered to be a model parameter rather than a true yield value (Mewis and Spaull, 1976).The Bingham model is widely used because of its simplicity. The equation is based on62observations made with paints and clay suspensions. Nguyen found that this equation fits flowcurves for red mud suspensions with low solids concentrations (<20% by volume) better thanthose with high concentrations. Other suspensions that have been modelled with this equationinclude suspensions of kaolinite clays (Nicol and Hunter, 1970, Czaban, 1988), drilling mud(Nguyen, 1983, Nguyen and Boger, 1984), flocculated brewing yeast suspensions (Speers, 1989)and many other mineral suspensions (Mewis and Spaull, 1976, Hanks, 1981).7.2.2.6 The Herschel Buildey ModelThe Herschel Bulidey model (Equation 7.10) is a combination of the Ostwald-De Waelepower law model and the Bingham plastic model. As the yield stress term becomes small, theequation assumes the form of the power-law model and, as the power coefficient,n, approachesunity, it becomes the Bingham plastic model.t=+ (7.10)where, tHB is the yield value, andk and n have the same meaning as described for the power law equation.This model fits the curvature at low shear rates and therefore provides better estimatesof yield stress than the Bingham model. Yield stress values determined using this equationcompare well with the values determined using direct measurement methods (Nguyen, 1983,Nguyen and Boger, 1983). This simple, versatile and practical empirical model has been widely63used to characterize both dilute and concentrated suspensions (Mewis and Spaull, 1976, Mun andBoger, 1988). Examples of the applications include coal slurries (Alessandrini et al, 1983,Casassa et al, 1984), red mud (Nguyen, 1983, Nguyen and Boger, 1984), drilling fluids(Alderman et al ,1988), kaolin suspensions (Czaban, 1988), highly concentrated ceramicsuspensions (Doraiswamy et al, 1988), and paraffin wax in oil solutions (Al-Farris and Pinder,1987).7.2.2.7 The Casson ModelThe Casson model (Equation 7.11) is a simple two parameter model that has a physicalbasis and is derived from structural arguments. It is proposed that particles form chain-likeaggregates, the dimensions of which control the viscosity. Under conditions of flow, disruptivestresses develop which are a function of shear rate and particle aggregate size. The disruptivestresses are responsible for the break up of these aggregates such that for a particular shear ratethere is a mean aggregate size. The formation of the aggregates is the result of net inter-particleattraction forces. The contribution of these aggregates to the viscosity depends on their shapeand orientation. It is assumed that the aggregates form chains that can be treated as cylindricalrods. The contribution of hydrodynanñc effects involving these rods to the energy dissipationwas used to develop the Casson model (Casson, 1959).= (t + ()112)2 (7.11)64where, t is the Casson yield stress, andflc is the limiting viscosity at high shear rates.The coefficients are related to the suspension solids concentration, the viscosity of thesuspended liquid and various parameters describing the rod size and orientation. Since theCasson yield stress is the flow curve intercept with the shear stress axis and the Casson viscosityis the slope of the flow curve at high shear rates, the coefficients are easy to determine. Inaddition, the coefficients have physical significance since they have stress (Pa.) and viscosity(mPa.s) units. Tadros (1980) developed a similar equation from fundamental principles ofparticle aggregation. Mills and Snabre (1988) applied fractal concepts to describe particleinteractions and also obtained a similar expression. This model is capable of fitting low shearrate curvature and therefore its estimates of the yield stress compare well to values obtained fromdirect measurement methods (Nguyen and Boger, 1983, Tung et al, 1989). Casson developedthe model for suspensions of pigments in varnishes. Examples of its applications include, kaolinsuspensions, drilling fluids (Czaban, 1988), yeast suspensions (Speers et al, 1989), coalsuspensions (Renehan, 1988a) red mud (Nguyen, 1983, Nguyen and Boger, 1983) and magnetitesuspensions (Klein et al, 1990).7.3 Time Dependent FlowMany suspensions exhibit time dependent flow properties. For such suspensions shearingat a constant rate results either in an increase or in a decrease in shear stress with time. A stressincrease over time is referred to as rheopexy and it is usually found in suspensions with dilatant65properties. If a stress decrease occurs over time, the suspension is thixotropic; this stressdecrease is commonly found in pseudoplastic suspensions (Van Wazer, 1963). Both types oftime dependent flow behaviour are exhibited by suspensions that have a yield stress. Thixotropyis much more common than rheopexy.The time dependent flow behaviours have been described in terms of a structure withinthe suspension. The structure is formed by the attachment of particles creating aggregates thatmay be bonded together. These same attachments may also be responsible for a yield stress (VanWazer, 1963, Cheng, 1971, Nguyen, 1989). Upon shearing, the structure changes with timeresulting in the increase or decrease in stress at steady shear. Shearing causes inter-particle andinter-floe attachments to either break, if the attachments already exist, or to form due to shearinduced collisions. A net breakage of attachments, producing smaller aggregates or dispersedparticles, is responsible for thixotropic behaviours. The opposite, net formation of attachments,is caused by shear induced collisions and is responsible for rheopexy. At a particular shear rate,the stress will typically initially change sharply and with time will asymptotically approach anequilibrium value. At this equilibrium stress, the number of attachments being broken equalsthe number being formed. If the equilibrium stress is reached very quickly, it may not bepossible to observe the time dependence. This process may or may not be reversible.Time dependent properties have also been observed in suspensions of non-interactingasymmetric particles. Flow causes elongated particles to align in the direction of shear, creatinga state of lower energy dissipation. In this case, the time required for the particles to align isresponsible for the measured thixotropic stress decay (Pinder, 1964, Brown and Pinder, 1971).This shape effect increases with particle aspect ratio to a limit (Pinder, 1964).66The breakdown and formation of structure has been modelled using a reversible kineticchemical rate equation. The level of an equilibrium structure is dependent on the rate of structurebreakage and formation (Pinder, 1964). The rate of structure breakdown can be described byEquation 7.12.= km— kr(T1o - (7.12)8twhere, lc and kf are rate constants for structure rupture and formation,i is the maximum apparent viscosity,T is the apparent viscosity at time t, andn and m are exponent parameters.This structure may also be expressed in terms of other rheological parameters such asyield stress. Several researchers have used this equation to model time dependent flow propertiesof suspensions. Various orders, m and n, have been tested and the best fit to stress decay datawas found to depend on the type of suspension (Pinder, 1964, Brown and Pinder, 1971, Honeand Pinder, 1979, Nguyen, 1983).Cheng (1971) modelled time dependent flow properties using an equation of state alongwith a rate equation. The equation of state (Equation 7.13) describes the shear stress as afunction of shear rate for a particular level of structure. The rate equation (Equation 7.14)describes the change in structure with time in terms of shear rate and the instantaneous amountof structure present.=j’)jr (7.13)67-= g(A,’) (7.14)where, g is the rate of structural build up, and L is a structural factor.The rate constant, g, is negative if structure breakdown occurs and positive for structureformation. The magnitude of the rate constant is a function of the magnitude of the differencebetween the instantaneous and equilibrium structures (Cheng, 1971, Mewis and Spaull, 1976,Cheng, 1985).The degree of time dependency can also be characterized by the hysteresis produced fromincreasing the shear rate to a given value and then decreasing it to zero. The area between theincreasing and decreasing shear rate curves is a measure of thixotropy or rheopexy which can becompared providing that a consistent measuring procedure is used. In this way the influence ofsuspension variables on thixotropy can be determined (Moore and Davies, 1956, Saunders, 1976,Mehta et al, 1983, Windhab et al, 1986, Alderman et al, 1988, Chen et al, 1988).7.4 Visco-elasticityVisco-e1astic properties have been measured in very fine and highly concentratedsuspensions (Tadros, 1980, 1988, 1990, Ahuja and Isganitis, 1988, Ohl, 1988, Doraiswamy et al,1988). In such suspensions, the structure, resulting from inter-particle interactions, may deformelastically under small stresses. When high stresses are applied the suspension flows irreversibly.Measurement of elastic properties provides information on the type of structure that exists.68CHAPTER 8: CONTROL OF RHEOLOGICAL PROPERTIES8.1 IntroductionMicro-rheological effects determine the rheological properties of a suspension. Themicro-rheological effects include hydrodynamic effects, electroviscous effects, aggregation effectsand granuloviscous effects. The magnitude of each of these micro-rheological factors dependson the physico-mechanical and physico-chemical properties of the suspension.Physico-mechanical parameters describe the physical components of the suspension and includesolids concentration and properties of the particles such as density, shape, size and sizedistribution. Physico-chemical parameters that influence the inter-particle forces of attraction andrepulsion include pH, dissolved ions, magnetization and chemicals such as dispersing agents.Both types of parameters can be altered to control the micro-rheological factors and thereby theflow behaviour of the suspension.8.2 Micro-rheologyThe macroscopic rheological properties of a suspension can be predicted from a detaileddescription of behaviour of elements from which it is composed; this is referred to as themicro-rheology (Goldsmith and Mason, 1967). In particular, energy dissipation due tohydrodynamic, electroviscous, aggregation and granuloviscous effects are responsible for themacroscopic rheological properties of suspensions. Hydrodynamic effects describe energy69dissipation resulting from the movement of particles in the liquid (Brenner, 1972).Granuloviscous effects describe the physical interactions between particles in dense suspensionsthat dissipate energy via friction (Cheng, 1978). There are three electroviscous effects; theseresult from electrostatic forces of repulsion and influence how the particles interact(Smoluchowski, 1916, Tadros, 1980, Goodwin, 1981). The aggregation effects describe theenergy dissipated from the rupture and formation of bonds that result from attractive forcesbetween particles (Papenhuijzen, 1972, Firth and Hunter, 1976).8.2.1 Hydrodynamic EffectsParticle movement in liquid results in viscous energy dissipation which is given off asheat. Einstein (1905) derived an expression for the rheological properties of dilute suspensionsfrom the energy dissipated due to fluid flow past hard, spherical, non-interacting particles. Theexpression obtained for the relative viscosity includes the first two terms on the right side ofEquation 8.1 in which the coefficient equal to 2.5 is referred to as the intrinsic viscosity. Thevalue of the intrinsic viscosity will vary depending on the size and shape of the particles(Goldsmith and Mason, 1967, Goodwin, 1981).1r = = 1 ÷ 2.54 + + k4 ÷ . . . (8.1)1•10where flr is the relative viscosity,Th is the suspension viscosity,r0 is the viscosity of the suspending fluid,70is the volume solids fraction, andk1 are coefficients.At higher solids concentrations, greater than approximately 1% by volume, hydrodynamicparticle interactions contribute to the relative viscosity; their contributions are described by thehigher order terms in Equation 8.1. Several investigators have used both theoretical andempirical methods to derive the values of these higher order coefficients; most of these termshave been summarized by Rutgers (1962a, 1962b) and Thomas (1965).Particle movement and interaction dynamics are related to flow behaviour (Goldsmith andMason, 1965, Brenner, 1972). In particular Brownian motion, particle shape and particledeformation influence the particle motion (ie. translation, rotation and orientation) in a flow field.The particles will tend to adopt that motion which corresponds to the least dissipation of viscousenergy (Goldsmith and Mason, 1967).The influence of interactions on the viscous dissipation is more difficult to describe.Krieger and Dougherty (1959) described the viscous properties of concentrated suspensions byconsidering the contribution of doublets. Doublets form as two rotating particles approach eachother; because of the viscous resistance between the approaching rotating particles, the particleswill rotate about each other before separating and continuing on their path of movement. Theviscosity was considered to be related to the concentration of doublets which in turn depends onthe rate of their formation and separation. Shearing forces contribute to the breakage of thedoublets thus explaining the shear thinning properties of concentrated suspensions.Frankel and Acrivos (1967) used lubrication theory to describe the energy dissipationassociated with the extrusion of fluid from the gap between two approaching particles. They71claimed that this type of hydrodynamic energy dissipation was much greater than that resultingfrom particles sliding past each other. While many of the types of hydrodynamic interactionsthat contribute to the viscosity have been identified, it is difficult to quantitatively assess theirimportance.For small particles (-10pm) and under low shearing conditions, Brownian movementdominates the translatory and rotational motion of particles. It acts to disperse the particles andit randomizes their position and orientation distributions (Goodwin 1981, Mewis and Spaull1976). Brownian movement is significant at low rotary and translational Peclet numbers, wherethe rotary Peclet number is the ratio of convective to Brownian rotation, Per, (Equation 8.2) andthe translational Peclet number is the ratio of inertial to Brownian translation, Per, (Equation 8.3).Particles coarser than 10 pm are not strongly affected by Brownian movement because of thegreater influence of the convective and inertial forces. With increasing shear rate, the orderingeffect of flow will become more important than the thermal energy (Mewis and Spaull, 1976).Per =-j- (8.2)Pe = (8.3)where, D is the convective diffusion coefficient,Dr is the rotational diffusion coefficient,D is the translational diffusion coefficient, andr is the particle radius.728.2.2 Granuloviscous EffectsFor dense suspensions, with solids concentration greater than 35% and approaching themaximum packing fraction, rheological responses have been related to granuloviscous effects(Cheng, 1978). At these high concentrations particle packing structure can strongly influence theflow properties of the suspension. The packing structure can change in response to: the type offlow (extensional versus simple shear), the rate of shear and the physico-mechanical andphysico-chemical conditions. Frictional energy is dissipated as the result of particles sliding pasteach other (Clarke, 1967).The granuloviscous effects are responsible for shear thinning and time dependentproperties, since packing structures change with shear rate over time contributing to the variancein the measured rheological responses. While granuloviscous effects are more significant at highsolids concentrations, the frictional energy dissipation also contributes to the viscosity of lessconcentrated suspensions (Cheng 1978, 1980, 1984).8.2.3 Electroviscous EffectsInter-particle electrostatic repulsion forces are responsible for viscous energy dissipationvia the three electroviscous effects. In suspensions with high particle zeta potential and lowcounter-ion concentration (high electrostatic repulsion) the electrical double layer may have asubstantial thickness. Under these conditions, soft particle interactions will influence the flowbehaviour (Smoluchowski, 1916, Tadros, 1980, 1985, Goodwin, 1981).73The primary electroviscous effect accounts for the dissipation of energy that results fromthe deformation of the diffuse part of the electrical double layer during flow (Smuluchowski,1916, Tadros, 1980, 1985, Goodwin, 1981). It contributes to the intrinsic viscosity term inEquation 8.1 (Papenhuijzen, 1972) and is responsible for elastic properties which result from thetendency of the double layer to reform to a spherical shape around a particle (Smoluchowski,1916, Goodwin, 1981, Tadros, 1985).The secondary electroviscous effect results from inter-particle repulsion that adds to theeffective radius of the particles and decreases the excluded volume of the suspension. Themagnitude of the effect is related to the thickness of the double layer and it becomes muchgreater than the primary effect with increasing solids concentration (Russel, 1980). It influencesthe paths of approaching particles and causes doublets to separate (Goodwin, 1981), thuscontributing to the second order hydrodynamic interaction coefficient, k2, in Equation 8.1(Papenhuijzen, 1972).The tertiary electroviscous effect results in the deformation of the particle as a result ofthe repulsive forces which causes them to change in size and shape (Mewis and Spaull, 1976).This effect may be neglected for suspensions of rigid particles (Tadros, 1985).8.2.4 Aggregation EffectsThe presence of aggregates in a suspension strongly influences the flow behaviour.Aggregates form as a result of net attractive forces between particles. London’s Van der Waalsand electrostatic forces are responsible for particle aggregation or dispersion. The theory74developed by Derjaguin, Landau (1941), Verwey and Overbeek, (1948), “DLVO theory”,describes the net potential energy of attraction and repulsion as a function of distance betweenparticles. A typical potential energy curve is presented in Figure 8.1 which shows the primaryand secondary minimum potential energy wells at which distances two particles would attach.Aggregation of particles in the primary minimum energy well is referred to as irreversiblecoagulation. Comparatively small shear forces are needed to disperse particles aggregated in thesecondary minimum and this is therefore referred to as reversible coagulation.In addition to the forces described above, remnant magnetic attractive forces will influencethe shape of the potential energy curve. Magnetized particles behave like small magnets witha north and south pole. When these particles are aggregated, the particle positions are alignedas the result of the attraction of opposite poles and the repulsion of like poles. These forces arelong range and may be quite strong.Aggregation effects are the most complex ones that contribute to the rheologicalproperties. Papenhuijzen (1972) described the viscous, elastic and thixotropic properties ofsuspensions in terms of a network model. The network consists of particles arranged in chainsthat are stretched during deformation until the bonds are broken. At high shear rates the structureis broken and non-interacting aggregates make up the dispersed phase. The elastic properties areassociated with the stretching of the chains, the viscous properties are related to the flow aroundthe aggregates and the thixotropic properties are related to the time required to break and formthe structural units.75Figure 8.1 Typical potential energy curve at the surface of a mineral particle.()CoI>-CoUI7LiiUIUI0LL—IH0H0SEPARATION. Hb)76Firth and Hunter (1976) developed the elastic floe model that describes the rheologicalproperties of aggregated suspensions in terms of the contributions to energy dissipation resultingfrom viscosity of the fluid, floe rotation, bond rupture and formation, and doublet rupture andformation. The energy dissipated from doublet rupture consists of the energy to rupture linksbetween the floes, to stretch links within a floe, and to move liquid inside a floe. In describingthis model the term floe refers to a coagulated group of particles. Van de Ven and Hunter (1977)found that the viscous dissipation transmitted by the particle movement within a floe, togetherwith the viscous flow around floes, described most of the total energy dissipation. Expressionsdescribing these types of energy dissipations are used to develop equations that estimate valuesfor the plastic viscosity, Bingham yield stress and critical shear rate. The plastic viscosity wasrelated to the hydrodynamic energy dissipation resulting from flow around the aggregates usingEinstein’s (1905) equation and more suitably Krieger’s (1971) equation, which applies to moreconcentrated suspensions. The yield value is determined from the energy dissipated from fluidflow in a floe. The critical shear rate, above which no doublets exist and the flow curve is linear,is determined from the number and strength of the inter-floe bonds. Many of the assumptionsof the model restrict its application to colloidal dispersions and it only predicts the shear stressat shear rates that are greater than the critical one (Hunter, 1985a).Van de Ven and Hunter (1977) suggested that suspensions that are wealdy coagulated (ie.reversible secondary minimum coagulation) become dispersed at low shear rates. At higher shearrates, primary minimum coagulation can be induced to form doublets. At yet higher rates, thekinetic energy may be large enough to cause these primary doublets to disperse (Russel 1980,Goodwin 1981).778.3 Physico-mechanical ParametersPhysico-mechanical parameters that affect the rheological properties of suspensionsinclude the solids content and the density, shape, size and size distribution of the particles.8.3.1 Solids ContentSeveral studies have shown that the viscosity of suspensions increase in an exponentialmanner with solids concentration and becomes infinite at the maximum packing fraction. Fordilute suspensions of non-interacting spherical particles (volume solids contents less than a fewpercent), Einstein (1905) derived a linear equation, based on the viscous energy dissipated by theflow around a sphere, relating the relative viscosity to solids content. With increasing solidsconcentrations, there is a greater number of particle interactions; these are responsible for theexponentially increasing viscosity. These interactions result in energy dissipation that can bedescribed in terms of the hydrodynamic, granuloviscous, electroviscous and aggregation effects(see Section 8.2). These effects are also responsible for the increased non-Newtonian behaviourthat is found at higher solids concentrations.The number of hydrodynamic particle interactions increases with solids content. Theseinteractions dissipate energy by extruding and shearing fluid as particles approach and slide pasteach other (Frankel and Acrivos,1967). If the particles are rotating, they will form doublets witha concentration that is proportional to the solids concentration. Since these dissipate more energythan two separated particles, they help to explain the exponentially increasing viscosity (Krieger78and Dougherty, 1959). Their concentration is also proportional to the shearing conditions, sincehigh shearing causes the break up of doublets; this break up can explain the shear thinningproperties exhibited by concentrated suspensions (Krieger and Dougherty, 1959, Krieger, 1971).At high solids concentrations, (greater than 30% by volume) granuloviscous effectsdetermine the frictional energy dissipation that results from crowded particles sliding past eachother (Cheng, 1978). At high solids concentrations, these effects dominate the flow behaviour.When these suspensions are sheared, the packing arrangement can change causing the suspensionto exhibit time dependent and non-Newtonian properties.Secondary electroviscous effects result in an increase in the effective solids content of asuspension and thereby enhance the contribution of the hydrodynamic interactions describedabove (Goodwin, 1981). Primary electroviscous effects, that are the result of the deformationof the electrical double layer, are responsible for viscoelastic properties (Tadros, 1985). Theseeffects become more pronounced as particle crowding increases.When aggregation effects exist, the aggregates may be considered to be the suspendedunits in the suspension. This results in an increase in the effective solids content as theaggregates will trap liquid (Lewis and Neilson, 1968). The size of the aggregates depends onthe types of attractive forces, the shearing conditions and the solids concentration in thesuspension (Firth and Hunter, 1976). At high solids concentrations, the aggregates mayinterconnect to form a network structure that is often associated with a yield stress (Papenhuijzen,1972). The main source of energy dissipation has been attributed to the viscous resistance byfluid movement in the deforming aggregates (Van de Ven and Hunter, 1977).Many of these effects have been considered in the evaluation of the coefficients of the79“general power formula” (Rutgers 1962a, 1962b). This model, which is an extension ofEinstein’s equation, applies only to moderately concentrated suspensions and does not cover theentire solids concentration range (Rutgers 1962b, Thomas 1965). A number of equations havebeen developed that relate the viscosity to the maximum solids packing fraction, Table 8.1. Assolids contents approach the maximum packing fraction, the suspension viscosity becomesinfinite.Eilers (1941) used the maximum solids content as an upper limit in relating relativeviscosity to solids fraction for bitumen emulsions. Chong (1971) modified Eilers equation tocorrelate the relative viscosity to solids content for poly-disperse suspensions. Mooney (1951)considered the crowding effects of mono-disperse spheres to obtain his equation. He also showedhow this approach could be extended to bimodal and poly-disperse suspensions (Mooney 1951).Krieger and Dougherty (1959) also used particle crowding, in a similar manner, to derive theirequation. Simha (1952) used a cage model to describe the extent to which particles beyondnearest neighbours can hydrodynamically interact to derive his equation. Frankel and Acrivos(1967) obtained an expression for the energy dissipated between two approaching particles andapplied it to obtain an expression for concentrated suspensions of spherical particles.Ting and Luebber (1957) considered the effects of liquid-solid density ratio, particle sizedistribution and particle shape on packing arrangements to derive an empirical relation betweenrelative viscosity and some function of these parameters for varying solids contents. Sherman(1965) derived an expression relating the relative viscosity to the solids content, maximumpacking fraction and mean particle size. He recognized the non-Newtonian behaviour of80Table 8.1 Models describing relative viscosity as a function of solids content and maximumpacking fraction.Eiler (1941) [ + [11] [1 -Mooney (1951) = exp [i1 / [i -Simha (1952) = [ / [i - ±]3] , = packing parameterTing & Luebbers (1957)(V,- 0) f [m&d]-+m[111eger & Doughefly (1959)=[i -81Table 8.1 Models describing relative viscosity as a function of solids content andmaximum packing fraction. (Continued)Sheman (1965) lr = exp [O.036d /_____- 0.15]Frankel & Acrivos (1967)r;[[i[i-[a]]Chong et al (1971)= 1+0.75 /2r4m21 -Mills&Snabre(1988) =(1_eff)/[eff]øeff_f(t)82suspensions in his derivation as being related to the particle size through its effects onaggregation and interaction energy. Mills and Snabre (1988) describe the non-Newtonian flowbehaviour of suspensions of aggregated particles by considering the radius of fractal clusters insimple shear.The equations described above are some of the better known ones. Many more modelshave been developed, some of which have been summarized by Rutgers (1962a, 1962b).Although most were derived for mono-disperse suspensions of spherical particles, they have beensuccessfully applied to systems such as non-Newtonian coal slurries (Castillo and Williams, 1979,Ogden and Rutter, 1984, Wildemuth and Williams, 1985) and various other mineral suspensionsthat contain poly-disperse and aggregated particles in a variety of physico-chemical environments(Lewis and Neilson, 1968, Fedors, 1973,1975, Renehan, 1988b). Examination of these modelsreveals that the viscosity of suspensions can be minimized by maximizing the packing densityof the suspension. The packing density is a function of the effective particle size distribution andthe state of aggregation.8.3.2 Particle DensityIn many industrial suspensions the solids density is greater than the fluid density. In thesesuspensions, shear forces and gravitational forces influence the behaviour of the particles bycreating inertia. This inertial force is countered by the viscous forces exerted by the fluid on theparticles.In the case of a suspension of high density particles in a low viscosity fluid, the particle83motion will be strongly influenced by the inertial forces. Such particles would collide morefrequently and with more impact than low density particles and therefore dissipate more energy.This effect will be enhanced with increasing particle size (Clarke 1967, Brenner 1972, Conchaet al, 1990). In addition, the effect becomes more pronounced at high solids concentrationswhere these types of interactions dominate the flow behaviour (Purohit and Roy, 1965, Clarke,1967). Clarke (1976) observed that the viscosity of settling suspensions increased with particlesize and he attributed this to inertial effects.At low solids concentrations, the high density particles will move more freely andtherefore dissipate more viscous energy. This results in an increased intrinsic viscosity withincreasing particle relative density. Ferrini et al (1979) measured the intrinsic viscosity forsuspensions of coal (density = 2000 kg m3) and magnetite (density = 4900 kg m3) as 4 mPa.sand 5.8 mPa.s, respectively. Inertia can also influence the measured intrinsic viscosity throughits effect on the particle orientation distribution (Brenner, 1972). As particles align with the shearflow or orientate as they settle, the magnitude of the viscous energy dissipation will change andthereby change the inthnsic viscosity.The greater number of particle interactions in settling suspensions than in stable ones,helps to explain their non-Newtonian flow behaviour (Clarke 1967, Brenner 1972, Laapas 1985).These suspensions typically exhibit shear thinning or yield shear thinning properties. Clarke(1976) found that the solids concentration above which the suspension exhibits non-Newtonianproperties is lower for suspensions containing particles with a higher relative density. Laapas(1985) obtained a relationship between yield stress and relative density. As the relative densityincreased, the yield stress increased.84Clarke (1967) also found that at high shear rates suspensions of settling particles exhibiteddilatant properties. At high shear rates Purohit and Roy (1965) observed the formation ofhorizontal bands in their transparent rotational viscometer. Taylor (1923) has described similarbands by the onset of turbulence. This turbulence explained the dilatant properties found byClarke (1967) at high shear rates. In particular, the shear forces induce inertia into the particlesin the Couette flow. As the particle velocity increases the particles tend to move to the outsideof the annular gap and thereby form the well known Taylor vortices. Kirchberg et al (1975)observed similar results and suggested that a solids concentration gradient forms in the annulargap with more particles concentrated near the outside wall.8.3.3 Particle ShapeFor a given suspension, particle shape is a difficult parameter to try to control. It dependson the physical properties of the solid and on the environment in which the particles wereformed. Despite this, an understanding of how particle shape influences suspension rheology isnecessary for the interpretation of measured rheological responses.In most natural systems the particle shapes vary from perfect spheres to rods and discs.The movement of these particles in a flowing fluid depends on a balance between opposingviscous stresses and Brownian movement (Goldsmith and Mason, 1967, Brenner, 1972). Theviscous stress aligns particles, such that their longest dimension is parallel to the flow (Horie andPinder, 1979), which reduces the energy dissipation and therefore the viscosity. At low shearrates, Brownian movement randomizes the orientation of smaller particles. Laapas (1982)85described the flow curves for suspensions of elongated particles using the Bingham plastic model;and he found that with increasing particle anisotropy the plastic viscosity increased. Laapas(1985) described the particle shapes in terms of sphericity as defined by Equation 8.4.Sphericily = (8.4)where, is the calculated surface area based on the particle diameter, andS is the measured surface area.For dilute suspensions, the particle shape contributes to the relative viscosity through itseffect on the intrinsic viscosity term (Ting and Luebbers, 1957, Goldsmith and Mason, 1967,Brenner, 1972). In suspensions containing elongated particles the intrinsic viscosity is highestat low shear rates where the particle orientation is random and it is lowest at high shear rateswhere the particles are aligned with the flow. The magnitude of the difference between the lowand high shear states is proportional to the particle aspect ratio (Goldsmith and Mason, 1967).In concentrated suspensions, particle shape affects the maximum packing density andthereby influences the relative viscosity (Ting and Luebbers, 1957, Wildemuth and Williams,1985). Unlike most models (described in the last section), the model developed by Ting andLuebbers (1957) considered the effect of particle shape on the maximum packing fraction.Wildemuth and Williams (1985) also considered the effect of particle shape through its effect onmaximum packing density as related to relative viscosity using the Eilers (1941) and Krieger andDougherty (1959) equations. The relationship between specific particle shapes and packingdensity were, however, not determined.86Suspensions containing elongated particles have been observed to exhibit time dependentproperties (thixotropy). Horie and Pinder (1979) observed that with increasing aspect ratio thereis an increase in the amount of thixotropy. However, the rate of change of thixotropic breakdown and recovery in these suspensions decreased with increasing aspect ratio. They alsoobserved that as the aspect ratio increased, the relative viscosity and the yield stress ofconcentrated suspensions also increased. The time dependent properties can be explained interms of the time required for particle orientation to occur. As the particles align with the flowthe viscosity decreases. With higher aspect ratios this orientation requires a long time period.8.3.4 Particle SizeThe size of particles in a suspension has been shown to have a strong influence on its’rheological properties. In particular, is has been shown that suspensions with very large (+100}lm) or very small (-10 .im) particles have a higher viscosity than suspensions containingintermediately sized particles (+10 im -100 tim) (Purohit and Roy 1965, Clarke, 1967, Renehan,1988a). These differences in viscosities can be explained by the contributions of theelectroviscous, aggregation, hydrodynamic and granuloviscous effects. Each effect contributesto the viscosity to a greater or lesser degree depending on the size of the particles.Many investigators have reported an increase in viscosity with a decrease in particle size(Williams, 1951, Roscoe, 1952, Sweeney and Geckler, 1954, Sherman, 1965, Clark, 1967,Parkinson et al, 1970, Saraf and Khullar, 1975, Rukin et al, 1977, Tsai 1986, Schreuder 1986).This increase in viscosity has been attributed to the electroviscous and aggregation effects that87dominate fine particle behaviour (Eveson, 1957, Sherman, 1965, Thomas, 1965, Saunders 1967,Krieger 1971, Renehan, 1988a). Inter-particle forces of attraction and repulsion are responsiblefor these effects which dominate the movement of colloidal size particles (Thomas 1965, Renehan1988a). The magnitude of these forces may be large enough to influence the movement of coarseparticles. Renehan (1988a) showed that the movement of coal particles as coarse as 200 pm wereinfluenced by surface charge related effects that were large enough to contribute to therheological properties. The maximum particle size affected by surface charge related effects wasreferred to as the reactive size limit. Sweeney and Geckler (1954) suggested that the contributionfrom electroviscous effects to the rheological properties of fine particle suspensions can be verysignificant. They showed that the viscosity of a suspension of glass spheres in an ionicsuspending fluid, where electroviscous effects should be large, was greater than the viscosity ofa suspension of the same glass spheres in a non-ionic fluid, in which electroviscous effects shouldbe small.For suspensions of glass and polystyrene spheres, Williams (1951), Saunders (1967) andParkinson et al (1970) explained the increases in non-Newtonian behaviour, yield stress andthixotropy with decreasing particle size, by the contribution of aggregation effects. Inter-particleforces of attraction dominate over inertial forces for small particles which makes them moresusceptible to aggregation than coarse ones. With increasing shear rate the attachments breakresulting in a more dispersed suspension. As the particle became dispersed the apparent viscositydecreased resulting in the shear thinning properties (Sherman, 1965, Laapas 1982,1985). Sincethis dispersion with shearing is not instantaneous, at a given shear rate the apparent viscosity willdecay with time resulting in the thixotropic characteristics of such suspensions. The structure that88forms as a result of the aggregation of the fine particles contributes to the yield stress. Belowa critical solids concentration the structure may not be continuous and therefore no yield stressmay be present (Sherman, 1965, Laapas 1982,1985). The effects of particle size are thereforemore pronounced at high solids concentrations than at low ones.The magnitude of the hydrodynamic effects is proportional to the specific surface area ofthe particles. Since the specific surface area increases with decreasing particle size, thecontribution of hydrodynamic effects also increases (Yucel and Hughes, 1984). Therefore theincrease in viscosity of suspensions resulting from decreasing particle sizes can be explained bythe greater amount of hydrodynamic energy dissipation (Sherman, 1965, Saunders 1967).The results of several investigations have shown that an increase in viscosity occurs asparticle size increases (Eveson, 1957, Purohit and Roy 1965, Clarke, 1967, Saraf and Khullar1975, Renehan 1988a). This result has been explained by the energy dissipated due to physicalparticle interactions as described by granuloviscous effects. Since coarse particles have a greaterinertia than fine ones they will collide rather than slip past each other. The physical collisionsdissipate energy through friction and loss of translational and rotational momentum (Thomas,1965).Saraf and Khullar (1975) showed that the viscosities of quartz particle suspensionsincreased as the mean particle size was increased from 37 im to 74 pm. Clark (1967) obtainedsimilar results by increasing the size of quartz particles from 30 pm to 180 pm. Similar resultswere obtained for suspensions of hematite and quartz by Purohit and Roy (1965) who alsomeasured the viscosity of coal suspensions which did not increase with particle size. Since thecoal has a significantly lower density than the quartz and hematite, the differences in the results89can be explained by the differences in particle inertia. The denser quartz and hematite particleshave a greater inertia than the coal and therefore dissipate more energy through collisions.Therefore, the size effects contribute to the rheological properties via inertial effects.The contributions of the four effects (electroviscous, granuloviscous, aggregation andhydrodynamic) clearly depend on the size of the particles. In order to minimize the viscosity,it seems that an optimum particle size exists that is not too large and not too small. Clarke(1967) determined this optimum size to be approximately 16 pm for suspensions of quartzparticles.8.3.5 Particle Size DistributionIt is well known that particle size distribution influences the rheological properties ofsuspensions. The explanation for this influence is, however, not well understood. Researchershave demonstrated that suspensions composed of particles with a wide size distribution are lessviscous than suspensions with a narrow size distribution (Castillo and Williams 1979). Otherresearchers have shown that suspensions with particle size distributions that have a high packingsolids fraction are less viscous than those with distributions that have a low packing fraction.In order to exploit this result, investigators have applied particle packing theory to produce sizedistributions that have a maximum packing density in order to produce suspensions with aminimum viscosity. Despite these investigations, there is little explanation of the physicalreasons for the observed results. Moreover, none of these results have been explained in termsof the micro-rheological interactions that occur between particles of different sizes.90Castillo and Williams (1979) showed that the relative viscosities of concentrated coalsuspensions with narrow size distributions are greater than the viscosities of suspensions withwide distributions. They related this result to the higher packing fractions of suspensions witha wide distributions than those with narrow distributions.Zheng et al (1984) found that coal suspensions had a minimum viscosity and maximumpacking fraction when the particle size distribution was characterized by a Rosin RammierBennett (RRB) distribution coefficient equal to 0.7 - 0.8. Similarly, Rukin et al (1977) found theoptimum value of the RRB distribution coefficient to be approximately 1.0. Kikkawa et al(1984) showed that a minimum viscosity and a corresponding maximum packing fraction wasachieved when the Gates Gaudin Schuhmann size distribution modulus equalled 0.4 - 0.5. Theseresults support the conclusion that the viscosity of a suspension can be reduced by manipulatingthe particle size distribution to increase the solids packing fraction.The effect of solids packing fraction has been incorporated into several rheologicalequations that relate relative viscosity to the maximum solids packing fraction. Many of theseempirical equations have been presented in Table 8.1. Each equation contains terms of the form:Tlr = fl_i-) (8.6)where, 0 is the suspension solids fraction, and. is the maximum solids packing fraction.As can be seen in the equation, at a given solids concentration, the relative viscosity canbe decreased by increasing the solids packing fraction. The solids packing fraction is a function91of particle size disthbution.Mooney (1951) considered the effect of particle size distribution on particle crowding.In particular, he assumed that large spheres are not crowded by small ones and that the smallspheres are crowded into the spaces between large ones. Ting and Luebbers (1957) suggestedthat the small particles fill the voids between the large particles which increases the packingfraction and thereby reduces the viscosity. Clarke (1967) explained that the small particles movein the voids between the large ones, the net effect being a decrease in the number of inter-particleimpacts and therefore a decrease in viscosity.Sweeny and Geckler (1954) considered the effect of the ratio of small to large particlediameters in a bimodal distribution on the packing fraction and viscosity. By increasing the sizeratio, the packing fraction decreased and the viscosity increased. Several investigators (Eveson1953, Chong et al, 1971 and Round and Hessari, 1984) explained the effect of size ratio asfollows. As the size ratio decreases, there is an increase in the number of small spheres. Thesesmall spheres may act as ball bearings between the large particles which thereby reduces theviscosity. In addition, below a size ratio of approximately 0.1, the small particles behave likefluid to the large particles.Fidleris and Whitmore (1961) observed that large spheres move through a suspension offine spheres as if it were a liquid with the same viscosity and density as the fine particlesuspension. As the size ratio of small to large particle diameters was increased to greater than0.1, the large spheres began to move in a zigzag motion indicating that interactions between thefine and coarse particles became more significant. Farris (1968) considered these interactionsin his model by including a crowding factor that increased as the size ratio increased.92Farris (1968) also showed that the viscosities of suspensions decreased with the increasein the number of component sizes; that is multi-modal suspensions are less viscous than bimodalsuspensions which in turn are less viscous than mono-modal suspensions. These results can beexplained by expressions developed by Gillespie (1963) which describe the rate constants ofcollisions for particles of different sizes. The expressions indicate that poly-dispersity reducesthe rate constant for shear induced collisions. This result is supported by observations made byWildemuth and Williams (1985) who observed that differences in the viscosities betweensuspensions composed of particles with a wide size distribution and those composed of a narrowsize distribution became more pronounced at high shear rates. At high shear rates, the shearinduced collisions would contribute more to the rheological properties than they would at lowshear rates.Not only is the size ratio important to the viscosity, but so are the proportions of each ofthe component sizes. For bimodal suspensions, the optimum proportion of small particles wasreported to be between 0.25 and 0.45 (Parkinson et al, 1970, Chong et al, 1971, Round andHessari, 1984 and Ferrini et al, 1984). The optimum proportion of fines was considered to bethe proportion that can fill the voids between the packed coarse particles without adding to thetotal volume of a packed bed of solids. Such a size distribution would clearly result in a highpacking fraction.Lee (1970) as well as Ferrini et al (1984) used particle packing theory in order to selectthe optimum size distributions. The optimum size distributions can be calculated fromrelationships between packing arrangements and the particle shape (Westman and Hugill, 1930,Furnas, 1931, White and Walton, 1937, McGeary, 1961 and Fedors, 1979a, 1979b, 1979c).93Ferrini (1984) determined from packing theory that for a coal slurry with a top particlesize of 300 jim and a minimum particle size of 1 pm, the optimum particle size distributionwould be bimodal. The mean size ratio used was set at 0.2 because of practical considerationsof producing the component sizes. The optimum proportion of fines was determined to rangefrom 0.35 to 0.45. It was also learned that the effect of size distribution became much morepronounced at high suspension solids concentrations.8.4 Physico-chemical ParametersPhysico-chemical parameters are the properties of the suspensions that influence theinter-particle forces of attraction and repulsion. As described by DLVO theory (Overbeek, 1952,Derjaguin, 1989), London’s Van der Waals and electrostatic forces are responsible for particleaggregation and stabilization. The magnitude of each of these forces depends on the chemicalcomposition of the particles, the concentration of potential determining ions in the suspendingfluid, the type and concentration of indifferent electrolyte in solution, the type and concentrationof dispersing agents and for ferromagnetic particles the state of magnetization.8.4.1 pH and Dissolved IonsSurface chemistry strongly influences the rheological properties of suspensions ofcolloidally sized particles. In particular, the magnitude of electrostatic repulsive forcesdetermines the state of dispersion of the suspension which affects the contributions to the94rheological properties from electroviscous and aggregation effects (Atlas et al, 1985). Theelectrostatic repulsive forces in turn depend on the surface chemistry of the particles and on thetype and concentration of dissolved ions (Overbeek, 1952, Derjaguin, 1989).The surface of oxide minerals, such as magnetite, is covered by hydroxyl groups. Thesesurface hydroxyl groups are amphoteric and behave as acids or bases; their ionization iscontrolled by the pH. As a result, at low pH most oxide minerals become positively charged andat high pH they become negatively charged. The point of zero charge (p.z.c.), varies frommineral to mineral and in practice also depends on the impurities present in the mineral(Kitchener 1969, Atlas et al, 1985). Since electrokinetic measurements are more common thantitration techniques used to determine the p.z.c., the iso-electric point (i.e.p.) is more practicallymeasured. These two points are identical in the absence of specifically adsorbing ions.At a pH near the i.e.p., electrostatic repulsion is at a minimum. This allows particles toapproach each other to a distance at which Van der Waals forces of attraction are large and asa result the particles coagulate into a primary minimum. Several investigations have shown thatnear such a pH value, the flow behaviour of suspensions becomes shear thinning and a yieldstress develops. This rheological behaviour has been explained in terms of aggregation effects;the particle aggregation results in the formation of a structure which when sheared breaks down(Atlas et al, 1985, Leong and Boger, 1988, 1990).At pH values higher and lower than the i.e.p., the aggregates disperse due to increasedelectrostatic repulsive forces. As a result, the viscosity decreases and the flow resumesNewtonian behaviour. However, with a further increase or decrease in the pH the viscosityincreases. This result can be explained by the increase in the magnitude of the electroviscous95effects (Smoluchowski, 1916, Leong and Boger, 1990). Therefore, a minimum suspensionviscosity exists at pH levels above and below the i.e.p.Coagulation can also be initiated by a high concentration of electrolyte. Under suchconditions, double layers surrounding particles are compressed and this leads to a reduction inthe range of the electrostatic repulsion forces resulting in aggregation and the formation of astructure. Such a structure is responsible for increased viscosity, shear thinning flow propertiesand the presence of a yield stress (Friend and Kitchener, 1973, Atlas et al, 1985, Meagher et al,1988).8.4.2 Dispersing AgentsDispersing agents can be classified into: (i) inorganic compounds, and (ii) polymericdispersants (natural and synthetic) (Laskowski, 1988, Laskowski and Pugh, 1992). Whileinorganic dispersants are used primarily to control the charge density at the solid/liquid interface,the polymeric compounds also provide a steric hindrance.As described in the previous Section (8.2.4), suspensions of aggregated particles canexhibit a yield stress and typically have shear thinning flow properties (Aarnio and Laapas, 1988,Jones and Chandler, 1989). Dispersing the particles results in a more Newtonian flow behaviourand a reduced apparent viscosity. It should be noted, however, that by increasing electrostaticrepulsion, electroviscous effects can also become more important (Aarnio and Laapas, 1988)resulting in greater apparent viscosities.Organic reagents typically used in iron ore processing are polysaccharides such as starch96and carboxyl methyl cellulose which are used to flocculate hematite (Iwasaki et al, 1969, Lin etal, 1988). The effectiveness of these reagents depends on the nature of the reagents, the particlesurface chemistry, the types of dissolved ions and the pH. Typical inorganic dispersing agentsare sodium polyphosphates and sodium silicates (Laskowski, 1988, Yang, 1988, Jones andChandler, 1989). These dispersing agents are widely used in the processing of iron ores.97CHAPTER 9: RHEOLOGY OF MAGNETITE DENSE MEDIA9.1 IntroductionIt has been established that the rheological properties of magnetite dense media areimportant to the process separation efficiency. As discussed in Section 4.5, recent investigationshave confirmed that these medium properties affect the performance of both static and dynamicseparators (Napier-Munn, 1990). While some information exits on the rheological properties ofmagnetite suspensions, a better understanding of how physico-mechanical and physico-chemicalparameters affect the medium properties is required.9.2 CharacterizationIt was established in early publications that magnetite suspensions exhibit non-Newtonianflow properties (Eveson, 1953). In particular, the rheological properties of magnetite suspensionshave been described as Newtonian at low solids contents, becoming pseudo-plastic withincreasing solids contents (Govier et al, 1957, Lilge et al, 1957, Berghofer, 1959). This flowbehaviour has been described with the Bingham plastic equation (Yancey et al 1958, Berghofer,1959, Klassen et al, 1964, 1966, Valentyik, 1972, Valentyik and Patton, 1976, Graham and Lamb1982, 1988) which implies that a yield stress exists. The available data indicate that the Binghamequation fits the data poorly at low shear rates (Berghofer, 1959). In particular, at low shearrates measured stress values are lower than the stresses predicted by the Bingham equation. In98addition, the Bingham yield stress is usually greater than yield values determined by using othermethods.Apparent viscosity values have been used to provide an indication of the viscousresistance of various magnetite suspensions. While this indicator of viscosity may be useful, suchdata are difficult to compare when values are obtained from different types of instruments atvarious shear rate conditions. Furthermore, an apparent viscosity value does not representviscosities over the range of shear conditions that are found in a dense media separator.As discussed in Section 6.3.2, measurements of the rheological properties of settlingsuspensions require that careful consideration be given to various potential errors. Since mostviscosity measurements have been made without accounting for these errors, much of theavailable rheological data are suspect. These data do, however, provide valuable informationconcerning the type of flow behaviour and trends associated with the levels of various parameterssuch as solids content and particle size.9.3 Control of Medium PropertiesAs stated, once it is understood how the physico-mechanical and physico-chemicalparameters influence the rheological properties of magnetite dense media, these parameters canbe manipulated to control the rheological properties. In this way, the rheological properties canbe optimized to improve separation performance.999.3.1 Physico-Mechanical ParametersPhysico-mechanical parameters, that affect the rheological properties of a suspension,include the solids content, and the density, size, size distribution, shape and roughness of theparticles.Since magnetite is a natural occurring mineral, its density varies with the types andamounts of impurities present. Typically, magnetite used in dense media must have a densitygreater than approximately 4800 kg m3 (pure magnetite has a density that is close to 5180 kgm3). The density of the magnetite determines the solids content required to produce a specificmedium density. Since this parameter is a difficult parameter to control, it will not be discussedfurther.9.3.1.1 Solids ContentThe effective medium density is determined by the density of the magnetite particles andthe solids content of the suspension. For coal preparation, media densities range from 1350 kgm3 to 1800 kg m3, requiring approximately 10% to 20% of magnetite by volume, respectively(Osborne 1988). For mineral separations, media densities as high as 2500 kg m3 (Burt, 1984),requiring a solids content of approximately 40% magnetite by volume, have been used.It is well known that the suspension viscosity increases with solids concentration. Severalinvestigators found that the apparent viscosity of magnetite suspensions increases proportionallywith magnetite content up to approximately 25% by volume and then rises sharply in an100exponential manner at higher solids content (DeVaney and Shelton, 1940, Geer et al, 1957,Chakravarti et al, 1958). Also, with increasing solids concentration the flow behaviours ofmagnetite dense media become more non-Newtonian (Govier et al. 1957) and a yield stressbecomes more pronounced. In fact, the exponential increase in apparent viscosity above 25%solids by volume can be attributed to the sharp increase in the Bingham yield stress, althoughthe plastic viscosity also rises with solids concentrations (Berghofer, 1959). The sharp increasein rheological parameters at these high solids concentrations was attributed to energy dissipationresulting from particle collisions and friction between particles (Berghofer, 1959). Clearly, it isnot practical to use magnetite suspensions for separation densities that require high solidsconcentrations due to the excessively viscous properties of the media.9.3.1.2 Particle SizeThe size of magnetite particles used in dense media suspensions is typically in the rangeof 90% -45 im with less than 30% -10 im (Osborne, 1988). This particle size range has beenselected based on considerations of:i. magnetite recoverability,ii. magnetite grindability,iii. medium sedimentation stability and,iv. medium rheology (Graham, Lamb, 1988).Despite evidence that medium rheology influences separation performance, it has receivedvery little attention in industrial applications.101Early investigations by DeVaney and Shelton (1940) revealed that as the mean particlesize of the magnetite was decreased from 51.7 pm to 15.8 pm, the apparent viscosity of themedium increased. This trend was attributed to the increase in particle surface area withdecreasing mean particle size. In particular, liquid becomes trapped in the irregularities of theparticle surface, thereby increasing the effective particle volume and therefore the effective solidsconcentration. Since the amount of immobile liquid present is proportional to the particle surfacearea, its amount increases with decreasing particle size. Therefore, the effective solidsconcentration and thereby the apparent viscosity increase with decreasing particle size (Eveson,1958). Berghofer (1959) investigated the effect of particle size on the coefficients of the fittedBingham Plastic equation. He found that the effect of particle size on these coefficients wasmore pronounced at a high volume solids content (>25%) than at low ones (15%). In addition,the yield stress was much more affected than the plastic viscosity. These results were explainedin terms of the energy dissipation resulting from inter-particle interactions. In particular, at highsolids concentrations, inter-particle interactions are the major source of viscous energydissipation. With decreasing particle size, there is a corresponding increase in the number ofparticles that interact and dissipate energy.In order to maintain a low medium viscosity, it is therefore recommended to use coarsemagnetite particles at high solids contents and to use fine particles at low solids contents(Chakravarti et al, 1958, Graham and Lamb, 1982). Since the apparent viscosity increases withdecreasing particle size, it is expected that media composed of micronized magnetite (-10 pm),used for the dense media separation of fine coal (600 x 38 pm) (Klima and Killmeyer, 1990),may be prohibitively viscous.1029.3.1.3 Particle Size DistributionAlthough investigations have shown that particle size distribution affects the rheologicalproperties of various suspensions (see Section 8.3.5), no similar work has been carried out withmagnetite. DeVaney and Shelton (1940) and Eveson (1953) suggested, however, that particlesize distribution could affect the rheological properties of magnetite dense media. In particular,it was suggested that magnetite suspensions could exhibit the same rheological trends as testedmodel systems. The main differences are that the solids concentrations of magnetite dense mediaare lower than those of the systems investigated, the particles have irregular shapes, and theparticles interact as a result of physico-chemical effects.9.3.1.4 Particle Roughness and ShapeMagnetite particles are generated by grinding in conventional rod and ball mills. Thesegrinding procedures produce irregularly shaped rough angular particles. It is known that particleroughness and shape affect the rheological properties of a suspension (see Section 8.3.3). Severalinvestigations with ferrosilicon dense media (Aplan and Spedden, 1964, Collins et al, 1974,Ferrara and Schena, 1986) have shown that medium composed of spherical atomized particleshas a lower viscosity than media composed of irregularly shaped ground material. In this case,atomized ferrosilicon is often used in dense media separation applications where high mediumdensities are needed and viscosity is of concern.The effect of particle shape on viscosity has been explained by the ease with which round103smooth particles can roll and slide past each other as compared to the wedging and interlockingof uneven angular particles (DeVaney and Shelton, 1940).Some smoothing and rounding of magnetite particles occurs as result of pumping and flowin a dense media circuit. The abrasion resulting from this flow removes sharp edges from theparticles which over time produces rounded and less angular particles (Eveson, 1958, Grahamand Lamb, 1988). Alternative sources of magnetite such as fly-ash from smelters (Osborne,1988) and naturally eroded particles from placer deposits (Klein et al, 1988) have beenconsidered. Particles from both of these sources are smoother and rounder than ground materialand the viscosities of corresponding media would likely be lower.9.3.2 Physico-Chemical ParametersIt is well known that physico-chemical parameters strongly influence the rheologicalproperties of magnetite dense media. Specifically, in order to improve the rheological properties,it is recommended to install demagnetizing coils in dense media recovery circuits and to adddispersing agents to the medium when clays or slimes are present. Despite this knowledge, therehave been few investigations into the effects of these parameters on the medium properties.9.3.2.1 pH and Dissolved IonsAs discussed in Section 8.4.1, the pH and dissolved ion concentration affect rheologicalproperties through their effect on the zeta potential of particles. In particular, the zeta potential104of the suspended solid is dependent on the pH and on the types and concentration of dissolvedions. When the zeta potential is large, strong electrostatic repulsion facilitates particle dispersion.Since rheological properties are influenced by the state of aggregation, the pH and dissolved ionscan influence the medium rheological properties (Graham and Lamb, 1982, 1988).While the main component of the medium is the magnetite, the effect of pH and dissolvedions on the zeta potential of clays and other slimes can have a large effect on the rheologicalproperties of the medium (Aplan and Spedden, 1964). No data are available on the effect ofdissolved ions and pH on the rheological properties of magnetite dense medium.9.3.2.2 Dispersing AgentsWhile it is believed that the rheological properties of magnetite dense media can beimproved by the addition of dispersing agent, few studies have been carried out. Kiassen et al(1966) found that sodium hexametaphosphate was effective in reducing the viscosity of magnetitedense media contaminated with clay. In particular, from two coal plant studies it was found thatthe additions of 3-5 grams of sodium hexametaphosphate per tonne of medium reduced theplastic viscosity and the Bingham yield stress. The addition of this dispersant also improved themedium stability. The net result was a decreased product ash content and a decreased magnetiteconsumption.Graham and Lamb (1988) compared the effects of various inorganic and organicdispersing agents on the zeta potential of fine magnetite. It was shown that sodiumhexametaphosphate increased the zeta potential value more than the other dispersants. From105rheological measurements, it was found that the addition of sodium hexametaphosphate had littleeffect on the yield stress and even less effect on the plastic viscosity of pure magnetitesuspensions. When slimes were present, however, the addition of dispersant significantlyreduced the yield stress.9.3.2.3 MagnetizationMagnetite particles are composed of a ferromagnetic material that, once introduced to amagnetic field, often exhibits remnant magnetic properties (see Section 4.2.3). This remnantmagnetism causes the particles to aggregate and thereby influences the rheological properties ofmagnetite suspensions.The magnitude of remnant magnetic forces vary with the composition and structure of themagnetite particles. These forces can be strong as compared to electrostatic repulsive forces, inwhich case it is not possible to disperse the particles using chemical methods (Meerman, 1958).The particles can be dispersed by demagnetizing them. This can be achieved by raising thetemperature above the Curie point (approximately 770 °C for iron) or by passing the magnetitethrough an alternating current (AC) magnetic field (Onstad, 1954). The demagnetizationrandomizes the orientation of magnetic domains within the particles such that the domains canceleach other leaving the particle with no net magnetic force (Tipler, 1979).Magnetically aggregated particles form chain structures whose size depend on the strengthof the magnetic forces and the shearing conditions in the suspension (Voet and Suriani, 1950,Kamiyama and Satoh, 1989). With shear, the magnetic attachments can break thereby reducing106the size of the aggregates. When such structures form, the suspensions exhibit pseudoplasticproperties and can have a yield stress. Kamiyama and Satoh (1989) found that the apparentviscosity increased with increasing number of particles in the aggregates. Demagnetizing theparticles results in the dispersion of the particles and a more Newtonian flow behaviour(Meerman, 1958).The effect of particle magnetization on the rheological properties of magnetite densemedia was investigated by Erten (1964). He observed that by magnetizing a suspension ofmagnetite, the yield stress increased although the plastic viscosity did not change significantly.Graham and Lamb (1982) explained such an increase in yield stress by the stress required tobreak aggregates of particles resulting from remnant magnetism (see Section 8.4.3). The strengthof the remnant magnetic forces depends on the types and amounts of impurities in the latticestructure of the magnetite.Erten (1964) also showed that the yield stress of a magnetized suspension could bereduced to its original state by passing it through a demagnetizing coil. Napier-Munn et al(1990) suggested that a coil with a larger field strength is required to demagnetize particles withhigh remnant magnetism and to demagnetize small particles. Despite the understanding of theeffect of magnetization on media properties, many coal operations do not use their demagnetizingcoils; many plants do not have coils at all.1079.3.3 ContaminationFine coal, mineral and clay particles that enter dense media are referred to ascontaminants. Inefficient de-sliming of the feed to the separators results in the introduction ofsuch contaminants into the medium. In addition, the abrasion of the coal particles in theseparator generates fines (DeVaney and Shelton, 1940) that also enter the medium. Thesecontaminants are almost always present in dense media and due to their small particle sizes,influence the rheological properties.As with magnetite, the physico-mechanical and physico-chemical properties of thecontaminants determine how they influence the medium rheology. For example, sincecontaminants typically have a lower density than magnetite, a higher medium solids content isrequired to achieve a specified medium density. Therefore contaminated media has a highersolids content and corresponding higher viscosity than uncontaminated media (DeVaney andShelton, 1940). In addition, contaminating particles change the effective medium particle sizedistribution. A reduction in the effective medium particle sizes can result in an increase in themedium viscosity (Ferrara et al, 1988).Fine coal particles, with sizes ranging from a few micrometers to approximately 100 kim,practically increase the effective solids concentration of the medium. At low solids contents, coalsuspensions exhibit Newtonian rheological properties and have a low viscosity (Castillo andWilliams, 1979, Wildemuth and Williams, 1985). However, the addition of a small amount offine material to a viscous suspension can result in a large increase in suspension viscosity(Thomas, 1965). The contribution of the coal fines to the rheological properties of the dense108medium, therefore, depends on the rheological properties of the pure magnetite suspension andon the amount of fine coal that contaminates it.The surface properties of the contaminating particles may have a large effect on themedium rheology. This is especially true in the case of clays. Bentonite and to a lesser extentkaolinite, swell in aqueous suspensions to create a “card house” structure. Even at lowconcentrations, this structure can result in a large increase in media viscosity (DeVaney andShelton, 1940, Geer et al 1957, Chakravarti et al, 1958).Clay suspensions typically exhibit a yield shear thinning flow behaviour (Nicol andHunter, 1970, Czaban et al, 1986) and thixotropy (Speers et al, 1987, Chen et al, 1988). Therheological properties are attributed to the structures formed by the fme aggregated particles.Kaolinite and montmorillonite form an extensive “card house structure” at neutral and acidic pHlevels with negatively charged cleavage surfaces attached to positively charged edge surfaces ofthe particles (Street, 1956). In the acidic to neutral pH range, these attachments can break duringshearing and reform which accounts for the yield stress and thixotropic properties of claysuspensions. Such structures are strongly influenced by pH, dissolved ion concentration and theaddition of dispersants (Klassen et al, 1966, Nicol and Hunter, 1970, Chen et al, 1988, Grahamand Lamb, 1988, Helfricht and Schatz, 1989). These rheological properties are found even indilute suspensions of clay particles (volume solids fraction less than 3%).The levels of contaminants found in magnetite dense medium vary widely and depend onthe softness of the coal, the amount of clay present and the design of the feed preparation anddense media recovery stages. Levels of contaminants have been reported to range from 0.1%(DeVaney and Shelton, 1940) to 15.4% by weight (Graham and Lamb, 1988).109CHAPTER 10: STABIIJTY OF MAGNET1TE DENSE MEDIA10.1 IntroductionThe medium stability, (settling) has been shown to be an important media parameter thatinfluences the performance of both static and dynamic dense media separators (See Section 4.5).The stability is a measure of the suspensions ability to remain homogeneous with respect tomedium density; it has also been defined as the degree of stratification of particles in theseparator (Graham and Lamb, 1988). Gravitational and centrifugal acceleration, however, causemedia particles to settle or segregate, creating a non-homogeneous environment.Both the physico-mechanical and physico-chemical parameters affect settling propertiesof dense media. Magnetite dense medium is a concentrated poly-disperse suspension ofinteracting, irregularly shaped particles. Specifically, the solids concentrations range of magnetitedense media is typically between 10% and 25% solids by volume, the particle sizes typicallyrange from a few im to 75 jim, and the magnetite particle density varies from 4800 to 5180 kgm3. The remnant magnetism exhibited by magnetite particles as well as colloidal forces, mayaffect media stability via formation of aggregates.10.2 Settling in SuspensionsThe settling in a suspension depends on the same physico-mechanical andphysico-chemical parameters that influence the rheological properties (Chapter 8).110Stokes (1891) developed an equation for the settling rate of non-interacting, sphericalparticles in a dilute (solids content less than a few percent) suspensions at low Reynolds numbers(Equation 10.1).= d2(p - p1)g (10.1)18This equation shows the relationship between the settling velocity, v, and particle size,d, particle density, p, fluid density, Pf, accelerating field, g, and fluid viscosity, i.Steinour (1944) considered that with increasing solids concentration, the particle settlingvelocity is lower than predicted by Stoke’s equation due to hindering effects which include:i. particle-particle collisions causing particles to lose momentum and,ii. hydrostatic pressures caused by the upward flowing fluid that is displaced by thesettling particles (Richardson and Zaki, 1954, Garside and Al-Dibouni 1977, Zimmels, 1985).Several equations have been developed to relate the settling velocities of particles to thesuspension volume solids fraction. Steinour (1944) developed an equation that is an extensionof Stoke’s equation. Similarly and more recently Zimmels (1985) developed an equation thatis also an extensions of Stokes equation (1891) as follows.— d2(p3 - p1)ng (1—) 10218rI 11 +4exp .3 1 -where, 4 is the solids volume fraction, andn is a multiple of the gravitational acceleration.111For poly-disperse systems, large particles settle faster than small ones; this leads todifferential settling. The amount of differential settling depends on the solids content in thesuspension. At intermediate solids concentrations, large particles displace small ones along withthe fluid; the result is a reduced or even a negative settling velocity for the small particles. Inaddition, the small particles and fluid provide “carrier” properties to the large particles therebyhindering their settling. These carrier properties have been explained by the buoyancy andviscosity exerted on large particles by the suspension of smaller ones (Selim et al, 1983, Williamsand Amarasinghe, 1989). At high solids concentrations, these hindering effects preventdifferential settling and the suspension settles with constant composition (Williams andAmarasinghe, 1989).A concentrated poly-disperse suspension settling in a column forms four distinct zones(Greenspan and Ungarish, 1982). As the particles settle, a supematant will form at the top ofthe column. This region extends vertically to the position of the smallest settling particle thatwas originally at the top of the column. Below this position is the transition region, which ischaracterized by an increasing particle size with depth. This region, also has an increasing solidsconcentration with depth. Below the transition region is the constant density zone, which has asolids concentration and size distribution approximately equal to that of the original suspension.Immediately below this zone is the consolidation zone in which the settling particles form asediment. With increasing solids concentrations, the transition zone will diminish in size suchthat at high solids content it will not exist.In the above discussion, the effects of physico-chemical parameters have not beenconsidered. When a net attraction occurs between the particles, aggregates form. These112aggregates are composed of particles and trapped liquid which reduces the effective density ofthe unit and increases the effective solids concentration of the suspension. At high solidsconcentrations these aggregates interact and may form a network resulting in a lower settling ratethan in a suspension of individual particles. At such high concentrations, the suspensions settlewith homogeneous size and solids compositions through the vertical extent of a column (Cheng,1980a). In the low to intermediate solids concentration range, however, the increased effectivediameter of the settling unit results in a higher settling rate than in a suspension of dispersedparticles (Michaels and Bolger, 1962, Zimmels, 1985). In addition, at low solids concentrationsdifferential settling occurs, that is large aggregates settle faster than small ones (Cheng, 1980a).The critical solids concentration, beyond which the suspension settles slower than a suspensionof non-interacting particles, may range from 15% to 45% and is a function of thephysico-mechanical and physico-chemical conditions in the suspension.Sadowski et al (1978) and Sadowski and Laskowski (1980) related the settling rates ofquartz, calcite, dolomite and magnesite suspensions to the surface properties of the minerals. Inparticular, it was shown that at a pH near the iso-electhc point (i.e.p.) for the minerals, thesettling rate increased due to coagulation. It was also observed that for very small particles (2-4jim), which can only experience primary minimum coagulation, the pH at which the settling ratebegan to increase was close to reported i.e.p. ranges. For larger particles (12-18 jim), settlingrates began to increase at pH values further away from the i.e.p. These results demonstrate theimportance of physico-chemical parameters to the settling of suspensions.In magnetite dense media, particle sizes range from the colloidal size to about 75 jim.For particles in the colloidal size range, the forces responsible for aggregation may have a113significant effect on their settling properties. In such a case, the reactive small particles and theliquid can form a structure that acts to support the large particles thereby increasing thesuspension stability (Yucel and Hughes, 1984, Renehan et al, 1988a).10.3 Measurement of StabilitySeveral techniques for measuring and characterizing the settling properties of suspensionshave been developed. The most commonly used method involves measuring the height of thesupernatant - suspension interface (mud line) with time from which a settling rate can becalculated. From the above discussion, it is clear that this measurement does not provide acomplete description of the settling properties. In systems where conditions are such that thesuspension settles with constant composition throughout its extent, the method does provide agood indication of the relative stability of suspensions (Williams and Amarasinghe, 1989).Graham and Lamb (1988) showed that magnetite dense media exhibits zone settlingproperties. It was found that little differential settling occurred and that a constant density zoneexisted that had a composition equal to that of the original suspension. They therefore suggestedthat interface falling rate is an accurate measure of stability for the static separation process. Theshear conditions and accelerating forces are, however, very different in dynamic separators fromthose in static ones. As a result, aggregation effects that are likely to contribute to the settlingproperties of magnetite in a settling column, are probably less significant in dynamic separators.Collins et a! (1983) suggested, however, that this settling rate does provide an indication of themedium stability in dynamic separators.114The magnetite settling properties are also characterized by the “F5 index”. This F5 indexwas recommended to determine the relative stability of magnetite dense media (Graham andLamb, 1982), and it is calculated from the ratio of the solids drawn from the upper and lowersection of settling column after a standard settling time. According to Williams et al, 1990, thismethod is of little use for diagnostic analyses.10.4 Settling Properties of Magnetite Dense MediaThe effect of various physicomechanical and physico-chemical parameters on the stabilityof magnetite dense media has been the subject of several publications. In particular, the effectsof the physico-mechanical parameters (solids concentration, particle size and particle density),the physico-chemical parameters (magnetization and dispersants) and of fine contaminatingparticles (coal fines and clays) have been considered. However, no data were found on theeffects of particle size distribution, particle shape, pH or dissolved ions. The followingsummarizes the available results.It is clear from Equation 10.1 that magnetite particles with a density close to 5000 kg m3,will settle quickly in water. It has been shown that the settling rate of magnetite increases in anexponential manner with decreasing solids content (DeVaney and Shelton, 1940, Berghofer,1959). Therefore, at low solids concentrations (low medium densities) stability is of greaterconcern. In particular, at low solids concentrations, large particles settle faster than small onesresulting in differential settling and poor medium stability properties (Berghofer, 1959). For lowmedium densities it has been shown that fine grades of magnetite provide greater stability115(DeVaney and Shelton, 1940). Fine size grades (95% -45 jim) are therefore recommended forlow density separations (1200 - 1500 kg m3), while coarser grades (95% -53 jim) can be usedat high densities (1400 kg m3 to 2000 kg m3) (Graham and Lamb, 1988).As has been discussed (Section 3.2.3), the remnant magnetism in magnetite particles mayresult in the formation of aggregates. This magnetic aggregation increases the settling rate of themedium. The effect of aggregation depends on the strength of the magnetic forces which isspecific to the sample. The effect of magnetic aggregation on the medium stability in dynamicseparators is not clear. Some investigators believe that the shear forces in a dynamic separatorwill break up the aggregates and reduce such effects. Graham and Lamb (1988) found thatshearing a suspension of magnetically aggregated particles had little effect on subsequent settlingresults and concluded that either the shearing did not break the aggregates or the aggregatesquickly reformed. It has therefore been suggested to install demagnetizing coils for dynamicprocesses as well (Graham and Lamb, 1988, Napier-Munn, 1990).The effect of a variety of dispersing agents on medium settling properties has beenstudied. It was found that they did not significantly influence the stability of pure suspensions.They have, however, been shown to affect significantly the settling properties of dense mediumcontaining fine clays. Aplan and Spedden (1964) found that sodium hexametaphosphate waseffective in dispersing clay which lowered the structure and resulted in higher settling rates. Thedispersants did, however, reduce the medium viscosity. Since clays such as bentonite andkaolinite can be added to dense medium to improve stability (DeVaney and Shelton, 1940, Aplanand Spedden, 1964, Graham and Lamb, 1988), the addition of dispersing agents can be used tocontrol their effects on medium viscosity.116CHAPTER 11: SUMMARY OF LITERATURE REVIEWDense medium separation is one of the most important processes used to upgrade coal andmineral ores. It is expected that the use of the process will increase in the future as a result ofnew applications such as for the cleaning of fine coal. To extend the use of dense mediumseparation to such applications, it is necessary to optimize the medium properties. Specifically,for optimum separation performance, the medium should exhibit a low viscosity and a goodstability. The viscosity affects separation performance via two mechanisms: i. it influences themotion of coal/ore particles, and ii. it controls the medium stability. The relationship betweenmedium properties and separation performance is complicated by its non-Newtonian flowbehaviour. Investigations with both static and dynamic separators have indicated that a yieldstress has a deleterious effect on the separation of small or near density particles. In addition,results from tests with hydrocyclones revealed that the existence of a yield stress impedes sizeclassification suggesting that the yield stress is related to medium stability. Based on the meagredata that is available, it is apparent that in order to understand the relationship between mediumproperties and separation performance it is necessary to have knowledge of the completerheology.Many studies have been carried out to characterize the rheological properties of magnetitedense media. Due to the different types of instruments that have been used and the difficultiesassociated with accurately measuring the rheological properties of settling suspensions, resultshave been difficult to compare. Several viscometers have been developed for measuring therheological properties of settling suspensions. Each device applies an undefined shear to inhibit117particle settling during the measurement. This undefined shear produces a measurement errorthat may be significant particularly for suspensions exhibiting non-Newtonian and time dependentproperties. A method that does not apply an undefined shear to maintain the particles in thesuspension would therefore be considered an improvement over existing methods. Other errorsassociated with measuring the rheological properties of suspensions can be reduced by properlydesigning the rheometer and by treating the rheological data.Magnetite dense media exhibit non-Newtonian rheological properties that have beenmodelled with the Bingham plastic equation. Examination of available flow curve data revealedthat the Bingham equation does not fit the low shear rate data. Since the viscous properties atlow shear rates may determine the separation efficiency of fine and near density particles, betterfitting models are needed.Various suspension parameters influence the rheological properties of magnetitesuspensions. How and to what extent these parameters influence the rheological properties is,however, unknown. From investigations with other coarse suspensions it has been shown thatphysico-mechanical and physico-chemical parameters can be manipulated to control the mediumproperties. For example, it has been shown that suspension viscosity can be minimized by usinga specific bimodal particle size distribution. Experiments were therefore designed to investigatethe influence of these parameters on the rheology and stability of magnetite suspensions.A considerable amount research has been carried out to study the rheological propertiesof suspensions of coarse hard particles. The rheological properties of these suspensions havebeen explained in terms of micro-rheological effects which describe the different types of particleinteractions that are responsible for viscous energy dissipation. The same theory can be used to118develop a better understanding of the rheological properties of magnetite dense media.Since medium rheology is interrelated with stability and since both properties areimportant to process performance, any study of the medium rheology should include asimultaneous study of the stability. The medium stability is affected by the same parameters asthe rheology. In most cases, changing parameter levels to increase the stability also results ina dethmental increase in the viscosity. Medium stability is typically characterized by a mudlinesettling rate. However, it is not known how the mudline settling rate relates to the stability ina separator. Some investigators believe that the medium exhibits differential settling propertiesalthough recent studies indicate that it exhibits bulk zone settling properties.119SECTION B: EXPERIMENTAL PROGRAMCHAPTER 12: EXPERIMENTAL PLAN12.1 IntroductionFollowing the literature review (Section A), an experimental program was designed toachieve each of the objectives. These objectives include:i. Development of a method to measure the rheological properties of settlingsuspensions such as magnetite dense media;ii. Characterization of the rheological and settling (stability) properties of magnetitedense media;iii. Investigation of the effects of physico-mechanical and physico-chemical parameterson the medium properties; andiv. Examination of the effects of particle size distribution on the medium properties.12.2 Measuring Rheological Properties of Settling SuspensionsThe errors associated with measuring the rheological properties of settling suspensionswere reviewed in Section 6.2.2. A suitable method should minimize these errors. Therefore, thefirst objective of the thesis was to develop a new method of measuring the rheological propertiesof settling suspensions.120The development of a device used to measure the rheological properties of sedimentingsuspensions involved:i. Designing a modified device based on known theory;ii. Working out details of the design from experiments;iii. Constructing a prototype; andiv. Calibrating the device.The new device was then evaluated to check assumptions used to design the device, andto determine the magnitude of potential errors.The design and evaluation of the measuring device are discussed in Chapter 15.12.3 Rheology and Stability of Magnetite Dense MediaOnce a method of measuring the rheological properties of settling suspensions wasestablished, the rheological properties of magnetite dense media were measured using thedeveloped procedure. The settling properties of the suspensions served as an indicator of densemedia stability. The first step was to select and prepare a magnetite sample and to characterizeits physical and chemical properties.The magnetite sample was obtained from the Craigmont Mine stock pile, which is themain source of magnetite used by western Canadian coal operations for dense media separation.The material was first upgraded and subsequently characterized with respect to:i. Elemental composition;ii. Density;121iii. Size distribution;iv. Surface properties (electrophoretic mobility);v. Magnetic properties; andvi. Per cent magnetics.The medium settling properties were characterized by determining the solids concentrationprofile as a function of time. In addition, the supematant - suspension interface was measuredwith time to determine a settling rate.The rheological properties were studied:i. Using the developed device to measure a rheological flow curve;ii. Fitting the flow curve data to several rheological models using a simplexoptimization non-linear regression program,iii. Determining the best fitting equation using a model discrimination program.The coefficients from the selected model were used to characterize the rheologicalproperties of the suspension. The time dependent properties were characterized by the flow curvehysteresis method.12.4 Effect of Parameters on Medium PropertiesThe effects of various physico-mechanical and physico-chemical parameters on theproperties of suspensions were discussed in Chapter 8. In Section 9.3, the effects of theseparameters on magnetite dense media properties were also analyzed. However, much of theavailable data for magnetite dense media were obtained using rheological measuring devices that122could not be considered accurate. The objective of this section is, therefore, to determineaccurately the effects of these parameters by using the measuring device referred to in Section12.2.A fractional factorial experimental design was used to determine the relative importanceof these parameters to the rheological and settling properties of magnetite dense media.The first step was to determine the levels of the variables over which the experimentsshould be carried out. This was achieved by using parameter levels reported in the literature, andby consulting with coal mining operations and carrying out preliminary experiments.Once the parameter levels had been determined and the suspensions had been prepared,the rheological and settling tests were carried out. The rheological data were modelled usingvarious equations to fit the flow curve. The best fitting model was then selected. A simplexoptimization non-linear regression program and a model discrimination program were written tofit the flow curve models to the data and then to compare the fits of the models, respectively.The relative significance of suspension variables to the measured responses (modelcoefficients, settling rate and sediment solids content) were determined from the magnitude oftheir effects. The variable effects were then discussed.12.5 Effect of Particle Size Distribution on Medium PropertiesFrom the reviewed literature, it was shown that it is possible to manipulate particle sizedistribution in order to control and therefore optimize suspension viscosity and stability (seeSection 8.3.5). Specifically, it was shown that suspension properties can be improved by using123a bimodal particle size distribution. The effect of particle size distribution was found to be mostsignificant at high solids concentrations. To investigate the effect of these variables on theproperties of magnetite dense media a central composite experimental design was used.From the results of this investigation, second order models were fitted to responses thatcharacterized the suspension stability and rheology. The second order models were then plottedto show minimum and maximum responses and corresponding variable levels. The responsesincluded the coefficients of the fitted flow curve equation and the suspension settling rate.To achieve the objectives, the following work was undertaken:i. Samples of narrow particle size fractions were prepared and characterized;ii. An experimental design was selected and set up;iii. Appropriate variable levels were established;iv. Media settling and rheological properties were measured;v. The rheological data were modelled; andvi. The rheological model coefficients and the settling rate were modelled as afunction of the suspension variables.124CHAPTER 13: SAMPLE PREPARATION AN]) CHARACTERIZATION OFMATERIALS13.1 IntroductionTo perform the proposed experimental program, it was necessary to obtain a suitablesample of magnetite and prepare it to meet the required specifications. In addition, samples offine coal and clays, as well as various chemical reagents (pH modifiers and dispersing agents)were used to carry out the experimental program.13.2 Magnetite Characterization ProceduresThe following summarizes the procedures set by ISO (Anon, 1985) and Mintek (Jonker,1984) that were used to determine the magnetite properties.13.2.1 Density DeterminationMagnetite density was determined using three separate methods:i. The wet pycnometer method;ii. The air pycnometer method; andiii. The volumetric flask method.For the wet pycnometer method, a known weight of solids is added to distilled water ina pycnometer bottle. The magnetite density was then determined from the total weight and125volume of the solids. To ensure particle wetting, sodium hexametaphosphate was added to thesuspension. Complete de-aeration was difficult to achieve as air appeared to be trapped betweenthe particles. To solve this problem, the bottle was tapped and evacuated in a desiccator.The air pycnometer method (Beckman Model 930) involved placing a known weight ofmagnetite into a pycnometer cup. The cup was then placed in an air pycnometer containing twochambers with pistons one of which contained the sample. A differential pressure indicatorconnected the two chambers. As the pistons were moved to increase the pressure in the twochambers, the pressure differential was maintained at zero. When the piston in the chamberwithout the sample displaced a defined volume, the volume of the sample was read from acalibrated indicator.The volumetric flask method is similar to the wet pycnometer method except that a onelitre volumetric flask was used instead of the pycnometer bottle. To ensure that trapped air wasremoved, the magnetite and water were heated to almost boiling and the suspension was lightlyagitated. After allowing the suspension to cool, the magnetite density was then calculated fromthe weight of magnetite, the weight of solids plus distilled water and the flask volume. Resultsproduced from the three procedures are compared in Section 13.3.2.1.13.2.2 Size AnalysesTwo different instruments were used to perform particle size analyses of the magnetitesamples, a Horiba Particle Size Analyzer (PSA) and an Elzone PSA. Results produced fromthese two instruments were compared to results produced by a Warman Cyclosizer which is more126commonly used by industry. The Horiba and Elzone PSA’s were used because they can providemore detailed size information than the cyclosizer. This was considered important particularlywhen characterizing samples with very narrow size distributions and samples with particle sizessmaller than the limits of the cyclosizer.The Horiba CAPA 700 PSA relates light transmittance through a settling suspension toparticle size distribution (Allen, 1990). Since coarse particles settle faster than fine particles, thetransmittance changes with time in a manner proportional to the particle sizes. The absorbenceis determined and related to the particle areas and number of particles. The particle areas arethen converted to volumes from which Stokes diameters are determined. As with most methodsthat rely on particle settling to determine particle sizes, particle shape can have a large influenceon the results. The Horiba PSA is capable of running in gravitational mode or, for measurementsof very fine (-10 jam) particles, in centrifugal mode.The Elzone PSA uses the electrical sensing zone method of particle size determination(the Coulter principle). The principle of the method is that a particle in an electrolyte solutionpassing through a small orifice with electrodes on each side will change the impedance acrossthe orifice. The change in impedance will produce a voltage pulse that has an amplitude whichis proportional to the particle volume (Allen, 1990). The pulses are counted to produce acumulative particle frequency versus particle size (volume diameter) plot. The accuracy of theElzone depends on the careful preparation of the sample to ensure that it is well dispersed in aconductive electrolyte solution (Berg, 1958).The Warman Cyclosizer consists of a series of five inverted classifying cyclones that aredesigned for sizing particles in the sub-sieve size range (-400 mesh). During a run, each of the127cyclone oversize products are collected and subsequently weighed. Since the undersize from thelast cyclone in the series is not usually collected, its weight is calculated from the differencebetween the feed and product weights. Since the size increments (Stokes diameters) are quitelarge, the instrument is not well suited to samples with narrow size distributions. In addition,since the finest cut size is approximately 10 jim, the instrument does not provide detailed sizeinformation for very fine samples.13.2.3 Magnetics ContentThe magneties content of the sample was determined with a Davis Tube. The methodinvolves passing an aqueous suspension of magnetite and water through a tube surrounded by amagnet. The tube rocks back and forth while water is washed through the sample to remove anynon-magnetic particles. The magnetics content can then be calculated as the weight of materialtrapped by the magnet divided by the total weight of the sample fed to the tube.13.2.4 Electrophoretic MobilityA Zeta Meter was used to determine the electrophoretic mobility (EPM) of the magnetiteparticles as a function of pH. The measurements involved determining the rate of particlemovement in a capillary in an electrical field. The electrophoretic mobility of particles isproportional to the applied potential. One difficulty associated with using the zeta meter inmeasurements with suspensions is that the instrument was designed to determine the zeta128potential for particles in the colloidal size range. Therefore, to determine the electrophoreticmobility of the magnetite, fine (-10 pm) particles had to be separated from a magnetite sample.To insure that the particles were dispersed, they were demagnetized which can be difficult forsmall particles.13.2.5 Chemical CompositionThe chemical composition of the magnetite samples was determined by using gravimetricand atomic absorption procedures. The samples were analyzed for the content of the followingelements: total iron, ferrous iron, silica, titanium, manganese, copper, aluminum, calcium,magnesium, chromium and sulphur.13.2.6 Magnetic PropertiesThe magnetic properties that characterize the magnetite sample include magneticsusceptibilities at low and high magnetic fields, the saturation moment and the coercive force.An EG&G PARC model 155 vibrating magnetometer was used for the measurements. Themeasurements produced a hysteresis curve for the intensity of magnetization, M, versus theinduced magnetic field, H. The magnetic properties can be determined from such a plot.The magnetic susceptibility, X, is defined as the ratio of intensity of magnetization, M,to the induced magnetic field strength, H, (Equation 13.1).129X = . (13.1)HFor a ferromagnetic material, the susceptibility is not a constant and it depends on themagnetic field strength. The saturation moment, M, is the limiting value at which the intensityof magnetization levels off. The coercive force, H, is the magnitude of the induced magneticfield that is required to reduce the intensity of magnetization to zero.13.3 Magnetite SampleThe magnetite used in the tests was obtained from the Craigmont mine which is the mainsource of magnetite for dense media separation in western Canadian coal operations. Adescription of the Craigmont deposit and its mineralogy were given in Section 5.2. Several othersources of magnetite from other deposits in British Columbia were also considered. A list of thedeposits from which samples were obtained is given in Table 13.1.13.3.1 Preparation of Magnetite SampleA 125 kg sample of magnetite concentrate from the Craigmont stock piles was obtainedfor the planned test work. The sample contained some undesirable non-magnetic material thataffects its quality. In particular, the sample density was 4690 kg m3, lower than the minimumrecommended density of 4850 kg m3. Such a low sample density was attributed to the presenceof low density non-magnetic minerals (silicates and calcite). The entire sample was therefore130Table 13.1 Magnetite samples considered for use in test work.Company LocationCassiar Mining Corporation Cassiar, B.C.Craigmont Mine Merritt, B.C.Falcon Iron Property MacKenzie, B.C.Iron River Property Campbell River, B.C.Island Copper Mine Port Hardy, B.C.Brynor Mine Kennedy Lake, B.C.131upgraded using several cleaning stages with a wet drum low intensity magnetic separator whichincreased the sample density to greater than 4850 kg m3.The procedure used to upgrade the magnetite is presented in Figure 13.1. Since themagnetite was already milled no grinding was necessary. A rougher stage plus three cleaningstages were needed to increase the density to 4857 kg m3 which meets the density specification.Based on microscopic examination of the non-magnetic particles, they appeared to be mostly non-liberated magnetite particles as well as liberated calcite and silicate particles. Standani splitling,riffling and sampling procedures were used to obtain suitable representative samples for analysesand test work.13.3.2 Characterization of Upgraded Magnetite SampleThe properties of the magnetite sample (density, size distribution, magnetics content,electrophoretic mobility, chemical composition and magnetic properties) were determined usingthe procedures described in Section 13.2.13.3.2.1 Magnetite DensityThe results of the magnetite density determinations using three different methods arepresented in Table 13.2. To ensure accuracy of measurements, the average of three volumetricflask determinations, the average of three air pycnometer determinations and the average of twowet pycnometer determinations are reported.132Cleaner #1 ConcentrateCleaner #2 WDMSFigure 13.1 Process flow sheet showing the procedure that was used to upgrade the magnetitesample.L Mixing Tank FeedRougher Wet Drum Magnetic Separation (WDMS)Mixing Tank Rougher ConcentrateCleaner #1 WDMSTaillings ProductCleaner #2 ConcentrateCleaner #3 WDMS• Drying OvenIMagnetite Product133Table 13.2 Comparison of density measurement results for upgraded magnetite using wetpycnometer, air pycnometer and volumetric flask methods.Method Density (kg m3)Measured Mean ± 95% C.I.Wet Pycnometer 45674564 4566 20Air Pycnometer 485748674849 4857 22Volumetric Flask 488048804872 4877 12134As seen, the volumetric flask results compare well to the air pycnometer results, but, thewet pycnometer produced lower density values. The lower densities determined by the wetpycnometer can be attributed to air trapped within the bed of solids which was difficult toremove. Higher and more accurate density values were obtained by heating the suspension ina volumetric flask which facilitated de-aeration. Good agreement between the air pycnometerand volumetric flask results indicated that the air pycnometer could be used to characterize thedensity of the solids accurately. It should be noted that while the air pycnometer provides arelatively quick and easy determination of the magnetite density, it was also found that theaccuracy of the results depended on frequent calibration of the instrument. For the purposesofthis dissertation, the air pycnometer densities were used since these measurements are relativelyquick to perform.13.3.2.2 Particle Size DistributionThe size distribution of the upgraded magnefite sample was determined using a HoribaPSA, an Elzone PSA and a Cyclosizer. The results of the three sets of measurements arepresented in Table 13.3 and are plotted in Figure 13.2.To ensure complete particle dispersion, the magnetite samples were demagnetized priorto measurements. The cyclosizer was run for 60 minutes with a water temperature of 11 degreesCelsius. For measurements with the Horiba PSA, a sucrose solution was used as the dispersingmedium. The density of the solution was determined using a volumetric flask and was found tobe 1270 kg m3. The solution viscosity, measured with a Haake RV2O viscometer at a135temperature of 25°C, was 40.0 mPa.s. The solids density was determined with an air pycnometerto be 4,857 kg m3. The expected particle size range was estimated to be between 2 pm and 70pm. To determine the size distribution, measurements were made over the 10 pm to 70 pm rangeand then over the 2 pm to 10 pm range. The Horiba software was then used to calculate thecombined size distribution results. Three sets of data were generated in each size range whichwere averaged before combining the two measured size ranges together.The results show that approximately 90% of the magnetite is finer than 45 pm (325 mesh)and that 30% is finer than 10 pm. Typical grades of magnetite used in dense media have aparticle size distribution characterized by particle sizes that are approximately 95% finer than 40pm and less than 10% finer than 10 pm (Osborne, 1988).The size data was fit to the Rosin Rammler Bennett (RRB) distribution function (Equation13.2) using non-linear regression (Newton’s method). The RRB size and distribution moduli foreach measurement technique are included in Table 13.3. Figure 13.2 shows that the size dataplot as straight lines on RRB graph paper indicating that the RRB function is well suited tocharacterizing the size distributions of the sample.dmF(cJ = 100 1 — exp - (13.2)d632where, F(d) is the cumulative percent passing on size d,m is the distribution modulus, andd632 is the size modulus (aperture through which 63.2% of material would pass).136807060504540353025222015.61511.31086410010099.396.693.688.279.769.358.949.640.129.524.719.112.992.189.788.586.884.081.975.868.260.553.949.236.429.124.917.1Table 13.3 Size analysis results for upgraded magnetite,Elzone PSA and Cyclosizer.determined using Horiba PSA,Size (tim) % PassingElzone Horiba Cyclosizer88.266.449.035.226.6d632 24.4 24.5 19.4m 1.26 0.96 1.44137S rt H C-) Ct Ci) H N a 0 aQPP—DCumulativePassing,F(d),(%)DLIiiuc-coCQOSoCJC C_flQ—.cjQCI I.Li) 0 Ni 0 Ni 0 0 0 U) 000NiU)Ni0 NiU)0 0 C’-,0 0 Ni0 0 U)0 0Ni0 Li)\\\\\\\\\\\\\Examination of Table 13.3 and Figure 13.2 reveals that each measuring techniqueproduced slightly different results. The differences in the results can be attributed to the differenttypes of particle diameters that are measured. The Horiba PSA and cyclosizer measure Stokesdiameters and the Elzone PSA measures spherical volume diameters. The difference betweenthese types of diameters is primarily due to the non-spherical shapes of the particles (Allen,1990). The data from the Elzone and the Horiba can be brought into coincidence with thecyclosizer data by multiplying their sizes by the (average) shape factors 1.18 and 1.05,respectively. The wider size distribution results obtained from the Horiba than from the Elzoneindicates that the particle shape changes with particle size. In this case, the shape factor will beslightly different for particles of different sizes.13.3.2.3 Electrophoretic MobilityThe electrophoretic mobility, EPM, was determined as a function of pH for the -10 pmsize fraction separated from the upgraded magnetite sample using a Warman Cyclosizer. Themeasurements were carried out with a Zeta Meter and the pH of the suspension was controlledwith HC1 and NaOH. For measurements in the acidic pH range, the EPM was first determinedat the natural suspension pH and then HC1 was added to lower the pH for subsequentdeterminations. Similarly, for measurements in the basic pH range, the measurements were firstcarried out at the natural suspension pH which was subsequently increased by adding NaOH.Two batches had to be prepared for these experiments, one for the acid range and another for thebasic range.139The electrophoretic mobility is plotted in Figure 13.3. It can be seen that the EPM wasnegative over almost the entire pH range and that an isoelectric point was situated around pH 2.3.According to the literature, pure iron oxide minerals have an isoelectric point (i.e.p.) in the pHrange of 6.0 to 7.0. Possible explanations for this low i.e.p. value are:i. Surface contamination of the magnetite with surfactants,ii. Leaching and precipitation at particle surfaces due to leaching, andiii. Mineralogical impurities in magnetite particles.It should be noted that the data presented in Figure 13.3 was produced from threeindependent sets of measurements. The -10 pm magnetite sample had a mean particle size of3.3 pm, a density of 4970 kg m3, a total iron content of 68.0% and a Si02 assay of 2.8%indicating its high purity. It is therefore not likely that the EPM of quartz was being measuredinstead of for the magnetite. It is also noted that these specifications are very close to those ofthe bulk sample and other size fractions and therefore the -10 pm sample can be considered tobe representative of these other samples.The magnetite was produced as a secondary product from the Craigmont copper minewhere the ore was subjected to flotation collectors, dispersing agents and flocculants. Traceamounts of any of these reagents can affect the EPM. In addition, the magnetite sample wasobtained from a stock pile which was exposed to weathering. The weathering could haveresulted in leaching and precipitation processes that altered the particle surfaces. It is alsopossible, however, that the magnetite contained fine inclusions of other minerals that affected thesurface charge of the particles. Quartz, for example, has an i.e.p. situated around pH 2, whichis very close to the measured i.e.p. values for magnetite. This supports the explanation that fine1404Figure 13.3 Electrophoretic mobility of -10pm magnetite sample showing an iso-electric pointin the pH range of 2.3.39 8II10 12pHI IK141quartz inclusions or contaminants determine the zeta potential of the magnetite particles.To support this explanation, scanning electron micrographs were produced for themagnetite sample. Figure 13.4 a) shows the electron micrograph of the magnetite sample. Figure13.4 b) shows an energy dispersive x-ray analyzer spectrum for the surface of the particles. Thespectrum shows an iron peak but also a distinct silica peak. These results confirm that silica waspresent on the surface of the magnetite possibly as a contaminant or as very finely disseminatedinclusions.13.3.2.4 Magnetics ContentThe magnetic s content of the upgraded sample was determined with a Davis Tube to be93%. This value is slightly lower than recommended limit of 95%. It should be noted, however,that such values are operator-dependent which explains why a magnetics content of 100% wasnot achieved despite prior upgrading of the sample with a wet drum magnetic separator.13.3.2.5 Elemental AnalysesThe assays levels of the elements found in the upgraded magnetite are presented in Table13.4. The total iron and ferrous iron assays are 71.0% and 27.9%, respectively, which compareclosely to the levels for pure magnetite of 72.4% and 24.1%, respectively. As indicated, themagnetite has a higher ferrous iron content than the pure magnetite which is based on itschemical formula. The difference cannot be explained by the presence of ferrous sulphide142Figure 13.4a Scanning electron micrograph of magnetite particles.14326—pr—1991 lU: 11:’L?FILTER Przt L1iYert = 2c1OL cc’jr t - I E- :...Hs.-. ,. ./,.•4—. Pij== 10.E30 kV 10. !1- -Inte.r.1 0 = 11-L0Figure 13.4b Energy dispersive x-ray analyzer spectrum for magnetite particles showing an ironpeak and a distinct silica peak.144Table 13.4 Elemental analyses of upgraded magnetite sample.Element Assay (%)Fe Total 71Fe Ferrous 27.9Si02 4.1Ca 0.34Al 0.76Mg 0.16Mn 0.01Ti 0.02Cr 0.15Cu 0.02S Total <0.01145minerals since the total sulphur content did not exceed 0.0 1%.Many metal ions can replace iron ions in the magnetite lattice and have an adverse effecton the magnetic properties. Specifically, titanium can replace iron ions; this results in highremnant magnetism levels. The titanium assay was only 0.02%, and therefore, the magnetitecould not be considered to be of the titaniferous form. The main impurity in the sample wassilica which assayed 4.9%. Microscopic examination of the sample revealed that some silicateminerals were locked within coarse (+38 jim) particles. In addition, it was found that some ofthe silicate minerals were finely disseminated in the magnetite (see Section 13.3.2.3).13.2.2.6 Magnetic PropertiesThe magnetic properties of the upgraded -45 jim magnetite were determined by using avibrating magnetometer to produce an intensity of magnetization, M, versus induced magneticfield, H, hysteresis curve. From the hysteresis curve, the magnetic susceptibility at field strengthsof 30 oersteds and 800 oersteds, the saturation moment and the coercive force were determined.The magnetic properties along with recommended levels (Osborne, 1986) are presented in Table13.5.Comparison of the results to the recommended levels indicates that the magnetite samplemeets the recommended susceptibility and saturation moment levels; the coercive force was,however, high. The saturation moment and susceptibility values provide an indication of themagnitude of the force experienced by a particle in a magnetic field which in turn relates to itsrecoverability by magnetic separation. Since magnetic separation is used to recover and upgrade146Table 13.5 Magnetic properties of the -400 mesh upgraded magnetite sample.Magnetic Property Determined RecommendedInitial Susceptibility - k30 (emulg) 0.055 >0.050Susceptibility - k8 (emu/g) 0.078 >0.053Saturation Moment- Msat (emu/g) 80.0 >80.0Coercive Force- H (Oersteds) 86.5 <50.0147magnetite for re-use in a dense medium recovery circuit, it is desirable for these magneticproperties to be as high as possible.The coercive force is a measure of the magnitude of the remnant magnetic attractionforces in a particle. If the coercive force is high, particles will attract to each other to formaggregates. The presence of such aggregates can have a deleterious effect on separationefficiency. Therefore, the coercive force should be as low as possible. The high coercive forceindicates that the magnetite sample is susceptible to magnetic aggregation and should bedemagnetized when used for dense media separation.Figures 13.6 a) and b) are scanning electron micrographs of magnetized particles. Themagnetized particles have a branched chain-like structure with small particles clinging to thesurface of the large particles. From Figure 13.4 a) it can be seen that demagnetized particles donot aggregate to form chains. Due to the nature of the branched chain structure, magnetizedparticles would likely form voluminous aggregates and at a sufficiently high solids content wouldform a network structure.13.3.3 Preparation of Size FractionsTo determine the effect of particle size on the properties of magnetite dense media,various size ranges of magnetite particles were prepared. Specifically, magnetite samples withsize ranges finer than 45 .im, 30 jim and 15 jim were prepared. To prepare the -45 jim sample,upgraded magnetite was wet screened with a 270 mesh (45 jim) sieve. The -30 jim and -15 jimsamples were prepared by using a Haultain Infrasizer.148Figure13.6Scanningelecuonmicrographsofa)magnetized(-75)Jm+38im)magnetiteparticlesandb)magnetized-75pmmagnetiteparticles.The Haultain Infrasizer has a series of six air classifying cyclones that are designed toseparate particles in the sub-sieve size ranges. The dimensions of the cyclones are designed toproduce a root two size classification series. The finest particles were trapped in a filter at theend of the series of cyclones. The size separation was controlled by manipulating the air flowrate which was set at 20 dm3 min1.To produce a sharp size separation in the Infrasizer, the particles must be dry anddispersed. To ensure that the standard grade magnetite samples were dry, they were placed ina drying oven for several hours. Since remnant magnetism could cause the particles to aggregate,the dried samples were passed through a demagnetizing coil immediately prior to classification.Samples were then fed to the Infrasizer, 0.5 kg at a time, which was run for twenty four hoursbefore removing the cone products and another 0.5 kg sample was reloaded. During theclassification, the cones were rapped periodically to remove particles that could have adhered tothe walls of the cyclone which would have prevented them from being classified. The -30 pmfraction was produced by combining the products from the second cyclone through to the filter.In a similar manner, -15 pm size fraction was produced by combining the products from thefourth cyclone through to the filter.13.3.4 Characterization of Size RangesThe -45 pm, -30 pm and -15 pm size ranges were characterized with respect to particlesize, density and chemical composition. The results of these analyses are summarized below.15013.3.4.1 Size Analysis of Size FractionsThe size distributions of the three size fractions were determined using the Horiba PSA.The size analyses results are presented in Table 13.6 and are plotted on RRB graph paper asshown in Figure 13.7. The RRB size and distribution moduli, presented in Table 13.6, indicatethat the samples differ in size but have almost the same distribution. The samples meet therequired size specifications of being finer than 45 j.im, 30 jim and 15 jim respectively.13.3.4.2 Density of Size FractionsThe densities of the size fractions were determined with the air pycnometer. The resultsare presented in Table 13.7 and reveal that density decreases with decreasing particle size. Thistrend can be explained by the density classification that also occurs in the air classifyingcyclones. Normally, any non-magnetite low density particles report together with smaller highdensity particles. The reported density values were the average of three determinations. Alldensities were greater than 4900 kg m3 which were greater than the density of the upgradedsample (4860 kg m3). It seems that the samples were upgraded by removing coarse low densityparticles such as non-liberated particles containing both magnetite and silicate minerals.13.3.4.3 Elemental Composition of the Size FractionsThe elemental compositions of the three size fractions are presented in Table 13.8. It is151Table 13.6 Size analyses of -45 pm, -30 pm and -15 pm size fractions determined using theHoriba Particle Size Analyzer.Size (pm) % Passing(-45 pm) (-30 pm) (-15 pm)38323026201817161412111086542100.095.776.759.351.141.532.421.710.51.7100.099.197.995.183.276.869.162.054.346.337.627.216.34.899.197.896.090.682.376.669.955.840.931.922.96.8d632 19.9 13.6 8.8m 1.79 1.54 1.7815211 I-. (D o z.,-CI)cM C cM Cf CD C,,CDCumulativePassing,F(d),(%)—a’a’ou’0 ‘-4a’ U,U,U,S%C’tJU,000000cma‘asao’a00saa’aU’‘00‘1 a U,N a 0 S0 U,0 K)0 U,0 0- 0 U,0 0 0 0 0 0 0 0 0--““‘.--I..__-,I—---------zzz:=zizi:z:::::—------—----———-—--———-----—--iriirmiit-tt:Ba-•0 U,U’•U,0 N)U’N) 0 U’II1J1II[II1——-11+44+—--—\\\\‘\‘c‘c—\\\00po0P.-,‘0’-,‘00Table 13.7 Densities of the -45 pm, -30 pm and -15 pm size fractions determined using airpycnometer.Sample Density (kg m3)Measured Mean [ ± 95% C.I.Magnetite -45 pm 497049704950 4963 29Magnetite -30 pm 493049604940 4943 38Magnetite -15 pm 493048604910 4900 90154evident that there is little variance in the elemental compositions of the different size ranges. Theferrous iron assays ranging from 28.5% to 29.1% were higher than the levels indicated by thestoichiometric composition of magnetite. The low sulphur assay cannot account for the highferrous iron assay which could be attributed to the presence of iron suiphide minerals. The mainimpurity in the samples is silica (Si02) which ranges from 2.3% to 2.4%.13.3.5 Preparation of Narrow Size FractionsIn order to study the effect of particle size distribution on the properties of magnetitedense media, it was necessary to prepare samples of narrow size fractions which could beblended to create specific size distributions. The narrow size fractions were prepared using theHaultain Infrasizer (see Section 13.3.3). The Infrasizer was operated using an air flow rate of20 dm3 min’. For each run, approximately 0.5 kg of sample was fed to the Infrasizer which wasallowed to run for 24 hours before removing the products and feeding another sample. The coneswere rapped periodically to detach particles that were stuck to the walls. A coarse fraction wasprepared by screening at 270 mesh (53 jim) and 400 mesh (38 pm) using Tyler sieves.13.3.6 Characterization of Narrow Size FractionsThe coarse fraction and Haultain Infrasizer cone products that were required forexperiments were characterized with respect to density, magnetics content and elementalcomposition.155Table 13.8 Elemental analyses of the -45 pm, -30 pm and -15 pm size fractions.Element Sample(-45 pm) (-30 pm) (-15 pm)Fe Total 70.0 71.0 70.0Fe Ferrous 29.1 29.1 28.1Si02 2.40 2.30 2.35Al 0.02 0.025 0.025Mg 0.07 0.09 0.10Mn 0.015 0.02 0.015Ti 0.0 0.0 0.0S Total <0.05 <0.05 <0.0515613.3.6.1 Size Analyses of the Narrow Size FractionsThe Elzone Particle Size Analyzer was used to perform the particle size analyses on theproducts. The results are presented in Table 13.9 and are plotted in Figure 13.8. The plot showsthat the size fractions have narrow distributions. The geometric mean size and RRB size anddisthbution moduli for each of the products are also presented in Table 13.9.13.3.6.2 Densities of Narrow Size FractionsThe density of each cone product was determined using an air pycnometer (see Section13.2.1). The average of two determinations are presented in Table 13.10. The table shows thatthe density of the products from cone #3 through to the filter are higher than the sample fromwhich they were separated (upgraded magnetite density was 4857 kg m3). This upgradingindicates that low density non-liberated particles must be in the coarser fractions. It is likely thatthe silica assays reported for the magnetite primarily result from the presence of these coarsemiddling particles. The coarse fraction density was very close to the upgraded magnetite density.13.3.6.3 Elemental Composition of Size FractionsThe elemental compositions of each of the size fractions are presented in Table 13.11.The results indicated little variation in the chemical compositions of the size fractions.157Table 13.9 Size analyses of narrow size fractions determined using Elzone PSA and RRB sizeand distribution moduli.Passing Size % Passing(pm) Coarse Cone #3 Cone #4__[__Cone#5 Cone #6__[ Filter99.781.054.624.810.05.31.60.07045403533313029272523211917151311975432193.186.375.861.242.725.412.96.03.32.01.20.40.0100.099.798.897.294.389.483.174.964.450.833.719.010.14.41.699.499.299.098.697.796.093.389.281.966.745.628.314.44.50.299.397.193.888.677.843.823.18.21.70.099.898.595.285.171.446.615.30.3Mean (pm) 38.1 25.4 14.7 8.5 5.1 3.3d632 (pm) 41.7 27.6 17.2 10.8 6.25 3.76m 6.59 6.64 3.16 2.48 2.68 2.45158xC 1-IPdN 0.Cl).“--N.—CD 1 CM 0 CD CD ICumulativePassing,F(d),(%) U,-a a N H.C) (a (I, H. N a-C a5--C U,U,•U,0 N)NJ 0 U,0 0 CU,N)\\\\\\\\\\\\\CCC00-:..J:eU,0Table 13.10 Densities of narrow size fractions determined using air pycnometer.Sample Density (kg m3)Measured Mean ± 95% C.I.Coarse Fraction 48704850 4860 127Cone #3 49404970 4955 191Cone #4 50205020 5020 0Cone #5 50405070 5055 191Cone #6 50505030 5040 127Filter 49904950 4970 254160Table 13.11 Elemental analyses of the narrow size fractions.{Element Sample(%) Coarse Cone #3 Cone #4 Cone #5 Cone #6 FilterFe Total 69.0 70.0 68.0 71.0 74.0 68.0Fe Ferrous 28.3 29.4 29.5 29.2 28.3 27.2Si02 4.4 3.6 2.6 2.2 2.25 2.8Al 0.36 0.3 0.26 0.26 0.32 0.4Mg 0.14 0.12 0.1 0.1 0.11 0.14Mn 0.015 0.012 0.01 0.015 0.015 0.015Ti 0.015 0.015 0.0 0.0 0.0 0.0S Total <0.05 <0.05 <0.05 <0.05 j <0.05 <0.0516113.4 Chemical Reagents and Medium ContaminantsAs part of the test program, the effects of various parameters on the properties ofmagnetite dense media were investigated. Specifically, the effects of pH, dispersing agents andvarious media contaminants were studied. The following describes the suspension additives usedin the test work.13.4.1 pH ModifiersThe dense medium pH levels were controlled by adding either hydrochloric acid orsodium hydroxide.13.4.2 Organic DispersantsOrganic dispersing agents, including Dextran and Carboxyl Methyl Cellulose (C.M.C),were used in the test work. The Dextran used was the Polysciences Incorporated brand (CatalogNumber 1341, Lot Number 84710). The molecular weight of the Dextran ranged from 15,000to 20,000. The Dextran solutions were prepared by adding distilled water to produce a 10 g/lsolution. To dissolve the Dextran, the solution was lightly agitated. Fresh solutions wereprepared on a daily basis as required.The C.M.C. used was from Polysciences Incorporated (Catalog Number 6140, Lot NumberS-137-7). The molecular weight of the C.M.C. was 80,000. The 10 g/l aqueous solutions were162prepared by adding the C.M.C. to distilled water with slow agitation. Fresh samples wereprepared on a daily basis as required.13.4.3 Inorganic DispersantsThe inorganic dispersing agents used in experiments included BDH brands of sodiumsilicate and sodium hexametaphosphate. These dispersants were used to prepare 1 g/l aqueoussolutions.13.4.4 Medium ContaminantsWhen run-of-mine coal is fed to a dense medium separator, inefficient desliming allowsfine coal and clays to enter the medium. In addition, since these types of particles are small,they are difficult to separate from the medium during the dense media recovery process. Thepresence of these particles can affect the properties of the medium. For these reasons the effectsof such contaminants on the medium properties were also investigated.Coal mined from the foothills of the Rocky Mountains in British Columbia and Albertais very soft and, through normal handling, a large amount of fine particles are generated. Thecoal fines used in the test work were from the Bullmoose property in north east British Columbia.The coal was screened at 325 mesh to produce the fine fraction used in the experiments. Theash content of the -325 mesh fraction was determined to be 18.3%. To determine levels ofcontaminants in dense media, magnetite was also obtained from Luscar Sterco and Cardinal River163Coal in Alberta.The most common clay minerals include kaolinite and bentonite. The Pioneer WashedKaolin manufactured by the Georgia Kaolin Company was used in the tests. This sample ischaracterized by the following specifications: Si02=45.68%, A1203=38.5 1%, Fe203=O.44%,Ti02=1.43%, CaO=O.24%, MgO=O.14%, L.O.I.(l000°C)=31.51 with average particle size=1.l urn.The bentonite sample used in the experiments was a sodium based montmorillonite from WesternBentonite. The specifications for the sample are 85% montmorillonite with a chemicalcompositions of: Si02=55.44%, Al203=20.14%, Fe203=3.67%, CaO=O.49%, MgO=2.49% andNa20=2.76%.164CHAPTER 14: SE’lTLING PROPERTIES OF MAGNETITE DENSE MEDIA14.1 IntroductionIn order to characterize the stability of magnetite suspensions, the mudline falling rate andthe solids concentration profile as a function of time were determined for a magnetite suspensionwith 15% solids by volume (this corresponds to a medium density of 1579 kg m3).14.2 Mudline Falling RateAs described in Section 10.3, the settling of suspensions can be characterized by thefalling rate of the supematant-slurry interface (mudline). A high falling rate corresponds to a lowmedium stability and conversely, a low settling rate corresponds to a high medium stability. Theinterface settling rate therefore provides a relative indicator of the stability.14.2.1 Procedure for Mudline Falling Rate DeterminationsSuspensions of dense media were prepared by mixing the upgraded magnetite withdistilled water to a volume solids content of 15%. This solids content is typical for dense mediaused in coal preparation and it corresponded to a medium density of 1579 kg m3. Thesuspensions were prepared in 250 ml graduated cylinders. To ensure that the suspensions werethoroughly dispersed, the graduated cylinders were inverted several times and placed in an165ultrasonic mixing bath. To eliminate remnant magnetism that could cause particle aggregationand thereby affect settling, the suspensions were passed through a demagnetizing coil three times.The settling measurements involved determining the height of the position of thesupernatant-slurry interface with time. The height was plotted against time and the initial slopeof the line reported as the falling (settling) rate. Three sets of measurements were performed toevaluate the reproducibility of the results.14.2.2 Results of Interface Settling TestsFigure 14.1 is a photograph of a settling suspension of magnetite with 15% solids byvolume. The suspension settled with a clear supematant and a sharp mudline. The sharpinterface indicates that the suspension settles as a bulk and that little differential settling occurred(hindered settling).Figure 14.2 is a plot of the interface height versus time for the three sets of data. Thefigure shows all three sets of data produced the same settling curve indicating goodreproducibility of results. The slope of the initial linear portion of the curve is taken todetermine the settling rate of the suspension. The curve shows that the suspension settled withan almost constant rate for approximately eight minutes. After this time the settling ratedecreased until the settling curve became horizontal as a result of the formation of a sediment.After 24 hours, the sediment height had decreased slightly as the result of subsidence. Accordingto Cheng (1980a), this type of settling curve indicates that the particles in the suspension areaggregated. This aggregation can be explained by secondary minimum coagulation or by166Figure 14.1 Settling suspension of magnetite particles with a solids volume fraction of 15%.The photograph shows that the magnetite settles with a sharp supematant/suspension interface.16720181614EC)‘ 120)z 100)C)642030Figure 14.2 Magnetite suspension mudline interface height versus settling time showing threesets of data (solids volume fraction = 0.15, pH = 8.24, temperature = 25°C).0 5 10 15 20 25Time (mm.)168magnetic aggregation resulting from remnant magnetic forces. Although the magnetite wasdemagnetized, small particles can still exhibit remnant magnetism since they contain only a fewmagnetic domains which if randomized may not completely cancel the polarity of the particle.Based on the average of the three tests, the initial falling rate was determined to be 1.42cm min1. According to Osborne (1988), typical settling rates for dense media that behaves wellin a plant are between 2.0 cm min’ and 6.5 cm min’. The settling rates for these samples,therefore, represent a medium with a higher than average stability.14.3 Solids Concentration ProfileThe suspension settling rate is only an indicator of stability and does not fully describethe settling properties of magnetite dense media. For a more complete description of the settlingproperties, the solids concentration profile as a function of time was studied.14.3.1 Procedure for Solids Concentration Profile DeterminationsThe solids concentration profile was determined by sampling a magnetite suspension froma graduated cylinder at several depths after allowing the suspension to settle for a pre-determinedperiod of time. The solids contents of the samples were then determined and the solidsconcentration profiles were constructed.The suspension used for the concentration profile determinations was a mixture ofupgraded magnetite (see Section 13.3.1) and distilled water. Several suspensions were prepared169in 100 ml graduated cylinders to produce medium with a density of 1579 kg m3 correspondingto a volume solids content of 15%. Prior to sampling, the suspension was demagnetized and thegraduated cylinder was inverted several times to disperse the particles. A pipette was used toobtain the samples from different depths in the graduated cylinder. After mixing the suspension,the cylinder was placed upright and the pipette submerged to a predetermined depth. Thesuspension was then allowed to settle for a designated time period prior to drawing a sample.The pipette containing the sample was then weighed before being emptied into a dish in whichit was dried. The solids content was then determined from the weight of the dried magnetite andthe weight of the wet sample. The weight fraction was converted to a volume fraction based onthe magnetite density of 4857 kg m3 The sampling heights ranged from 100 ml at the top ofthe graduated cylinder to 0 ml at the bottom of the cylinder. Samples were taken at heightscorresponding to 10 ml intervals along the cylinder. The settling times at which the sampleswere taken ranged from 0 to 10 minutes. For each settling time, a fresh suspension was preparedand the entire set of experiments were repeated to ensure reproducibility of results.14.3.2 Solids Concentration Profile ResultsSolids concentration profiles for each settling time were plotted (Figure 14.3). The figureshows that magnetite dense media exhibit zone settling properties. As the suspension settled, asupernatant was formed at the top of the column. Below the supernatant, a small transition zonedeveloped which had a lower solids content than the initial suspension. Below the transitionzone, a constant density zone existed with approximately the same solids content as the initial170suspension. At the bottom, the solids built up to form a sediment with a high solids content.Figure 14.4 is a contour plot showing the suspension solids concentration as a functionof column height and settling time. The contour lines represent the borders between the zonesand the slopes of the lines represent the interface falling rates. With time, the extent of thesupernatant increased until after approximately 8 minutes it met the sediment. During this time,the constant density zone diminished in size from the entire column height to zero. Thetransition zone was quite small although its extent increased slightly with time. The smalltransition zone indicated that very little differential settling occurred; ie. most large and smallparticles settled at the same rate. This result supports Napier-Munn’ s (1984) conclusion thatmedia segregation is controlled by bulk hindered settling rather than by classification in cyclones.However, at low solids concentrations Davis (1987) has shown that size classification does occur.The magnitude of the accelerating force likely influences the type of settling that occurs.The supernatant-transition zone interface falling rate was determined to be 1.22 cm min1and the transition zone-constant density zone settling rate was 1.36 cm min’. These rates aresimilar to the rate determined from the settling test performed in Section 14.2.2 of 1.42 cm min’.The constant density zone-sediment interface falling rate was determined to be -0.97 cm min’;the negative sign indicates that the sediment height increased with time.If it can be assumed that the extent of the constant density in a dense medium separatorrepresents the medium stability, then the transition zone-constant density zone interface settlingrate provides is a good indicator of this stability. Since the extent of the transition zone is smalland the falling rates of these two interfaces are similar, the supematant-transition zone interface(mudline) falling rate can be considered a good indication of media stability.171CC)U0C’,o 0.15C0.350.30.250.20.1• 0 minutes—D---—— 0.5 minutes1.0 minutes—0-—-— 2 minutes—A-—-— 3 minutes—&--—— 4 minutes—•—-— 5 minutes—°-——— 10 minutes0 5 10 15 200.050Column Height (cm)Figure 14.3 Volume solids fraction versus height in column of settling magnetite particles forsettling times of zero minutes to ten minutes (solids volume fraction = 0.15, pH= 8.52, temperature 25°C).172Figure14.4Magnetitevolumesolidscontentasafunctionof heightandsettlingtimeshowingsettlingzones(solidsvolumefraction-0.15,pH=8.52,temp.=25°C).SOLIDSCONCENTRATIONPROFILEDATAFOR15SQLIDSMAGNETITITESUSPENSION00000000 0SUPERNATANT—TRANSITIONZONEINTERFACE020.019.018.017.016.015.014.012.011.0—10.09.0—8.0UJ7.06.05.04.03.02.01.00.019.017,115.213.311.49.57.65.73.81.90.015 15 14 15 14 17 161515116151415151415151615161515161415151415151416171513 13 18 1515 15 14 16 15 170ITIONZONE—CONSTANTDENSITYZONEINTERFACE0 014 14 1530 29 30IONZONE—CONSTANTDENSITYZONEINTERFACE3226 29292929343401234567TIME(mm)8910As discussed in Section 10.2, particle interactions are responsible for bulk zone settlingproperties of suspensions. The shape of the settling curve indicates that the particles may bepartially aggregated. This aggregation can explain the zone settling properties exhibited by thesuspension. In particular, aggregates of similar size would settle at the same rate. Therefore asmall transition zone would be expected with the bulk of the suspension settling together in aconstant density zone.14.4 ConclusionsIt was found that a typical magnetite dense media suspension exhibits zone settlingproperties that are characterized by bulk settling rather than by differential settling. Thesuspension settling was characterized by the presence of four zones: a supematant, a transitionzone, a constant density zone and a sediment. The constant density zone had a solids contentthat was approximately equal to that of the initial suspension. The mudline falling rate wasdetermined to be 1.42 cm miii’ which compared closely to the falling rate of the transition zone-constant density zone interface of 1.36 cm min1. Since these rates are similar and since theextent of the constant density zone should be directly related to dense media stability, themudline settling rate should provide a good indication of the stability.The settling characteristics of the suspension were explained by particle aggregation.Evidence of aggregation was based on the shape of the mudline settling curve and on the bulksettling properties determined from the solids concentration profile tests.174CHAPTER 15: RHEOMETER FIXTURE FOR SE’lTLING SUSPENSIONS15.1 IntroductionThe device constructed to measure the rheological properties of unstable mineralsuspensions, consists of a specially designed cup and bob fixture that attaches to a concentriccylinder viscometer. This fixture was designed for suspensions that exhibit zone settlingproperties such as magnetite dense media (see Chapter 14) as well as many other mineralsuspensions (see Section 10.2). In a column of suspension, settling particles form distinct zonesincluding (from top to bottom) a supernatant, a transition zone, a constant density zone and aconsolidation zone. With time, the extent of each of these zones changes until only a supematantand a consolidation zone remain. The results presented in Chapter 14 indicated that magnetitesuspensions exhibit this type of settling and that in a sufficiently long column, an extensiveconstant density zone would exist for a certain period of time. The measuring device wastherefore designed so that the bob would be positioned within the constant density zone duringrheological measurements.The fixture was attached to a Haake viscometer (Searle type) in which the bob rotates andthe shear stress is determined from the torque applied to the bob from the suspension. Theviscometer used was a Haake RV2O with an M5 measuring head for low viscosity systems. Theviscometer was interfaced to a PC which controlled the measurement and record the data. Aphotograph of the rheological laboratory equipment is presented in Figure 15.1.175Figure 15.1 Rheologic laboratory facility showing a) the Haake RV2O controller, b) the M5viscometer, c) the PC and d) the temperature controller.L17615.2 Details of the Fixture DesignA schematic diagram of the fixture is shown in Figure 15.2. It consists of an elongatedcup and inner cylinder with a bob attached to an elongated shaft. It is arranged so that the bobis positioned in the constant density zone of the settling suspension. The extent of the constantdensity zone is proportional to the height of the settling column and it decreases at a rate that isproportional to the mudline settling rate. Therefore, to ensure a sufficient height of constantdensity zone, a rapidly settling suspension would require a tall settling column. These factorswere taken into consideration when determining the height of the cup and the position of the bob.Since the correct cup height and bob position is specific to the settling properties of thetested suspension, it was necessary to develop a concentration profile as a function of time forthe system. The height of the column, H, was determined from the transition zone - constantdensity zone interface falling velocity, v, the constant density zone - sediment rising rate, v,the height of the bob, hb, and measurement time, t. The column height was calculated from thefollowing relationship (Equation 15.1).H = v t + v t + h (15.1)cs bOnce the column height was established, the position of the bob was set so that it wasmaintained completely within the constant density zone during the time of measurement. Theheight from the bottom of the cup to the top of the bob, Hb, was calculated from Equation 15.2.1775ELONGATED SHAFTEIIiiISUPERNATANT‘‘ , . .. V.......‘.‘.•‘•••‘•‘•‘ IRANSII1ON ZONEELONGATED CUP hq i% I% Iqqqqqqivqqqqqqqqqq qqqqqqqqqOPENINGS CONSTANT DENSWY ZONEq qq iq qINNER GAP‘ qqIJTER GAPqq %‘‘‘ ,INNER CYLINDER :::; •:•:q qII i Ii 11 Ii 1II I1IaII1l1iI1uI11131 IIII 11aI11i1i1Il1I11Il4II 1lIIl1I11IliJiJl1J. Ii11 jajaj1jjjJJiJ1IiIIl 1I— —Figure 15.2 Rheometer fixture for settling suspensions showing the bob positioned in theconstant density zone of a settling suspension.178Hb H—vQt (15.2)There are several fixture geometries for concentric cylinder rheometers. Most have asingle gap between the cup and the bob. With a single gap cup and bob arrangement,however,settling particles can build up on top of the submerged bob and result in the formationof a cone of particles. The particles would eventually slide into the annular gap and thereby alterthe solids concentration in the measuring region. For this reason a double gap arrangement,modified to prevent the accumulation of solids, was used. The modification consisted of an opentop on the bob with a hollow inner cylinder which allowed particles to settle through the top ofthe fixture. In order to define the shear stress at the inner side of the bob it was necessary to addthe inner cylinder and thereby create the double gap arrangement. An advantage of the doublegap arrangement was that it provides a greater fixture surface area than a single gap arrangementresulting in more accurate measurements.The inner hollow cylinder was coaxially positioned within the cup and its height extendedto just below the top of the bob. The radii were fixed so that the gaps between the bob and theouter cylinder and the bob and the inner cylinder provided an equal shear rate on the surfacesof the bob. In order to achieve equal shear rates, the radii had to satisfy the conditions given byEquation 15.3 (Moore and Davies, 1956).r r_1._.(15.3)r2 r4179where, r1 is the radius to the outside of the inner cylinder,r2 is the radius to the inside of the bob,r3 is the radius to the outside of the bob, andr4 is the radius to the inside of the cup (see Figure 15.3).The gap sizes between the concentric cylinders were set to be as small as possible toreduce the potential for non-Newtonian shear rate effects (see Section 6.2.2.2). Conversely, thegap size must be at least ten times the size of the diameter of the largest particle to prevent theparticle from physically jamming (Sherman, 1970). If large particles bridge the gap and causethe rotating bob to jam, erratic shear stress values are obtained.Other design features take end effects, wall slip effects and temperature effects intoconsideration. End effects were considered to be small because of the small surface area at thebottom of the double gap bob (Moore and Davies, 1956). The shaft and spoke arrangementsupporting the bob, however, are immersed in the suspension and when rotating contribute to themeasured torque.Wall slip was minimized by using roughened cup and bob surfaces. The surfaces wereroughened by cutting vertical grooves into them; the depths of these grooves were set to be atleast as large as the largest particle in the suspension (Nguyen, 1983, Cheng, 1978 and Cheng1984).Rheological properties are very temperature sensitive. For this reason the entire cup andbob arrangement was surrounded by a temperature controlled water jacket.180,,1.,,a.a,I IIJiII,I,,,•h1, •IJ3I•IIIIJSJII 111.1.. ii‘‘•“ .:“ r4 ‘:. “:: :,(7 t’Y /:f //)2\..:‘::‘..‘:: :::a:ii a...:Figure 15.3 Plan view of a double concentric cylinder viscometer fixture.18115.3 Fixture DimensionsThe height of the elongated cup was determined based on the requirement to maintain thebob within the constant density zone for a measurement time period of six minutes. Thismeasurement period was considered to be an adequate time to produce rheological flow curvedata; Haake recommended a measurement time of at least two minutes for their viscometer. Theinterface velocities, determined by measuring the solids concentration profile in a column ofsuspension after various settling times (see Chapter 14), were needed to design the dimensionsof the fixture (Equations 15.1 and 15.2).The falling rate of the transition zone-constant density zone interface, v, and rising rateof the constant density zone-sludge interface, were determined to be 1.36 cm min’ and 0.97cm min’ respectively for a typical magnetite suspension with 15% solids by volume. For a bobheight of 6 cm and a measurement time period of six minutes, the height of the suspendingcolumn was determined to be 20.0 cm. To allow for variations in settling rates of differentsuspensions, a settling column 23 cm in height was selected. Equation 15.2 was then used toestablish the position of the bob to ensure that it was placed in the constant density zone for theduration of the measurement. The height from the bottom of the cup to the top of the bob wascalculated to be 11.8 cm.The gap size was set to be only slightly larger than ten times the largest particle diameterin order to avoid particle bridging and reduce potential non-Newtonian shear rate effects. Sincethe size of magnetite particles used is generally much finer than 100 pm, the gap sizes were setat 1000 pm and 1100 pm for the inner and outer gaps, respectively.182The radii of the surfaces in the double gap geometry were selected to meet therequirements of Equation 15.3. The radii selected were 2.11 cm for the inside radius of the cup,r4, 2.00 cm for the outside radius of the bob, r3, 1.95 cm for the inside radius of the bob, r2, and1.85 cm for the outside radius of the inner cylinder, r1 (Figure 15.3).To minimize the effects of wall slip, vertical grooves were cut into each of the shearingsurfaces. The grooves were cut into the surface with a knurling tool and the depths weremeasured to be 250 im which is approximately 2.5 times the size of the largest magnetiteparticles (100 }lm).Using the above dimensions, a prototype of the device was machined from brass.Photographs of each of the components of the fixture are presented in Figure 15.4. A samplesize of 350 ml was needed for each rheological measurement.15.4 Calibration of the FixtureThe Haake viscometer applies a rotational speed (o) to the bob which is also attached toa strain gauge that measures a strain that is proportional to the torque (T) caused by thesuspension. As indicated by Equations 15.4 and 15.5, to determine the shear rate and shear stressthe rotational speed and torque values are multiplied by fixture constants.= Mo (15.4)t = AT (15.5)183b.C-.00/Figure15.4Rheometerfixtureformeasuringrheologicalpropertiesofsettlingsuspensionsshowinga)thebob,b)theinnercylinder,andc)thecup.where, M can be determined from equation 15.6.r rM—_( + ) (15.6)2 2 2 2‘-‘ (r2 — r1) (r4 — r3)The value of A was determined from measurements with standard viscosity oils(Brookfield Standard Viscosity Oils were used for calibrating the device). The procedureinvolved setting the value of A to 1.00 and measuring the viscosity of oils with known viscositiesof 9.5 mPa.s and 50 mPa.s. Based on the measured viscosity, the value of A was adjusted sothat the measured viscosity equalled the actual viscosity. The procedure was repeated until thedetermined level of A produced the correct viscosity results. The values of M and A for thefixture were determined to be 10.348 and 1.435 respectively. Figure 15.5 shows three sets offlow curves for each of the 9.5 mPa.s and 50 mPa.s oils. The data were fitted with a straight line,the slope of which is the fluid viscosity. The measured viscosities were 9.53 mPa.s and 49.45mPa. s, respectively, which are sufficiently close to the actual values. The three sets of data foreach oil agree very well indicating good reproducibility of the results.15.5 Fixture EvaluationOnce the fixture was built and calibrated, the next step was to evaluate it with respect tomeasurement errors. Since the shaft and spokes that support the bob rotate in the suspension,a torque is applied to these components adding to the torque of the bob. Therefore, thecontribution of the shaft and spokes to the measured stress had to be determined. In addition,185U.B.C.Figure 15.5 Flow curves produced with the developed rheometer fixture, for 9.5 mPa.s and 50mPa.s standard viscosity oils. Three sets of data were plotted for each oil.OloeratorlSubsta,ce:BROOKFIELD OILTest No.:49.8 cP (2)Test, of:30.Jun 1989System1’15/ESSPTeynierat,ure:25.0°CA816.ROTAR17.ROT8818.ROTA813.ROTARI4.ROTAR15.ROTI4PKE Rot 2.3186the shearing created by the rotating bob can affect particle settling. It was therefore necessaryto check whether the bob remained positioned in a constant density zone during shearing.As stated, the measurement errors associated with the end effects were considered to benegligible due to the small surface area of the bottom part of the bob (Moore and Davies, 1956,Sherman, 1965, Whorlow, 1980). The potential for wall slip was reduced by cutting grooves intothe shearing surfaces of the fixture (see Section 15.3).15.5.1 Effect of Shaft and Spokes on Measured StressesIn order to quantify the error resulting from the additional torque produced by the shaftand spokes, each component was built and tested separately (Figure 15.6). Flow curves werethen produced for a 49.8 mPa.s standard viscosity oil using:(a) the entire fixture,(b) the shaft, spokes and narrow cylinder,(c) the shaft and spokes, and(d) the shaft.As can be seen from the flow curves in Figure 15.7, the contribution of each of thecomponents to the measured stresses is small compared to the stress from the entire bob. Thecontribution of component (c), the shaft and spokes, best represents the magnitude of themeasurement errors which were less than 5% of the measured stress. This effect could either besubtracted from the measured stress or it could be ignored since it is small and would not greatlyaffect the experimental results.18700000b..11Figure15.6aPhotographsoftherheometercomponents:a)entirefixture,andb)shaft,spokesandcylindricalring.ci.100Figure15.6bPhotographsoftherheometercomponents:c)shaftandspokes,andd)shaft.U.B.C.Operator:Substance:BROOKFIELD OILTest Ho.:498 oP (2)Test, of:iø.Jan 1989System:t15/ESS3Temperature:25.0°CI4AAKE Rot 2.3V1.ROTV17ROTV20.ROTV35.ROTFigure 15.7 Flow curves produced for 10 mPa.s standard viscosity oil using a) the entire bob,b) the shaft, spokes and cylindrical ring, c) the shaft and spokes, and d) the shaft.flI/s]19015.5.2 Particle Settling in the Elongated FixtureSince the settling of particles in the elongated fixture occurs in a sheared environmentduring measurements, the settling properties may be different from those in an un-shearedcolumn. To confirm that zone settling takes place in the elongated fixture and that measurementswere made within the constant density zone, the solids concentration profile in the elongatedfixture under sheared and un-sheared conditions was determined. Samples were taken at variouspositions in both of the annular gaps to determine if any variation in suspension compositionoccurred as a result of shearing. A duplicate fixture was machined with sampling points fromwhich samples could be drawn using syringes so that the solids content of the suspension couldbe determined throughout the fixture. Figure 15.8 is a schematic diagram showing the samplingpoints and Figure 15.9 is a photograph of the fixture. This fixture had the same geometricdimensions as the device constructed for rheological measurements.The solids concentration profile as a function of time was determined under un-shearedand sheared conditions. Samples were drawn from each position at specific times for subsequentsolids content determinations. Between sampling periods, the suspension was inverted severaltimes until the suspension was thoroughly mixed. Samples were then taken from top to bottomso that the compositions of successive samples were not greatly affected by changes in thesuspension composition due to the removal of the previous samples.The solids content for each sample position was used to construct the solids concentrationprofiles versus time for the suspension. The suspension was prepared by mixing upgradedmagnetite and distilled water to a solids content of 15% by volume.191CENTREABOVE BOBCENTREFigure 15.8 Rheometer fixture for settling suspensions showing sampling points for solidscontent determinations during rheological measurements.OUTER GAPCENTREBELOW BOBINNER GAP192Figure 15.9 Constructed rheometer fixture for solids content determinations during rheologicalmeasurements.I a II193Figures 15. lOa, b, c and d and 15.11 a, b, c and d show the solids concentration profilesin the elongated fixture under un-sheared and sheared conditions, respectively. The suspensionwas sheared at a rate of 500 s’ which represents an extreme high shear rate. The graphs showthat zone settling conditions exist in the elongated fixture for both sheared and un-shearedconditions. Comparison of Figures 15. lOa, b, c and d and 15.11 a, b, c and d reveal that shearinghad little effect on particle settling since solid concentration profiles are similar at any given timefor the two systems.The settling results showed that the bob was completely within the constant density zonefor at least five minutes. At six minutes the top of the bob penetrated the supernatant zone. Itis therefore expected that, for measurement times longer than six minutes, the stress would dropoff as the solids content in the measuring region of the fixture declined.To determine the acceptable measuring time period, the shear stress of the magnetitesuspension, with a solids content of 15% by volume, was measured as a function of time at ashear rate of 500 s’. Figure 15.12 is a plot of the shear stress versus time showing that afterapproximately six minutes, the shear stress begins to decay. This measurement period coincidedwith the settling period required for the supernatant to reach the top of the bob and the periodof time used to calculate the fixture dimensions. For the suspension with 15% solids by volume,the maximum measurement time was therefore determined to be approximately six minutes. Fora faster settling suspension, a shorter measurement time would be appropriate while for a slowersettling suspension a longer measurement time could be used.194Figure 15.lOa Solids concentration profile in the rheometer fixture at a settling time of2 minutes determined while the bob was not rotating.0.3500.300 V Center0.2500C-)0u— 0.200U)00.1500.1000.0500.000° Outer GapI I• inner Gap• •. pI0 5 10 15 20Height (cm)25130195Height (cm)Figure 15.lOb Solids concentration profile in the rheometer fixture at a settling time of4 minutes determined while the bob was not rotating.0.3500.3000.250.Center000L_ 0.200U,00(F)U) 0.150E00.1000.0500.000Outer GapInner Gap•o ..0.•I I• • •I0 5 10 15 20 25 30196r Center° Outer Gap• Inner GapI•U°°I • I_______J0 5 10 15 20 25 30Height (cm)Figure 15.lOc Solids concentration profile in the rheometer fixture at a settling time of6 minutes determined while the bob was not rotating.0.350-0.3000.250=0()u- 0.200C,,0.1500.1000.0500.000I197Figure 15.lOd Solids concentration profile in the rheometer fixture at a settling time of8 minutes determined while the bob was not rotating.0.3500.3000.250Center0C—)L 0.200C!)00.1500.1000.0500.000° Outer GapI• inner Gap•ILIC••I CU .____. —0 5 10 15 20 25 30Height (cm)1980.350Height (cm)Figure 15.lla Solids concentration profile in the rheometer fixture at a settling time of2 minutes determined while the bob was rotating at a shear rate of 500 s’.=0C)UtZ30(I)ci)E0Center0.3000.2500.2000.1500.1000.0500.000° Outer Gap• Inner Gapa •a a U a aI I I0 5 10 15 20 25 30199Height (cm)Figure 15.llb Solids concentration profile in the rheometer fixture at a settling time of4 minutes determined while the bob was rotating at a shear rate of 500 s_i.0.3500.3000.2500C)0L 0.200Cl)0.150Center° Outer Gap• Inner Gap0.1000.0500.000•np.Li•I I I. • .10 5 10 15 20 25 30200Height (cm)Figure 15.llc Solids concentration profile in the rheometer fixture at a settling time of6 minutes determined while the bob was rotating at a shear rate of 500 s’.0.3500.3000.250CC-.)CL 0.200 -U,0.1500.1000.0500.000CenterU Outer Gap• Inner Gap.• UU.•I •..___L_____0 5 10 15 20 25 30201Figure 15.lld Solids concentration profile in the rheometer fixture at a settling time of8 minutes determined while the bob was rotating at a shear rate of 500 s_i.0.3500.3000.250=QC-,L. 0.200a-,E0.1500.1000.0500.000s CenterD Outer GapInner Gap..LI Li.I S0 5 10 15 20 25 30Height (cm)20215.6 The Rheological Measurement ProceduresTo determine the rheological properties of the magnetite suspensions, it was necessary toproduce accurate rheological flow curves. Procedures were developed taking into considerationthe possible errors associated with particle settling, turbulence and non-Newtonian flow.Measurements were carried out using the new elongated fixture attached to a Haake viscometer.15.6.1 Measurement Time PeriodsAs previously discussed, the measurement period was constrained by the settling rate ofthe suspension. Conversely, for accurate rheological measurements, it was necessary to have ameasuring period of sufficient length to minimize the effects of bob inertia on measured stresses.Since the bob has mass, if its rotational speed is abruptly changed, the inertia affects themeasured stress values. Haake recommends periods of at least two minutes for a shear rate rampmeasurement to avoid errors associated with the inertia. For example, when measuring shearstress over the shear rate from 0 s_i to 300 s_i, the ramped time should be at least two minutes.Based on the settling test results in the elongated fixture, measurement periods of at least twominutes could be used to eliminate inertia errors.203HARICEOperator:Substance:tiagnetite SuspensionTest Ho.:Solids Volume 15Test of:26.Hov 1991System:/Temperature:25.0°C+++ FIO.ROTFigure 15.12 Measurement of shear stress at shear rate equal to 500 s versus time for amagnetite suspension with a solids volume fraction of 0.15.HARKE Pot Z.3ttmin]20415.6.2 Shear Rate Measurement RangeThe shear rate range over which the flow curves were measured was selected to covershear conditions in dense media separators. In particular, the effective shear rates between coalparticles and the dense medium should be used in any rheological measurements. In a densemedia separator, the shear rates range from nearly zero to high shears where turbulence mayprevail (see Section 4.2). The upper shear rate limit depends on the ability of the viscometer tomake accurate measurements. At high shear rates, turbulence exists in the annular gap betweenthe cup and the bob which would erroneously add to the measured viscous resistance (see Section6.2.2.2). The onset of turbulence occurs with the formation of Taylor vortices in the annular gap(Schlichting, 1968). Taylor (1923) developed an empirical relation that provides an estimate ofthe shear rate at which this turbulence would form (see Equation 6.19). Using the dimensionsfor the outer gap and by making some assumptions regarding the properties of magnetite(suspension viscosity approximately equal to 5 mPa.s, suspension density of 1600 kg m3), thecritical shear rate was calculated to be approximately 548 s_i. It should be noted that Equation6.19 does not take into consideration the effects of particle size, particle density or suspensionsolids content on the critical shear rate. Each of these factors could affect the suspension inertiaand thereby the critical shear rate for Taylor vortices formation. It is expected that withincreasing particle size and density, a lower critical shear rate would apply.Rheological tests were carried out with a transparent fixture in which horizontal bandswere observed at shear rates greater than approximately 350 s. Rheological measurementsrevealed that the flow curve turned upwards at shear rates greater than approximately 400 s (see205Figure 15.13). The visible horizontal bands and the erroneous dilatant properties can beexplained by the onset of turbulence. To ensure that turbulence did not affect experimentalresults, the maximum shear rate used was 300 s.15.6.3 Non-Newtonian Shear Rate CorrectionsSince dense media exhibit non-Newtonian flow properties, the shear rate across theannular gaps in the fixture will not decay in a linear manner. Shear rates must therefore becorrected to account for non-Newtonian properties. A program (Appendix II) was written usingthe method developed by Krieger (1968a, 1968b) to correct the shear rates (see Section 6.2.1).The basic functions of the program were to read the shear rate and shear stress data, the shearrates were then corrected using the calculation procedure outlined in Section 6.2.1. Preliminarytests with magnetite suspensions revealed that the corrected shear rate values were not verydifferent from the original values. It is likely that the narrow gap size minimized the effects ofthe non-Newtonian flow. Therefore, the shear rate that is calculated based on the assumption thatthe velocity profile across the gap is linear provides a good approximation of the non-Newtonianvelocity. Furthermore, it can be assumed that the narrower the gap, the smaller the error. Figure15.14 shows a flow curve produced for a magnetite suspension with corrected and uncorrectedshear rates. The two sets of data produce the same flow curve indicating that the corrected shearrate values are approximately the same as the uncorrected values. Since under extremeconditions, the magnetite suspensions could exhibit much more non-Newtonian flow propertiesthan those found in the above tests, all of the rheological data were corrected.2063rCPaJ HRRKE+Operator:+4:Substance:+ tIROHETITE SkJSPEHDilatent 510K* Test No.:t 15’ SOLIDS BY VO2 LUIIE4 Test of+ 5.Jui 1989+++ + System:M57ESSPInflection Point++ Temperature:++ 23.006Shear Thinning+4:v++++++ AB1.ROT++++ AB5.ROT4:*: *+ide 2é0 3d0 4ë0 500ni/siHRRKE Rot Z.3Figure 15.13 Rheological flow curve for a magnetite suspension with 15% solids by volumeshowing apparent dilatant flow behaviour at shear rates greater than approximately405-1207uCPa).r U.B.C.‘44- Operator:“4-.Substance:‘4” MAGNETITE SIJSPEN.4’-” SIGNTest No.:15 SOLIDS E’ VO*4.LUME*.4.Test of:-44’-44’‘4’ 5.Jul 1989-*4’ System;** t15/ESSPTemperature:+ ‘4’ 23.0°C+,I’-4’+ * Uncorrected Data÷ Corrected Data0.5 4.1-,44-4*** AB8.ROTi-++ RFIBS.ROT24.20 3007’El/s)I4flK Pos .3Figure 15.14 Flow curve for magnetite suspension (solids volume fraction = 0.15) withuncorrected shear rate data (AB8), and corrected shear rate data (RAB8).20815.7 ConclusionsA device to measure the rheological properties of settling suspensions was developed andevaluated. This device is an elongated double gap cup and bob arrangement (with somemodifications) that can be attached to most rotational viscometers. The device was designed tomeasure the rheological properties of suspensions exhibiting zone settling properties characterizedby the existence of a constant density zone. It was shown in Chapter 14 that magnetite densemedia exhibits such zone settling properties.The fixture was designed in such a way that the errors associated with measuringrheological properties of suspensions, such as wall slip and non-Newtonian shear rate effects areminimized. To minimize wall slip, vertical grooves were cut into the shearing surfaces of thecup and bob. Non-Newtonian shear rate effects were minimized by using narrow gaps and bycorrecting the shear rates using the method developed by Krieger (1968a, b).The measurement procedures were developed to provide accurate results without errorsassociated with particle settling and turbulence. Measurement periods of at least two minutescould be used without concern of particle settling errors. To avoid turbulence, the maximumshear rate was determined to be 300 s_i.209CHAPTER 16: RHEOLOGICAL PROPERTIES OF MAGNETITE DENSE MEDIA16.1 IntroductionRheological flow curves were obtained for magnetite suspensions using the developedfixture and following the procedures described in Chapter 15. The flow curves were thenmodelled with equations that fit the flow curve shape using the simplex optimization non-linearregression procedure. The fitted equations were compared to determine which model was bestsuited to describe the flow curve for the magnetite dense medium. Finally, the time dependentproperties of the magnetite dense medium were characterized.16.2 Flow Behaviour of Magnetite Dense MediaFlow curves were produced for a magnetite suspension with a solids content of 15% byvolume corresponding to a medium density of 1579 kg m3. The flow curves were obtained forthe shear rates ranging from 0 s_i to 300 s’ using a ramp time of two minutes while maintainingthe suspension temperature at 25°C. Shear rates were calculated using Krieger’ s method (seeAppendix II). Figure 16.1(a) is a plot of the shear stress versus shear rate showing three sets ofdata with each set consisting of fifty points. The plot shows a band of data points rather thana single line; such bands of data are typical for coarse particle suspensions and have beenattributed to variations in suspension composition in the annular gap of concentric cylinderviscometers (Cheng, 1978, 1982).210The shape of the flow curve indicates that magnetite dense media exhibits shear thinningnon-Newtonian flow properties. This result is supported by results obtained in Chapters 17 and18. Figure 16.1 (b) is a plot of apparent viscosity versus shear rate for the same sets of data.As the plot indicates, the apparent viscosity decreases with increasing shear rate which ischaracteristic for shear thinning flow properties. From Figure 16.1 (a), it appears that thesuspension has a yield stress, however, due to the sharp curvature of the data band towards theorigin at low shear rates, the presence of a yield stress is not conclusive.At high shear rates, the data of the shear stress versus shear rate is almost linear.Between the curved and linear segments of the curve, there is an inflection point (shear rateapproximately 120 s’). The shape of the flow curve is believed to depend on the types andmagnitude of inter-particle interactions that occur during shearing. The strong curvature over thelow shear rate range and the possible existence of a yield stress indicate that a structure is presentin the suspension. At high shear rates, shearing could break down this structure and viscousproperties would likely result from other particle interactions such as hydrodynamic effects (seeSection 8.2).16.3 Flow Curve ModellingIn order to describe mathematically the flow behaviour of magnetite dense media, the flowcurve equations were fitted to the rheological data. This was accomplished using the simplexoptimization non-linear regression procedure developed by Nelder and Mead (1965). To selectthe best fitting model, a model discrimination procedure was used.21115CPaJI IJ.B.C.++ Operator:+ + Substance:II ++ 1RONETtTE SUSPEN+++:+ +++ +4 + Test No.:+ * + ++ 15 SOLIDS BY VULUME+Test of:+-5.Jul 1989+ ++ System:+ + * M5/ESSP+++,+++ Temperature:++ 23.0°C*0.5++ * +,+* +*+4+4 AB6.ROT+ * i-+++++ RB8ROT18 20 300‘C1/sJPoS 23Figure 16.la Flow curve for magnetite suspension with a solids volume fraction of 0.15showing a band of data points produced from three consecutive measurements onthe same suspension.212Operator:Substance:+ MFGNETITK SUSPEN2 SION+ Test No.:+ t5 SOLIDS BY VOLUME+ Test of:5.Jul 1989System:M5/ESSP++ Temperature:23.80C* +++ t 4:4-+* ,+ *s + ÷++ AB6.ROT5 :::2G 308>[1/s]Ilf4eIKE Rot 2.3Figure 16.lb Apparent viscosity versus shear rate for a magnetite suspension with a solidsvolume fraction of 0.15 showing data points for three consecutive measurementson the same suspension.21316.3.1 Model FittingFour flow curve equations, including two equations with a yield stress term (the Cassonand the Herschel Bulkley models), and two equations without a yield stress term (the Carreau andthe Cross models) were fitted to the rheological data. All four equations can be applied tosuspensions exhibiting shear thinning properties. The equations have been discussed in Section7.2.2 and are presented in Table 16.1. The Bingham equation was not selected as it cannotmodel the curvature of the flow curves at low shear rates.A simplex optimization regression program was written to fit the equations to the data.The program reads up to three sets of data (150 points) which is fitted to a selected equation.The simplex optimization method is a direct search method that can be used for non-linearequations (Nelder and Mead, 1965, Mular, 1972). This method moves a simplex towards aminimum weighted residual sum of squares. The simplex can expand, contract and reflect tolocate the minimum. Once the objective function (weighted residual sum of squares) met apredetermined limiting value (1 x 10.8), the program reached convergence and the equationcoefficients were printed, If convergence was not achieved, the program was terminated after1000 iterations. The weighting factor is defined as the inverse of the variance of the measuredvalues. It was determined that the variance of the measured shear stress value was constant asa function of shear rate and therefore could be set to equal 1.0. The program was adapted froma program written by A.L. Mular (Appendix Ill). The coefficients for the four tested equationsare presented in Table 16.2. Figures 16.2 a) to d) are plots of the fitted equations along with theflow curve data. All four equations appeared to fit the general flow curve shape.214Table 16.1 Rheological flow curve equations used to model flow curve data for magnetitesuspensions.Models EquationsEquations with a yield stress coefficientCasson = [t +Herschel Bulkley=+Equations without a yield stress coefficientt ‘110Caneau TI‘[1 + (t1t)2]st 10-1LCross rj ==TI +______2150 CD 0 CD Cl) 0 I 0 C CD Cl)L’JC-) -tCD0Cl)CCl)-Cl)Cl)aCD0D,—CCD — C CD <: 80IIIIII920IIIIIIIILI9IiIIII499C -\0ppp%C‘.0‘.0‘.000Lu‘.0)CCU.B.C.OperatorSubstance:P1RGNETITE SUSPENSIONTest. No.:I5 SOLIDS BY VOLUMETest of:5.JuI 1989System:M5/ESSPTemperature:23.øC+++ RB6.ROT+4+ RB7.ROT+4+ RB8.ROTCSFiB1.ROTFigure 16.2a Rheological flow curve for a magnetite suspension with a solids volume fractionof 0.15 and fitted Casson model.HRnE Rot 2.3‘C1/s)217U.B.C.Operator’:Substance:MAGHETITE SUSPENSIONTest, No.:15 SOLIDS BY VOLUFIETest of:5.Jul 1989SystemM5/ESSPTemperature:23.8’C+++ RB6.ROT+++ fl7.ROT+++ AB8ROTHBRB1.ROTFigure 16.2b Rheological flow curve for a magnetite suspension with a solids volume fractionof 0.15 and fitted Herschel Bulkley model.HRRKE Ro Z.3fll/s)218U.B.C.Operator:Substance:MAGNETTE SUSPENSIONTest No.:15 SOLIDS BY VOLU1ETest of:5.Jul 1989System:M5/ESSPTemperature:23.8°C+++ A36.ROT+++ AB7.ROT+++ RB8.ROTCARB1.ROTFigure 16.2c Rheological flow curve for a magnetite suspension with a solids volume fractionof 0.15 and fitted Carreau model.HflRKE Ro .3380‘[1/sJ219U.B.C.Operator:Substance:IIAGNETITE SUSPENSIONTest No.115 SOLIDS B VOLIMETest of:5.Jul 1989System:M5/ESSPTemperature:23.0°C+++ RB6ROT+++ AB7.ROT÷++ RB8.ROTCRR1.ROTFigure 16.2d Rheological flow curve for a magnetite suspension with a solids volume fractionof 0.15 and fitted Cross model.HKE Re 2.3‘C1/sJ22016.3.2 Model DiscriminationTo determine which of the equations should be used to model the rheological propertiesof magnetite dense media, it was considered that:i. the model must fit the data over a wide range of shear rates;ii. the equation should be simple with a minimum number of coefficients; andiii. the coefficients should have physical significance.Figures 16.2 a) to d) show that although each of the equations fit the shape of the flowcurve, the equations with a yield stress term appear to fit the data better at the low shear raterange. To evaluate how well the four equations agree with the experimental data, Multiple Indexof Determination values, R2, were calculated and are presented in Table 16.2. Based on thesevalues, the Casson equation was found to fit the data best. However, since the models arenon-linear, a better comparison of the equations could be obtained using a model discriminationprocedure.In order to compare the fitted equations, the model discrimination procedure developedby Williams and Kloot (1953) was applied. This method can be used to compare two modelsat a time. Assuming that model one correctly represents the data, a variable described byEquation 16.1 is defined and by substituting the predicted value from model one for the observedvalue, Equation 16.1 becomes Equation 16.2. If model one is better than model two, a plot ofthe variable calculated from Equation 16.1 versus (Y2-1)will produce a line with a negativeslope, if model two is better, the slope will be positive.2211’ -‘Z [Y — —(Y + Y2)] +€ (16.1)Z = - +€ (16.2)where, Z is a defined variable,Y is the observed value,is the predicted value from model one, and‘2 is the predicted value from model two.A program was written to compare the models using the described model discriminationmethod (see Appendix IV). The results of the comparison of the fits of the four models arepresented in Table 16.3. The results indicate that the Casson model fit the experimental resultsbetter than the other equations. It is also apparent from the results that models with a yield stressterm are better than models with no yield stress term.The Casson equation has only two coefficients, while the other equations have three. Inaddition, the Casson equation coefficients have physical significance in that they represent theyield stress and the high shear rate viscosity. It is worth noting that the coefficients have shearstress (Pa.) and viscosity (mPa.s) units respectively. Therefore, the Casson equation satisfies theconditions stated above: it is simple and easy to use, its coefficients have physical significance,and the equation fit the data better than other equations. It should be noted that the Casson yieldstress is referred to as an apparent yield stress which means that it is determined using an indirectmeasurement method (see Section 6.3). Based on this evidence alone, it can not be concludedthat dense media exhibits a true yield stress. However, studies have shown that Casson yieldvalues compare well to values determined using direct measurement procedures (Nguyen, 1983).222Table 16.3 Results of model discrimination procedure to determine which flow curve equationbest fit the rheological data.Model #1 Model #2 SlopeHerschel Bulkley Casson 0.985Casson Carreau -0.926Casson Cross -0.502Herschel Buildey Carreau -0.676Herschel Buildey Cross -0.500Carreau Cross -0.50022316.4 Time Dependent Flow PropertiesSuspensions exhibiting shear thinning flow properties can also exhibit time dependentproperties (Van Wazer, 1963). Time dependent properties are related to the rates of structureformation and breakdown in a suspension. As shown in Section 16.2, magnetite dense mediaexhibits shear thinning flow properties which can be explained by the existence of a structure.To develop a better understanding of the structure in dense media suspensions, rheologicalhysteresis was measured for demagnetized and magnetized magnetite suspensions with a solidscontent of 15% by volume.Time dependent properties were difficult to measure for the suspensions since beforemaking a measurement, the suspension had to be mixed to re-suspend the particles. Mixingbreaks down the structure and little time could be allowed for structure reformation prior tocommencing the experiment. To provide time for structure formation, the suspension was placedin the viscometer one minute before commencing the test.Figure 16.3 shows flow curve hysteresis for a demagnetized suspension that was producedby increasing the shear rate from 0 s_i to 300 s-i and subsequently decreasing it to 0 s_i using twominute ramp times. Both the up ramp and down ramp curves exhibit shear thinning propertiesand an apparent yield stress. The down ramp curve lies below the up ramp curve indicating thatafter shearing the suspension exhibited a lower degree of structuring. This type of hysteresis isrefereed to as thixotropy. If the experiment was carried out immediately after re-suspending themagnetite, no hysteresis was observed. Since the medium is constantly moving in separators, thestate of the suspension following mixing is likely representative of real conditions.224L5(Pa] U.B.C.Operator:+*•4f ++ Substance:+ +4-f + r + + MRONETITE SUSPEN+ 444** ++ SION+Test No.:+ + ++ l5 SOLIDS BY VOUp Rai’p + + + + + LUME+ + ++++ Test of:+ + + 5.Jul 1989+ +++ +++++ System:+ *++ + ++ M5/ESSP+++++++++ Temperature+ + + 4r * + Down Ra..ip 23.8CC++:+ +++÷ +++++ ++++:++++++ + + + ÷+++ + * ÷÷÷ R87.ROTt +÷++ RB8.RQTide 2d0 308E1/sJI4AAKE Rot 2.3Figure 16.3 Flow curve hysteresis for demagnetized magnetite suspension with a solids volumefraction of 0.15.225Thixotropic properties can be explained by the time required to either align asymmetricparticles during shearing (Pinder, 1964) or by the break up of aggregates to increase the particledispersion to a state determined by the shear rate (Cheng, 1971). While magnetite particles areangular in shape, they do not have pronounced elongation. Therefore, the time dependentproperties are better explained by the change in structure resulting from breakage of aggregates.Although the suspension was demagnetized, some remnant magnetism is believed to remain inthe finest particles. The aggregation of these particles would explain the structure that isapparently present in the magnetite suspensions.Figure 16.4 shows a hysteresis curve for a magnetized suspension. The flow curves showmore pronounced non-Newtonian properties than the demagnetized suspension (see Figure 16.3).The hysteresis only occurred in the low shear rate range suggesting that at high shear rates theaggregates become dispersed. It was found that the structure in the magnetized suspensionformed relatively quickly, since experiments performed immediately following mixing producedthe same hysteresis. As shown in Section 13.2.2.6, magnetized particles form branched chain-likeaggregates. In a suspension, these aggregates could attach to each other to form a continuousnetwork structure. Shearing would break the attachments and with time breakdown the structure.2261.5 ‘riTa] U.B.C.Operator:Substance:+ magnetite suspen++ +4Z sionTest Ho.:+44+4 + 14—day magnetise+ d+ + Test of:+ 4::+ * +4: 4.Oct 1988+++System:+ 4: P15/ESS2+++Temperature:Up Rain’ ++4: + 4+ * 4: 25.8°C+*+ ++$4:4.4++8++++ DownRaMp4*+ +++ +*+4+ P273.ROT+ +4+ P275.ROT++2é8 308fll/s)I4RRKE Rot 2.3Figure 16.4 Flow curve hysteresis for a suspension of magnetized magnetite particles (volumesolids fraction = 0.15).22716.5 ConclusionsThe suspension of magnetite dense media used in the test work exhibited shear thinningrheological properties with an apparent yield stress. The flow behaviour was modelled using theCasson equation (see Table 16.1) which was found to fit the experimental results better than otherrheological equations. The equation has a yield stress term which implies that the medium hasa structure. As shown in Section 13.2.2.6, remnant particle magnetism results in the formationof a loose branched chain-like structure which may be responsible for the yield stress and shearthinning properties. The existence of a structure is supported by the thixotropic propertiesexhibited by the medium. The thixotropic properties were enhanced by magnetizing the particles,which indicates that remnant magnetism is at least partially responsible for the presence of astructure.228CHAPTER 17: EFFECT OF PHYSICO-MECHANICAL AND PHYSICO-CHEMICALPARAMETERS ON MEDIUM PROPERTiES17.1 IntroductionVarious physico-mechanical and physico-chemical parameters are known to influence theproperties of suspensions (see Chapter 8). Many of these parameters also affect the propertiesof magnetite dense media (see Chapter 9). Since the dense medium separation process is usedin various applications under diverse conditions, media properties can vary extensively. Theobjective of this chapter is to characterize and model the rheological properties of magnetitedense media with diverse parameter conditions and to determine the relative significance of theparameters to the medium properties. The parameters investigated included: solids content,particle size, pH, magnetization, dispersing agents, coal fines, bentonite and kaolinite clays.17.2 Determination of Parameter LevelsTo investigate the effect of various parameters, suitable levels of the variables had to bechosen. The levels were determined from those found in industrial practice and, in the case ofdispersing agents, the levels were determined from preliminary settling tests.The suspension solids content is known to affect settling properties (see Section 10.2).Settling tests were performed on magnetite suspensions over the volume solids contents rangingfrom 5% to 25%. Figure 17.1 is a plot of settling rate versus solids content. The figure showsthat at low solids content the suspension settles very quickly and, conversely, at high solids229content the settling rate is low. For coal preparation, media densities typically range from 1400kg m3 to 1800 kg m3 which correspond to volume solid contents of approximately 10 % to 20%. As seen from the plot, over this range of solids contents, the settling rate decreasedsignificantly with increasing solids content. The results agree well with well known relationshipsbetween media stability and solids content; media stability is of greater concern at low solidscontents.The levels of particle sizes used in test work ranged from -45 pm to -15 pm (see Section13.3.3). Figure 17.2 is a plot of settling rate versus particle size which shows that the settlingrate decreased as the particle size decreased. The magnetite dense medium particle size istypically 90% finer than 45 pm. Since very fine magnetite has recently been tried in dense mediaseparation tests on fme coal, there is a need to study the influence of much finer grades.Many coal preparation plants use demagnetizing coils in their dense media recoverycircuits to reduce the magnetic aggregation of the particles. Figure 17.3 shows settling curvesfor magnetized and demagnetized suspensions with a volume solids content of 15%. Thedemagnetized suspension settles much slower than the magnetized suspension indicating theimportance of demagnetization to media stability. The settling rates for the demagnetized andmagnetized magnetite were determined to be 1.58 cm min’ and 3.80 cm min’, respectively.From the sediment height at the end of the settling test, it is apparent that the volume of settledsediment was larger when particles were magnetized; this indicates that magnetized particles forma loose aggregated structure.Settling tests were performed on magnetite suspensions with 15% solids by volume overthe pH range of 2.0 to 12.0. The settling rates from these tests were plotted as a function of pH23012EE0C.)=C)(I-)Figure 17.1 Effect of magnetite solids content on the settling rate.23110864200.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25Volume Solids Fraction1.5 -EEC-)Q)CDCDa)(I-)1.2510.750.50.25025 30 3590% Passing Size (iJm)I-10 15 20 40 45 50Figure 17.2 Effect of particle size on settling rate of magnetite suspensions (volume solidsfraction = 0.15).23220181614EC)12-cQ)C-,0)c86420Settling Time (mm)16Figure 17.3 Supernatantlslurry interface height as a function of time for magnetized anddemagnetized magnetite suspensions with a solids volume fraction of 0.15.DemagnetizedMagnetized0 2 4 6 8 10 12 14233(Figure 17.4) which showed that the settling rate was not significantly influenced by the pH.Electrophoretic mobility (EPM) measurements (see Section 13.3.2.3) indicated that themagnetite isoelectric point was approximately at pH 2.3 but that over the remaining pH rangethe EPM was negative and therefore particle dispersion should be maintained. The pH can,however, influence the dense medium behaviour through its influence on the coagulation of claysand on the mode of action of dispersing agents.Dextran and carboxyl methyl cellulose have been tested for use in the processing of ironore (see Section 8.4.2). To compare the effectiveness of these two reagents as dispersants andto establish suitable dosage levels, settling tests were performed using a magnetite suspensionwith 15% solids by volume. Figure 17.5 shows suspension settling rates as a function of dextranand C.M.C. dosage, respectively. For dosages up to 2.5 kg/T, dextran had only a small effecton the suspension settling rate. Over the same range of dosages, C.M.C. addition significantlyreduced the settling rates of the suspension. The decreased settling rate indicated that particleinteractions were affected by the adsorption of C.M.C..Sodium silicate and sodium hexametaphosphate have been widely used as dispersingagents by the mineral industry. Therefore, settling tests were carried out with both of thedispersants so that their effectiveness could be compared. The settling rates were plotted as afunction of dispersant dosages for the sodium silicate and sodium hexametaphosphate in Figure17.6. The figure shows that for the range of levels tested, the settling rates were not significantlyinfluenced. Since inorganic dispersants could have a significant effect on the properties of clays,and since the use of sodium silicate has been reported in iron ore processing (Yang, 1988),sodium silicate was selected as the inorganic dispersant for further testing.2342.42.221.8CE6 1.4C)12CC,’C0.80.60.40.200 2 4 6 8 10pH12Figure 17.4 The effect of pH on the settling rates of magnetite suspensions (volume solidsfraction = 0.15).2351.81.61.4ciEE1a)cic 08ci0.60.40.20Reagent Dosage (kg/T)2.5Figure 17.5 Effect of carboxylmethyl cellulose and dextran on the settling rates of magnetitesuspensions (volume solids fraction = 0.15).CCCarboxlymethyl CelluloseC Dextran0 0.5 1 1.5 22362.52EEC-,a)ci,0.500 0.05 0.1 0.15 0.2 0.25 0.3Reagent Dosage (kg/T)0.35 0.4 0.45 0.5Figure 17.6 Effect of sodium hexametaphosphate and sodium silicate on the settling rates ofmagnetite suspensions (volume solids fraction = 0.15).a0Sodium Hexametaphosphate0 Sodium Silicate237To determine the levels of contaminants in dense media, samples of media were takenfrom two western Canadian coal operations, Cardinal River Coal and Luscar Stereo. The sampleswere taken from the dense medium cyclone circuit at Cardinal River and from both the densemedium cyclone and Wemco drum circuits at Luscar Stereo. A Davis tube was used to separatethe magnetics from the non-magnetics and the percent of -325 mesh (-45 pm) non-magnetics perunit volume of medium was determined. The results are presented in Table 17.1.As seen from the table, the percent of fine non-magnetic particles in the medium rangedfrom 1.6% w/v to 13.9% w/v (contaminants lelves were determined on a weight per volume ofmedium basis). Luscar Stereo is known to have kaolinite with some bentonite clays in their rawcoal which are difficult to remove with deslime screens and separate from the dense medium.The high ash contents of the fine particles reported in Table 17.1 reveals that the fines arecomposed of clay rather than of coal. The levels of contaminants found in the medium fromCardinal River were believed to be more typical for raw coals that do not contain clay.To determine the effect of coal fines on the settling properties of dense media, coal fromthe Bullmoose Operating Corporation in north eastern British Columbia was added to densemedium with a magnetite solids content of 15% by volume. The -325 mesh size fraction, withan ash content of 18.3%, was used in the settling tests. The suspension settling rates were plottedas a function of fine coal addition (Figure 17.7) which showed that even small amounts of finecoal significantly decreased the settling rate.238Table 17.1 Levels of -325 mesh (45 tim) contaminants in dense media.Operation Non-Magnetics -45 jim Ash Content(% w/v) (%)Cardinal River CoalD.M. Cyclone 1.58 24.7Luscar StereoWemco Drum 7.57 96.1Luscar StereoD.M. Cyclone 13.9 88.5239Similarly, clays were added to dense media with a magnetite solids content of 15% byvolume for settling tests. As indicated in Figure 17.7, kaolinite addition decreased the settlingrate much more significantly than fine coal. When bentonite was added the settling rate droppedoff very sharply and at an addition of 5% w/v the suspension was stable.Comparing three curves in Figures 17.7 revealed that for the same levels of contaminantaddition, the settling rates were reduced most by bentonite, second most by kaolinite and wereleast affected by fine coal. However, the addition of small amounts of each contaminant had asignificant effect on settling rates.17.3 Experimental DesignExperiments were performed to investigate the effects of physico-mechanical parameters,physico-chemical parameters and contaminants on the settling and rheological properties ofmagnetite dense media. The objective of these experiments was to determine the relativesignificance of each parameter to the medium properties and to characterize and model therheological properties of the medium with diverse parameter conditions. The effects of nineparameters were investigated including solids content, particle size, magnetization, pH, inorganicdispersant (sodium silicate), organic dispersant (carboxylmethyl cellulose), coal fines, kaoliniteand bentonite.In order to minimize the number of experiments performed and still provide the necessaryinformation, a fractional factorial design was chosen. For this experimental design,2401.61.41.2EE080.20Figure 17.7 Effect of coal fines, kaolinite and bentonite content on the settling rate ofmagnethe suspensions with a volume solids fraction of 0.15.• Kaolinite Clay0 Coal Fines• Bentonite Clay0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Contaminant Content (%w/v)241sixteen sets of experiments plus four sets of centre point experiments were carried out. Thisdesign allowed for the determination of fifteen effects plus the mean effect. The principlegenerators for the design were:X0 = X1235 = X1347 = X2346=X1X248 = X12349 (17.1)The design is of resolution three, where main effects are confounded with two factorinteractions and higher order interaction effects. A Plackett and Burman (1946) experimentaldesign was considered; however the fractional factorial design was selected because it had amuch less complicated alias structure.The alias structure for the295 design is presented in Table 17.2; it shows the confoundedmain, two factor interaction and three factor interaction effects. Examination of the table revealsthat all the main effects except for L9 were confounded with only one two factor interactioninvolving L9. Therefore, parameter nine was selected as the parameter that would least likelyinteract with the remaining parameters. It was not expected that coal contamination wouldstrongly interact with the other eight parameters and it was therefore selected as parameter nine.The remaining eight parameters were randomly assigned to variable numbers by drawing numbersfrom a dish. The order of performing the experimental runs was also determined by randomlyselecting numbers from a dish.In order to interpret the results, main effects were considered to be more significant thantwo factor interaction effects and two factor interactions were considered to be more significantthan three factor interaction effects.242£VZS..E6T...L&...9Q.=‘i=i69f6PIrSLr9b..Wr5Tr6LIrEWr...LS..Sh5&’=t1i=i=Ltr=‘i9S==“i=‘i=i=“Itbi=1S9h.95&.fl tq...SEF.=‘‘I=KIri=9Cb=I=itLt...LUrsr.asri=i-i=i=‘i=iSKrjUtrSLb9frTe•tiIrSb1frssI...StTe=1U==5i=‘i=“i=b1aSPI=b=i=“i=‘i=‘=“i=t‘IL5b•SLfr==SP TI==i=tisarI•9SbI=PILSPIarrIIIa1“i=4511tiLl1bI_sioqzuopowwxajoauppuscoqyouopiamosj0*2towiqswpopunojuoowtuaoqsutisopspomcsjvuopoanjauuonasssqvtaa,qsjThe experimental design is presented in Table 17.3 showing the coded high (+1), low (-1)and centre point (0) levels used for each of the twenty sets of measurements. These high, lowand centre point variable levels were chosen based on the results presented in Section 17.2. Thevariables and their respective levels corresponding to the coded levels are given in Table 17.4.The measured responses (dependent variables) were the suspension settling rate, thesediment solids content and the coefficients of the fitted rheological models. Four differentrheological models were fitted to flow curve data using the simplex optimization regressionprogram described in Section 16.3.1. The best model was selected based on multiple index ofdetermination values, R2, and the results of a model discrimination procedure (see Section16.3.2). The coefficients of the best fitting model were then used as the dependent variablesrepresenting the rheological properties.17.4 Sample PreparationTo reduce the potential for systematic errors associated with procedures used to preparethe suspension, all suspensions were prepared using exactly the same procedure.The suspensions were prepared in cleaned 350 ml graduated cylinders. The glassware wascleaned by adding a few millilitres of concentrated nitric acid to the glass container. A few(three or four) drops of concentrated ethanol were then added to the nitric acid which producesa strongly oxidizing environment resulting in the breakdown of any organics that might bepresent. The glassware was then rinsed ten times with distilled water to remove any dissolvedspecies. This cleaning procedure was used prior to preparing all of the suspensions.244Table 17.3 Coded levels for 295w fractional factorial experimental design used to investigatethe effects of suspension variables on rheology and stability.Run # Coded_Experimental_Variable_LevelsX1 X, X X4 X5 X6 I x7 X8 Xi1 liii245Table 17.4 Variable levels corresponding to coded levels.Variable Description Variable LevelsCoded Levels -1 0 1X1. Carboxylmethyl Cellulose (kg/T) 0.5 1 1.5X2. Passing Size (!Jm) 45 30 15X3. Volume (%) Solids 10 15 20X4. Magnetization Mag. Demag.X5. Sodium Silicate (kg/T) 0.05 0.1 0.15X6. Kaolinite (% w/v) 0.25 0.5 0.75X7. pH 4.0 7.0 10X8. Bentonite (% w/v) 0.25 0.5 0.75X9. Coal Fines (% w/v) 0.25 0.5 0.75246The levels of the additives for each suspension are presented in Table 17.4. Since thebentonite was found to be difficult to disperse, it was added first to the graduated cylinder with50 ml of distilled water and was thoroughly shaken and placed in an ultrasonic mixing bath. Thebentonite suspension was allowed to wet overnight. Kaolinite, not as difficult to wet as thebentonite, was then added and once again the suspension was shaken and placed in an ultrasonicbath until the suspension was dispersed. The coal, sodium silicate and magnetite were thenadded in the presented order, with shaking and ultrasonic mixing between each addition.Distilled water was added as needed to disperse the particles. The suspension was then eithermagnetized by placing the cylinder in a demagnetizing coil and inducing a magnetic field forapproximately five seconds or demagnetized by drawing the graduated cylinder through thedemagnetizing coil three times. At this time the C.M.C. was added and the suspension waslightly shaken. The remaining water was then added before adjusting the pH using either sodiumhydroxide or hydrochloric acid as required.Once the suspensions were prepared, settling tests were performed. The same suspensionswere then poured into the cup of the developed rheometer fixture (see Chapter 15) to carry outrheological measurements. Three flow curves were produced for each suspension to ensurereproducibility of results.17.5 Characterization of Medium PropertiesThe settling curves for the twenty suspensions are presented in Appendix V. The mudlinefalling rates were used as the responses characterizing the stability of the suspensions. In247addition, the sediment volume was measured after twenty fours hours from which the sedimentvolume solid content was determined. Since the sediment solids content provides an indicationof the state of the aggregation, it was included as a response. The settling rates and sedimentsolids contents for each suspension are given in Table 17.5.The rheological flow curves exhibited shear thinning properties as was shown in Chapter16. With some suspension compositions, the non-Newtonian properties became very pronouncedand the flow curve data intercepted the shear stress axis indicating the suspensions exhibited ayield stress. The rheological flow curves for all twenty sets of measurements are presented inAppendix V.The coefficients of the best fitting flow curve model were used as the rheologicalresponses (dependent variables) for the experimental program. The flow equations were fit tothe data by using the simplex optimization non-linear regression program described in Section16.3.1. The fitted models are graphically presented along with the flow curves in Appendix V.Multiple index of determination values, R2, were determined for each model and a modeldiscrimination procedure was used to determine which equation fit the data best. Table 17.6shows the R2 values calculated for each of the equations for the twenty suspensions. Theequation fits each have 47 degrees of freedom except the Casson equation which has 48.Examination of the table reveals that the models with a yield stress term were better than modelswith no yield stress term. More importantly, in all twenty sets of experiments the Cassonequation was found to fit the data best.The validity of using the multiple index of determination values to compare the suitabilityof non-linear equations is questionable. Therefore, a model discrimination procedure developed248Table 17.5 Responses of rheological properties and settling properties for each of theexperimental runs.Run # Casson Yield Casson Viscosity Settling Velocity Solids PackingStress (Pa.) (mPa.s) (cm min’) Fraction1 2.43 5.86 0.115 0.3242 2.94 1.61 0.000 0.3403 0.46 5.37 0.203 0.6144 2.74 1.84 0.036 0.4935 1.57 0.85 0.015 0.1996 0.15 2.62 0.290 0.4277 0.42 0.88 0.293 0.3728 0.03 3.20 1.535 0.6709 8.56 1.47 0.033 0.33510 3.37 2.33 0.022 0.30711 2.43 1.55 0.021 0.44912 1.50 2.12 0.650 0.56713 0.20 3.49 0.473 0.40914 1.38 0.96 0.169 0.22315 0.06 4.86 1.903 0.52216 0.31 1.61 0.965 0.40217 0.24 3.27 0.186 0.49118 0.27 2.84 0.197 0.49519 0.39 2.67 0.411 0.47320 0.31 3.47 0.457 0.491249Table 17.6 Multiple index of determination values for each of the rheological equations fit tothe measured flow curve data from the experimental program.Run # Coefficient of Multiple Determination, R2Herschel Buildey — Casson Carreau Cross1 0.978 0.999 0.967 0.9412 0.911 0.998 0.904 0.6643 0.984 0.997 0.980 0.9794 0.841 0.975 0.839 0.6435 0.720 0.912 0.662 0.0296 0.970 0.986 0.964 0.9667 0.940 0.983 0.924 0.8588 0.992 0.995 0.99 1 0.9939 0.959 0.978 0.943 0.22010 0.988 0.998 0.941 0.70111 0.631 0.871 0.582 0.12512 0.913 0.971 0.895 0.77613 0.979 0.992 0.976 0.98714 0.850 0.969 0.818 0.77115 0.989 0.993 0.988 0.99316 0.932 0.971 0.922 0.94717 0.973 0.991 0.969 0.98418 0.964 0.988 0.958 0.97619 0.937 0.974 0.928 0.95420 0.957 0.982 0.95 1 0.967250by Williams and Kloot (1953) was used to determine the best fitting model. Details of themethod have been discussed in Section 16.3.2 and the program is presented in Appendix IV. Theresults of this exercise confirmed that the Casson equation describes the rheological data betterthan the other rheological equations. The coefficients of this equation, including the Casson yieldstress and the Casson viscosity, became the dependent variables for the experimental program.Hereafter, the terms yield stress and viscosity refer to the respective Casson equation coefficientsunless otherwise stated. The yield stress and viscosity responses for each suspension arepresented in Table 17.5 along with the settling rates and sediment solids contents.17.6 Evaluation of the Effects on Medium PropertiesThe variable effects for each of the responses and their confidence intervals werecalculated. The estimates of the effects were calculated as follows:L.=l1 ± tv,i_aV(ii)5 (17.2)in which,Yx.1. = 1 + (17.3)n12and,Y.1 = (17.4)where,L. is the value of the effect,251l is the estimated values of the effect,i is the mean effect,ç is the t-statistic probability,V (l) is the variance of the estimated effects based on the repeat runs,Y1 is the measured value of the response,X1 is the level of the variable, andn is the number of experimental runs.The 95% confidence intervals were calculated from the repeat runs. The effects for eachof the responses as well as their respective confidence intervals are presented in Table 17.7.Based on the calculated confidence intervals, effects that were determined to be insignificant havebeen highlighted in the table.17.7 Results of Experimental ProgramThe relative significance of the variables to media properties was determined from theresults of the experimental program. Table 17.8 presents the variable effects in order ofmagnitude. The table reveals that:i. Several parameters affected the Casson yield stress while only a few parametersinfluenced the Casson viscosity;ii. The four most significant variable effects for the Casson yield stress and for thesettling rate are the same;iii. Both main effects and interaction effects are important;252Table 17.7 Estimated effects of each variable for each of the determined responses.Variable Casson Yield Casson Settling Solids PackingStress Viscosity Velocity FractionL0 1.49 2.64 0.399 0.473L1 0.46 1.01 -0.076 -0.027L2 1.58 -0.28 -0.561 -0.192L3 2.54 0.46 -0.570 0.027L4 -0.88 0.48 -0.219 0.027L5 0.74 0.07 0.032 -0.014L6 -0.74 -0.16 -0.026 0.008L7 -1.52 2.38 0.457 0.130L8 -0.07 0.28 0.114 -0.036L9 -0.56 -0.03 -0.287 -0.037L12 0.77 0.03 0.115 0.020L13 0.37 0.58 -0.008 0.028L14 -0.71 -0.08 -0.232 -0.078L15 0.96 0.38 0.376 -0.015L17 -0.94 1.32 0.126 -0.001L1 -0.72 0.19 0.149 -0.02395% Confidence 0.08 0.98 0.050 0.020Interval253iv. The most significant main effects are due to changes in solids content, particle sizeand PH; andv. The most significant interaction effects are L15 and L17 (see Tables 17.2 and 17.4).17.7.1 Analyses of Measured ResponsesTable 17.8 reveals that most parameters had a significant effect on the yield stress andthat only a few parameters influenced the Casson viscosity. Therefore the results indicate thatthe Casson yield stress is the primary controllable rheological property. Since the existence ofa yield stress has been associated with the presence of a structure resulting from particleaggregation (Papenhuijzen, 1972, Hunter and Firth, 1976), it is apparent that changes in theparameter levels affected the magnitude of aggregation. It should be noted that the Cassonequation was developed for aggregating suspensions (Casson, 1959).For all suspensions, the yield stress dominated the rheological properties. This result canbe demonstrated by calculating the contributions of the yield stress and Casson viscosity to theapparent viscosity. For example, the apparent viscosity can be calculated from Equation 17.5.The first term on the right side of Equation 17.5 represents the apparent viscosity resulting fromthe yield stress, the second term represents the Casson viscosity contribution and the third termrepresents the interaction between the two coefficients that account for curvature of the flowcurve.ii = I = + 11 + (tflC)oS (17.5)C254Table 17.8 Statistically significant estimates of the effects in order of magnitude.Casson Yield Casson Settling Solids PackingStress Viscosity Velocity FractionL0=1.49 L0=2.64 L0=O.399 L0=O.473L3=2.54 L7=2.38 L3=-O.570 L2=-O. 192L2=1.58 L17=l.32 L2=-O.561 L7=O.130L7=-1.52 L1=1.O1 L7=O.457 L14=-O.078L15=O.96 L15=O.376 L9=-O.037L17=-O.94 L9=-O.287 L8=-O.036L4=-O.88 14=-O.232 L13=O.028L12=O.77 L4=-O.219 L1-O.O27L5=O.74 L18=O. 149 L3=O.027L6=-O.74 L17=O. 126 L4=O.027L18=-O.72 L12=O. 115 L18=-O.023L14=-O.7 1 L8=O. 114 L12=O.020L9=-O.56 L1=-O.076L1=O.46L13=O.36255Based on the mean values of the responses (mean Casson yield stress = 1.49 Pa, meanCasson viscosity = 2.64 x i03 mPa.s) at a shear rate of 100 s_i , the apparent viscosity is 23.8mPa.s. The contribution of the yield stress, viscosity and third term to this apparent viscosityare 14.9 mPa.s, 2.64 mPa.s and 6.27 mPa.s, respectively. The yield stress clearly contributesmore to the apparent viscosity than the other terms.As can be seen from the flow curves presented in Appendix V, the apparent viscositydecreased with increasing shear rate and the flow curves became linear. These results can beexplained by changes in the structure resulting from shearing of the suspension (Cheng, 1980b).By increasing shear rate, the rate of aggregate breakages exceeds the rate of aggregate formationleading to shear induced dispersion and the break down of the structure. Therefore, as thestructure breaks down, the apparent viscosity decreases (Sherman, 1965, Laapas, 1982, 1985,Sherman, 1965). Once the particles are dispersed, hydrodynamic effects determine the viscosityresulting in a linear shear stress to shear rate relationship.Since the four most significant variables that influence both the Casson yield stress andthe settling rate are the same, the yield stress and the settling rate are apparently interrelated.Specifically, if the variables affect the yield stress through their influence on the suspensionstructure, the same structure may determine the settling properties of the suspensions.In this case, a clear relationship should exist between the suspension settling rate and theyield stress. Figure 17.8 is a plot of the Casson yield stress versus the settling rates for thetwenty sets of experiments. The figure shows that when settling rates are low the yield stressis high and vice versa. These results support the explanation that the structure that determinesthe yield stress also determines the settling rate. The non-linear relationship between the yield2569.008.007.00aci 6.00U,3.002.001.000.000.00 0.20 040 0.60 0.80 1.00 1.20Setthng Rate (cmlmLn)1 40 1 60 1 80 2.00Figure 17.8 Relationship between the Casson yield stress and the settling rate.257stress and settling rate indicates that it is possible to optimize the medium properties by reducingthe yield stress while maintaining relatively low settling rates.Cheng (1980a) stated that the zone settling properties of suspensions could be explainedby the existence of a structure resulting from particle aggregation. It was shown in Chapter 14,that magnetite suspensions exhibit such settling properties. The apparent relationship betweenthe yield stress and the settling rate also support the explanation that the suspension has astructure that determine its physical properties.The sediment volume solids contents in the experiments ranged from 19.9% to 67.0%(Table 17.5). Sediment solids contents less than approximately 50% indicate that some type ofloose aggregated structure exists. Such a structure has been associated with coagulated clayparticles (Street, 1956, Kitchener, 1969). In addition, it was shown in Section 13.2.2.6 thatmagnetically aggregated particles form a loose structure. Both types of structure likely contributeto the physical properties of the suspensions.17.7.2 Effects of Suspension Parameters on Medium PropertiesChanges in the particle size, suspension pH and suspension solids Content had the greatesteffect on the medium properties. Other main effects that significantly influenced the mediumproperties were due to demagnetization and the additions of coal fines and carboxylmethylcellulose. Over the range of levels tested, changes in bentonite, kaolinite, and sodium silicateadditions had only small effects on the medium properties. It should be noted that these variablesmay have had a large effect on the medium properties; however, the changes in the responses258over the ranges of variable levels may have been small.The most important interaction effects were, L15 and L17, although, L14, L12, L18 and L16were also important. To determine which interactions were responsible for these effects, the aliasstructure was examined to identify which could physically account for the effects.To inteipret theresults, main effects were considered to be more significant than two factor interaction effectsand two factor interaction effects were considered to be more significant than three factorinteraction effects. While it is not possible to determine the importance of algebraicallyconfounded effects independently of each other without further experimentation, a physicalunderstanding of their influences allows for some interpretation. These results highlight therelationship between the medium properties that are important to separation performance and theparameters and their interactions that influence these properties.17.7.2.1 Effect of Solids ConcentrationThe signs (+1-) of the effects indicate that with increasing solids content, the settling ratedecreased and the Casson yield stress increased; however the Casson viscosity was not affected.Several investigators have shown that above a critical solids content, the relative viscosityincreases in an exponential manner with increasing solids concentrations (Rutgers, 1962a, 1962b).For suspensions exhibiting non-Newtonian flow properties, the relative viscosity is equivalent toan apparent viscosity divided by the viscosity of the suspending fluid. The results indicate thatfor magnetite dense media, the increase in apparent viscosity with increasing solids concentrationis primarily due to the increase in the Casson yield stress.259Papenhuijzen (1972) attributed the existence of a yield stress to the presence of a networkstructure that is formed by aggregating particles. Furthermore, with increasing solidsconcentration, particle aggregation increases which in turn increases the suspension yield stress.The decrease in settling rates with increasing solids content of suspensions has beenattributed to an increase in hindered settling effects (Richardson and Zaki, 1954, Garside andAl-Dibouni, 1977, Zimmel, 1985). However, the presence of the structure described above couldeffect the settling rate by physically supporting the particles (Cheng, 1980a). As was shown, theyield stress and the settling rate are inter-related. Therefore, the same structure that is responsiblefor the increase in yield stress due to increasing solids content is likely responsible for thecorresponding decrease in settling rate with increasing solids content.17.7.2.2 Effect of Particle SizeBy decreasing the particle size, the signs (+1-) of the effects indicate that the suspensionsettling rate decreased, the Casson yield stress increased and the Casson viscosity was notaffected. Since particle size influenced the yield stress and not the viscosity, the contribution ofparticle size to medium rheological properties can be attributed to the effect of particle size onthe suspension structure. For small particles, inter-particle forces of attraction and repulsiondominate over particle inertial forces. Therefore, small particles are more susceptible toaggregation effects than coarse ones (Williams, 1951, Saunders, 1967, Parkinson et al, 1970).Enhancing the magnitude of aggregation effects by decreasing the particle size facilitates theformation of a structure.260The decrease in settling rate with decreasing particle size can be explained by the Stokes(1891) relationship between particle settling rate and particle size as well as by the enhancedstructure formed by small particles (Cheng, 1980a). A network structure would physicallysupport the particles and thereby prevent them from settling. Such a structure also helps toexplain the zone settling properties exhibited by magnetite suspensions. In Chapter 14,experimental results indicated the particles settled as a bulk (hindered settling) rather thandifferentially based on size. The presence of aggregates and a particle network structure inhibitsdifferential settling.The interaction effect, L23, for particle size and solids content (confounded with L15) hada significant influence on both the settling velocity and the yield stress. The interaction effectindicates that the dependency on solids content is different for particles of different size.Sherman (1965) and Laapas (1982, 1985) explained the relationship between the suspension yieldstress and the interaction effect of solids concentration and particle size as follows. Below acritical concentration, the structure may not be continuous, resulting in a low or non-existentyield stress. This critical concentration is a function of particle size and it decreases as theparticle size decreases. Therefore, to reduce the yield stress (apparent viscosity) at high solidsconcentrations (medium densities), a coarse grade of magnetite should be used. Conversely, toimprove media stability, at low solids concentrations (media densities), fine grades of magnetiteshould be used.26117.7.2.3 Effect of Suspension pHThe suspension pH was found to be the third most important variable. Although pH wasshown to have no significant effect on settling rates of pure magnetite suspensions (see Section17.2), the effects on settling rates, yield stress and viscosity were very significant for the presentset of experiments. It is therefore likely that pH influenced the medium properties through itseffect on clays and interactions with dispersing agents.By increasing the pH from 4.0 to 10.0, the yield stress decreased, the viscosity increasedand the settling rate increased. At a low pH, clay particles coagulate to form a Thouse of cardsstructure as a result of positively charged edges and negatively charged surfaces (Street, 1956,Kitchener, 1969). Even with small amounts of bentonite, this structure may be quite profound.The structure is responsible for a high suspension yield stress (Nicol and Hunter, 1970) and itsupports the magnetite particles and thereby prevents them from settling. At a high pH, the clayparticles become dispersed and the structure breaks down resulting in a lower yield stress (Nicoland Hunter, 1970). In addition, the magnetite particles, which are no longer supported by thestructure of the clay, can settle faster, thereby increasing the settling rate of the suspension.Although the yield stress decreased with increasing pH, the Casson viscosity increased.At a high pH, the particles disperse due to higher electrostatic repulsive forces. Leong andBoger (1989) observed that with increasing electrostatic repulsion between particles, thesuspension viscosity increased while the yield stress remained small. They attributed the increasein viscosity to an increase in the magnitude of electroviscous effects. Electroviscous effectscould therefore explain the increase in the Casson viscosity with increasing pH.262While changes in the levels of bentonite and kaolinite additions had only small effects onthe suspension properties, the explanation of the effects of pH on clays suggests that theirpresence had a large effect on the properties of the medium.The pH also jointly interacts with dispersing agents to influence the responses (Laskowski,1988). From examination of the alias structure (Table 17.2) and the list of significant effects(Table 17.8), it can be seen that the interaction effects between pH and C.M.C.(L17)and sodiumsilicate (L57 confounded with L18) influence the properties of the suspension. By increasing boththe C.M.C. dosage and the pH, the yield stress decreased, the viscosity increased and the settlingrate increased. Similarly, increasing the sodium silicate dosage and the pH, resulted in adecreased yield stress and increased settling rate.The effects of C.M.C. and sodium silicate can be explained by their effectiveness indispersing particles. At low pH, C.M.C. can precipitate to form fine colloidal particles renderingit less effective. At high p11, C.M.C. is ionized and disperses the magnetite and clay particles.It is also possible that at low pH, polysilicic acid precipitates from the sodium silicate renderingit less effective as a dispersing agent, and at high pH, ionic species electrostatically stabilize thesuspension.The dispersion of the particles resulting from greater repulsive forces decreases thestructure of the suspension and therefore also decreases the yield stress. In addition, morenegative values of the zeta potential enhance electroviscous effects which can increase theviscosity. The lack of a structure to support and thereby prevent particles from settling resultsin an increased settling rate.26317.7.2.4 Effect of MagnetizationThe signs (+1-) of the effects of magnetization (Table 17.8), reveal that settling rate andyield stress decreased by demagnetizing the magnetite. Demagnetizing results in better dispersionof particles which decreases the size of the settling units and, therefore, also decreases theirsettling rates. The yield stress decreases as a result of the decrease in the inter-particleinteractions that are responsible for the formation of a structure. Clearly, demagnetization resultsin improved media stability and rheology.17.8 ConclusionsSuspensions were prepared with a diverse set of parameter conditions to determine theinfluence of the parameters on the properties of dense media. Based on the experimental results,the following conclusions can be drawn.The suspensions exhibit shear thinning rheological properties and have an apparent yieldstress. These rheological properties were successfully modelled using the Casson equation whichfit the flow curves better than the Herschel Bullcley, Carreau and Cross equations.The Casson yield stress term was found to be the most controllable rheological parametersince it was influenced by most of the suspension variables. The Casson viscosity was onlyaffected by a few of the parameters. In addition, it was determined that the Casson yield stresscontributed more to the apparent viscosity of the suspensions than the Casson viscosity term.The settling rates of the suspensions were affected by many of the same parameters as264the yield stress. It was revealed that the settling rate and the yield stress are inter-related in anon-linear manner. The settling properties and yield stress could be explained by the presenceof a structure resulting from particle aggregation.Although all parameters influenced the medium properties, for the ranges of variables thatwere tested, the solids content, particle size and pH were determined to be the most significant.Increasing the solids content and decreasing the particle size resulted in higher yield stress valuesand lower settling rates. An interaction effect between solids content and particle size indicatedthat the critical medium solids content, above which the medium becomes excessively viscous,is different for media particles of different size. The effect of pH was explained by its influenceon clays and dispersing agents. Most notable was that increasing the pH resulted in a lowerCasson yield stress, a higher Casson viscosity and a higher settling rate.Demagnetization improved both the medium rheology and the medium stability bydecreasing the yield stress, and by decreasing the settling rate, respectively. This resultemphasizes the importance of demagnetization to the properties of magnetite dense media.265CHAPTER 18: EFFECT OF PARTICLE SIZE DISTRIBUTION ON MEDIUMPROPERTIES18.1 IntroductionAs discussed in Section 8.3.5, the viscosity of dispersed particle suspensions can bereduced by controlling the particle size distribution. Specifically, viscosities can be reduced byusing a bimodal particle size disthbution characterized by a low small particle to large particlediameter ratio and a fine particle fraction of between 0.25 and 0.50 of the total solids content.The objective of this chapter is to investigate the effects of particle size distribution on therheology and stability of magnetite suspensions by:i. Developing a model to predict the rheological and settling properties of magnetitedense media as a function of particle size distribution and solid contents, andii. Identifying how particle size distribution variables affect the rheological andsettling properties of magnetite suspensions.18.2 Experimental DesignBased on the reviewed literature, important size distribution variables for bimodalsuspensions include the ratio of small to large particle diameters (Equation 18.1) and the smallparticle fraction of the total solids content (Equation 18.2). Since the effect of particle sizedistribution is more pronounced at high solids contents than at low ones (Ferrini et al, 1988),solids content was also included as a variable.266dSize Ratio = ...L (18.1)d,where, d is the mean particle size of small particles, andd1 is the mean particle size of large particles,= Fine Fraction = 1.00 — Coarse Fraction (18.2)The variable levels were selected based on the levels reported in the literature (see Section8.3.5). The optimum fraction of fine particles has been reported to range from 0.25 to 0.45(Chong et al, 1968, Parkinson et al, 1970, Round et al, 1984, and Ferrini et al, 1988).Fidleris and Whitmore (1961) found that for bimodal suspensions with fine particle tocoarse particle diameter ratios of less than approximately 0.1, the fine particles flowed betweencoarse particles together with the suspending liquid and did not physically interact with the largeparticles. As the particle diameter ratio increased, the small particles began to interact with thelarge ones resulting in an increase in the suspension viscosity. The size fractions that wereprepared for the test work had geometric mean particle sizes ranging from 3.3 pm to 25.5 pm forthe small particles and 38.1 pm for the large particles. The small particles were mixed with thelarge particles to produce suspensions with mean particle size ratios ranging from 0.086 to 0.669.The suspension solids contents ranged from 11.6% to 28.4% solids by volume, whichcorresponded to media densities of approximately 1450 kg m3 to 2100 kg m3. The size fractionsand the preparation procedures are described in Section 13.3.5..The experiments were carried out using a central composite experimental design. Table26718.1 shows the coded levels of variables for the sixteen sets of experiments. The design includesa 2 full factorial design portion, involving eight runs, six star point runs and two centre pointruns. Table 18.2 shows the variable levels corresponding to the coded levels. This experimentaldesign provided sufficient information to fit the responses to second order equations involvingthe variables. The experimental runs were carried out in random order determined by selectingnumbers from a dish.The dependent variables included settling rates and the coefficients of the Casson equationwhich was fit to flow curve data for each suspension. The Casson equation was fit to the databy using a simplex non-linear regression program (see Section 16.3.1). All the rheologicalmeasurements were made using the developed rheometer fixture for settling suspensions and theprocedures described in Chapter 15.Once the measurements were completed, statistical models were developed for eachresponse as a function of the investigated variables. Linear regression was used to fit theequations to the responses using SYSTAT which is a statistical program system. From theregression, the values of the coefficients were determined. By using a step-wise regressionprocedure, insignificant coefficients were removed from the model based on a t-statisticprobability. The fit of the equation was then evaluated based the coefficient of multipledetermination, R2 (48 degrees of freedom). From the fitted second order equation, responsesurfaces were produced to illustrate how the parameters affected the medium properties.268Table 18.1 Coded variable levels for central composite experimental design.Run # Experimental VariableSize Ratio, X1 Fine Fraction, X2 Volume Fraction, X31 1 1 12 -1 1 13 1 -1 14 -1 -1 15 1 1 -16 -1 1 -17 1 -1 -18 -1 -1 -19 * 0 010 0 011 0 * 012 0 -* 013 0 0 *14 0 015 0 0 016 0 0 0Table 18.2 Variable levels corresponding to coded levels.Variable Description Variable LevelsCoded Levels -* -1 0 1 *X1 Size Ratio 0.09 0.13 0.22 0.39 0.67X2 Fine Fraction 0.199 0.25 0.325 0.40 0.451X3 Volume Fraction 0.116 0.15 0.20 0.25 0.28426918.3 Experimental ProcedureIn order to reduce the possibility of systematic errors, each suspension was prepared usingthe following procedure:i. The appropriate weight of fme magnethe particles was added to a cleaned 350 mlgraduated cylinder with 50 ml of distilled water. The suspension was shaken and placed in anultrasonic bath to disperse the particles.ii. The weighed coarse particles were then added to the fine particle suspension andthe mixture was again shaken and placed into an ultrasonic bath.iii. The remaining weight of distilled water was then added to the graduated cylinderwhich was shaken and placed in an ultrasonics bath to ensure particle dispersion.iv. Prior to proceeding with any measurements, the suspension was demagnetized bypassing the graduated cylinder through a demagnetizing coil three times and the suspension pHwas measured.v. Once the suspension was prepared, a settling test was performed which involvedrecording the supernatant-slurry interface height for a period of an hour and then taking a sludgedepth reading.vi. Following the settling test, the suspension was demagnetized again and then pouredinto the cup of the rheometer fixture. Three sets of flow curve data were produced for eachsuspension. The temperatures of the suspensions were maintained at 25°C for all rheologicalmeasurements. Between each set of measurements, the cup was removed from the rheometer andinverted several times to re-suspended the suspension.270Once the measurements were completed, settling rates were determined and the Cassonequation was fit to the flow curve data to determine the flow curve model coefficients. TheCasson equation coefficients and settling rates for each of the experimental runs are presentedin Table 18.3. The settling curves and fitted flow curves for the sixteen sets of experiments arepresented in Appendix VI.18.4 Modelling the Effects of Particle Size DistributionThe Casson yield stress, Casson viscosity and settling rate of the suspensions were fit toa second order polynomial equation using linear regression. The general form of the polynomialequation that was fit to each set of responses is presented in Equation 18.3.Y = A0 + A1X + A2X + A3X + A12X2+ A13X3+ A23X3+ A11X2+ A22X + A33X2 +A123X3 (18.3)where, A represent the model coefficients, andX1 represent the un-coded variable levels.Significant coefficients along with multiple index of determination values for each of thefitted equations are presented in Table 18.4. The t-test results along with an analyses of variancefor each fitted equation are presented in Appendix VII.271Table 18.3 Settling rate, Casson yield stress and Casson viscosity responses for experimentalprogram.Run # ResponseCasson Yield Casson Viscosity Settling RateStress (Pa) (mPa.s) (cm min’)1 0.125 7.2 1.232 1.587 1.2 0.463 0.060 7.3 1.474 0.725 2.6 0.805 0.050 2.4 4.676 0.130 3.1 1.117 0.070 1.4 5.088 0.024 3.8 1.879 0.000 7.1 3.2210 0.910 2.1 0.5211 0.125 4.8 1.1812 0.019 5.9 2.0313 0.721 4.5 0.6214 0.049 1.5 5.3215 0.015 6.4 1.5116 0.076 4.8 1.49Standard Error 0.043 1.1 0.01272Table 18.4 Casson yield stress, Casson viscosity and settling rate coefficients for fitted secondorder models.Coefficient Casson Yield Casson Viscosity Settling RateStressA0 7.84A1 -45.6 32.5A2 -3.11A3 -9.53 75.6 -76.1A12A13 261 -97.1A23 28.2A11 6.12 -10.0A22A33 31.0 -303 189A123 -87.7R2 0.89 0.96 0.97273The coefficient of multiple determination, R2, values (see Table 18.4) indicate that theequations for the settling rate and Casson viscosity provide good fits to the data. The expressionfor the yield stress has a slightly lower index (R2 = 0.894). The fit was, however, considered tobe adequate to indicate trends in the yield stress as a function of the variables. Predicted versusestimated responses are plotted in Figures 18.1, 18.2 and 18.3 for the yield stress, viscosity andsettling rate respectively. These figures also indicate that while the models for the settling rateand viscosity provide good fits, the yield stress model fit is also adequate. The analyses ofvariance and degrees of freedom for each model along with the t-statistic probability for eachcoefficient are presented in Appendix VII.18.5 Analyses of Regression ModelsFrom the fitted second order models for each of the responses, the response surfaces wereplotted. These response surfaces reveal: the variable levels that correspond to maximum andminimum response levels; and the relationships between the variable levels and trends in theresponses. The results can be explained in terms of the effects of solids content, particle size andparticle size distribution, on the rheological and stability properties of suspensions. In thediscussion of the results, the terms yield stress and viscosity refer to the Casson yield stress andCasson viscosity, respectively.2741.61.4- 1.20C,)“ 10.)(F)0)0.2ol . I I0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-0.2Estimated Gasson Yield Stress (Pa.)Figure 18.1 Predicted versus estimated Casson yield stress responses.27587()0E>-‘Li-)00Cl)C0U)U)000)C-)00)03210Figure 18.2 Predicted versus estimated Casson viscosity responses.276.a0 1 2 3 4 5 6 7 8Estimated Casson Viscosity (mPa.s)65E0)C,,a)- C)0)a-210Estimated Settling Rate (cm/mm)Figure 18.3 Predicted versus estimated settling rate responses.aa0 1 2 3 4 5 627718.5.1 Effect of Particle Size Distribution on the Casson Yield StressAs indicated in Table 18.4, the Casson yield stress was affected by each of the variables;mean size ratio, fine fraction and suspension solids content. The table shows that interactionsterms and second order terms were required to fit the yield stress to the data.Figures 18.4 and 18.5 are contour plots of the yield stress determined with the solidscontent set at 15% and 25%, respectively. Both plots show that a minimum yield stress valleyexists that is a function of both the size ratio and the fine fraction. This minimum yield stressvalley has a trend along a diagonal line that corresponds to increasing size ratios and finefractions. From the contour intervals it can be seen that the yield stress increases in a non-linearmanner above and below this diagonal line.By comparing Figures 18.4 and 18.5, it can be seen that the effect of particle sizedistribution is more pronounced at a high solids content. At 15% solids content, the minimumyield stress valley is quite broad and the increase in the yield stress perpendicular to the trendof the valley is gradual. At 25% solids, the valley is defmed better showing more pronouncedincreases in the yield stress perpendicular to the trend of the valley. The plot indicates that theyield stress valley dips with increasing fine fraction and size ratio.The figure indicates that at low particle size ratios (less than approximately 0.20), theyield stress increases with increasing fine fraction. This increase can be explained by the effectof larger amounts of fine particles on the yield stress. In Chapter 17 it was shown that as theparticle size decreased, the yield stress increased. The result was attributed to the greatersusceptibility of small particles to aggregation which leads to the structure formation. The2780.6000.4750.3500225Fine Fraction050Figure 18.4 Response contours of the Casson yield stress (Pa.) as a function of size ratio andfine fraction (magnetite volume solids content = 0.15).0I,cc0c101000.15 0.20 0.25 0.30 0.35 0.40 0.45279:::0 /E 0.350C):.:::0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50Fine FractionFigure 18.5 Response contours of the Casson yield stress (Pa.) as a function of size ratio onfine fraction (magnetite volume solids content = 0.25).280magnetite particle aggregation is believed to result from remnant magnetism. Although theparticles were demagnetized, it is difficult to demagnetize very small particles (-10 pm) sincesuch particles may contain only a few magnetic domains in which case the poiarity of the particlemay not be completely cancelled (Graham and Lamb, 1982).At high particle size ratios (greater than approximately 0.30), the yield stress decreasedwith increasing fine fraction. In this case the particles comprising the fine fraction are relativelylarge (+ 10 pm), and can therefore be demagnetized more effectively. Therefore, particleaggregation should not be as pronounced. Despite the reduction in magnetic aggregation withincreasing size ratio, the suspensions still exhibit an apparent yield stress.At high size ratio and low fine fraction levels, the suspensions are nearly mono-dispersewith large particles. Since the density differential between magnetite and water is high (almost4000 kg m3), the large magnetite particles experience large inertial forces allowing them tophysically collide and dissipate energy through friction and the loss of translational and rotationalmomentum (Thomas, 1965, Clarke, 1967, Brenner, 1972). Laapas (1985) found that forsuspensions of large particles, the suspension yield stress increased as the density differencebetween the particles and the suspending fluid increased as a result of these physical interactions.The apparent yield stress at high size ratios can therefore be explained by physical interactionsrather than by particle aggregation.As the fine fraction of non-aggregated small particles is increased, there is correspondingreduction in the fraction of large particles (see Equation 18.2). Therefore, the amount of energydissipated from the large particle interactions is decreased and the yield stress decreases.Based on the above explanations, the yield stress valley from the contour plot corresponds281to conditions for low aggregation effects and low particle inertia effects. Along a line of constantfine fraction, the yield stress is high at low size ratios due to aggregation effects. As the sizeratio is increased, the yield stress decreases until it reaches the bottom of the yield stress valleyafter which it begins to increase due to particle inertia effects. At small particle size ratios, theparticle inertia effects must therefore be quite small even if the suspension is composed of mostlylarge particles. It has been suggested that small particles act like ball bearings between coarseparticles (Eveson, 1953, Chong et al, 1971 and Round et al, 1984), which would reduce thefrictional energy dissipation. As the size ratio is increased above 0.1, the small particles beginto interact with the coarse particles (Fidleris and Whitmore, 1961) and therefore the ball bearingeffect is reduced. In addition, bimodal suspensions have been described as a suspension of largeparticles in a liquid with the viscosity and density of the fine particle suspension (Fidleris andWhitmore, 1961). In this case, the effective density differential between the large magnetiteparticles and fine particle suspension would decrease. As found by Laapas (1985), a decreasein density differential would result in a lower yield stress.For dense media separation it is desirable to minimize the yield stress of a suspension,since the yield stress contributes to its apparent viscosity. From the results, at low solids contentsthe yield stress is low and is not greatly affected by the size distribution. At high solids contents,particle size ratios and fractions of fine particles can be set to reduce the yield stress. For thetested particle size distributions, the results indicate that particle size ratios betweenapproximately 0.2 and 0.3 correspond to a low yield stress.28218.5.2 Effect of Particle Size Distribution on the Casson ViscosityOver the tested ranges of the variables, the Casson viscosity was found to depend on theratio of mean particle sizes and solids content but was not dependent on the fine fraction (Table18.4). A contour plot of the Casson viscosity against solids content and size ratio shows that amaximum viscosity exists along a ridge that rises along a diagonal line with increasing solidscontent and size ratio (Figure 18.6).The Casson viscosity represents the suspension viscosity at high shear rates. At such highshear rates, the magnetite particles are expected to be dispersed due to the shear conditions.Therefore particle aggregation is not considered to be significant. Hydrodynamic effects,electroviscous effects and inertial effects can, however, be important.The plot indicates that for a low suspension solids content (less than approximately 15%),decreasing the size ratio increases the Casson viscosity. Since the coarse fraction size is fixed,decreasing the size ratio corresponds to a decrease in the particle size of the fine fraction. Asthe size of fine particles is decreased, the specific particle surface area of the suspensionincreases. Since the magnitudes of hydrodynamic effects (Yen, 1968, Yucel and Hughes, 1984)and electroviscous effects (Goodwin, 1981) are proportional to the specific surface area, theviscosity increases with decreasing particle size ratio.Conversely, at a high suspension solids content (greater than approximately 20%),increasing the particle size ratio results in an increase in the Casson viscosity. Since themagnetite is much denser than the water, at the high shear rates, solids contents and size ratios,particles can collide and dissipate energy as a result of friction and losses of translational and2830.300.26C0 665[ 0Z ?‘73G) 0.18FD>0.140.100.100 0.225 0.350 0.475 0.600Size RatioFigure 18.6 Response contours of the Casson viscosity (mPa.s) as a function of size ratio andvolume solids fraction.284rotational momentum (Clarke, 1967, Brenner, 1972). It has been shown that physical interactionsbetween the small particles and large particles become more significant as the size ratio isincreased (Fidleris and Whitmore, 1961), resulting in an increased viscosity.Based on the above explanations, the maximum Casson viscosity along the rising ridgecorresponds to conditions of high inertial, hydrodynamic and electroviscous effects. To reducethe high shear rate viscosity of magnetite dense media at low solids contents (less thanapproximately 15%), the particle size ratio should be as large as possible to minimizehydrodynamic effects and electroviscous effects. To reduce the viscosity at high media densities(greater than approximately 20%), the particle size ratio should be as small as possible tominimize the contribution of the small particles to the inertial effects.From previous investigations with bimodal suspensions, Klein et al (1988) showed thatthe plastic viscosity (Bingham plastic equation) was a minimum at a fine fraction ofapproximately 0.30. No such minimum was observed for the Bingham yield stress whichgradually increased with increasing fine fraction. From the experiments carried out in this study,a minimum Casson yield stress occurred along a line of increasing fine fraction and size ratio andit was found that over the tested levels of variables, the Casson viscosity was not dependent onthe fine fraction. The apparent discrepancy can be explained by the different fits of the twoequations to the flow curves. It should be noted that the Casson equation fits the rheologicalcurves better than the Bingham equation. In particular, the minimum obtained for the plasticviscosity corresponds to the minimum in the Casson yield stress rather than to a minimum in theCasson viscosity.28518.5.3 Effect of Particle Size Distribution on the Settling RateTable 18.4 indicates that each of the variables, size ratio, fine fraction and solids content,affected the settling rate of the suspensions. The table shows that second order terms andinteractions between the variables influenced the settling rate. To illustrate how the settling rateis affected by the variables, contour plots of settling rate as a function of fme fraction and sizeratio at solids contents of 12.5% and 17.5% are presented in Figures 18.7 and 18.8, respectively.The plots show that the suspension settling rate is lowest when the size ratio is small andthe fine fraction is large. The effect of small particles on the settling rates of poly-dispersesuspensions has been explained in terms of the “carrier” properties provided by small particlesto large particles (Selim, 1983, Williams and Amarasinghe, 1989). Specifically, the fine particlesand water behave like a dense viscous liquid to the large particles and thereby decrease thesettling rate.As discussed in previous sections, the fine magnetite particles can form a loose aggregatedstructure as a result of remnant magnetism. The existence of a continuous structure depends onthe size and solids fraction of fine particles. At sufficiently high fraction of small particles, thisstructure can support the larger particles and thereby reduce their settling rate. The existence ofa structure is supported by the relationship between the yield stress and the settling rate (Figure18.9). The figure shows the same type of relationship that was observed in Chapter 17.Specifically, a non-linear relationship exists between the settling rate and the yield stress in whicha low yield value corresponds to a high settling rate and vice versa. This relationship indicatesthat the settling rate is affected by the same structure that is responsible for the yield stress.286C0I.0cv5UG)CU-Figure 18.7 Response contours of the settling rate (cm min’) as a function of size ratio andfine fraction (magnetite volume solids fraction = 0.125).0500.450.400,350.300.250.200.150.100 0.225 0.350 0.475Size Ratio0600287Figure 18.8 Response contours of the settling rate (cm min’) as a function of size ratio andfine fraction(magnetite volume solids fraction = 0.175).C00UCU-0500.450.400.350.300.250.200150,100 0.225 0.350 0.475Size Ratio0.600288CD 0 ce. CD CD CD CD C’)“C< CD C’) CD C’) C’) CD (4) CDICCassonYeIdStress(PG.)CCCPC\)•o:.-I’.).0)U)CD D CD c)CD C) 3 3 DCi,.C)It is worth noting that no relationship was found between the viscosity term and thesettling rate. It is therefore apparent that the relationship between the apparent viscosity and thestability of magnetite dense media that is referred to in the literature (Davis, 1987, Napier-Munn,1990) can be attributed to the contribution of the yield stress to the apparent viscosity.Examination of the contour lines in Figures 18.7 and 18.8 indicates that the size ratio hasa more significant effect than the fraction of small particles. This result suggests that to achievea good media stability, either a small amount of very fine particles, or significantly larger amountof slightly larger particles, can be added to the medium. Therefore, to improve media stabilityit may be possible to add small amounts of very fine magnetite to the dense medium circuitperiodically.18.5.4 Optimization of Medium PropertiesAs discussed in the previous sections, particle size distribution can be manipulated tocontrol the properties of magnetite dense media. Optimum media properties refer to a mediumwith a low settling rate, a low Casson yield stress and a low Casson viscosity. For coalpreparation, medium solid contents range from 10% to 20% over which range rheologicalproperties must be compromised to ensure adequate stability. At higher medium densities usedfor the separation of minerals, the medium can be excessively viscous while the stability is oflesser concern. The results indicate that the medium properties can be improved by manipulatingthe particle size distribution of the dense medium.The results imply that the medium stability can be improved at low medium densities by290the addition of a small amount of very fme magnetite particles. Alternatively, the same stabilitycan be produced by adding significantly larger amounts of slightly larger particles (15 l.im). Theresults showed that adding a small amount of very small magnetite particles (- 10 .im) did notgreatly increase the Casson yield stress. However, adding larger amounts of slightly largerparticles (15 im) increased the yield stress substantially. Therefore to improve the mediumstability without adversely affecting the yield stress, it is recommended to add a relatively smallamount of very fine magnetite to the medium.At high medium densities (2000 kg m3), the suspension yield stress is lowest for the sizeratio range of 0.20 to 0.35. However, over this range of size ratios, the Casson viscosity is quitehigh. To reduce the viscosity, lower size ratios should be used (Figure 18.6) which increases theyield stress (Figure 18.5). Therefore, at high medium densities there must be a compromisebetween the Casson yield stress and the Casson viscosity.18.6 ConclusionsExperiments were performed to investigate the effect of particle size distribution on theproperties of magnetite dense media. The suspensions exhibited shear thinning rheologicalproperties that were modelled with the Casson equation.Models were developed for the suspension settling rate, the Casson yield stress and theCasson viscosity as a function of the solids content and the bimodal size distribution parameters,mean size ratio and fine fraction. It was found that second order models with interaction termswere required to fit the responses to the variables.291The Casson yield stress was found to depend on each of the variables; size ratio, finefraction and solids content. At a given solids content, it was found that a minimum yield stressexisted that is a function of the size ratio and the fine fraction. Contour plots of yield stress asa function of size ratio and fine fraction showed that the minimum yield stress occurred alonga valley with a trend corresponding to increasing size ratio and fine fraction. At size ratios ofapproximately 0.2 to 0.3, the fine fraction had only a small effect on the yield stress. Increasingthe solids concentration enhanced the effect of size distribution on the yield stress.The Casson viscosity was found to depend on the size ratio and solids content; however,for the investigated levels of the variables, the viscosity did not depend on the fine fraction. Acontour plot of viscosity as a function of the size ratio and solids content, showed that a viscositymaximum exists along a ridge. The trend of the ridge corresponded to increasing size ratios andsolids contents.The settling rate was found to depend on each of the variables; size ratio, fine fractionand solids content. Contour plots at given solids contents revealed that the settling rate decreased(stability improved) with decreasing size ratio and increasing fine fraction. The results indicatedthat the size ratio affected the settling rate more than the fine fraction. At low solids contentsthe effect of size ratio was very pronounced indicating that media stability could be easilyimproved by adding a small amount of very fine magnetite particles.It was found that the settling rate and the Casson yield stress are interrelated in a nonlinear manner. A suspension with a high yield stress has a low settling rate and vice versa. Therelationship can be explained by the existence of a structure in the suspension.292CHAPTER 19: CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK19.1 ConclusionsThe conclusions drawn from the experimental programs carried out in the thesis are asfollows.1. Settling tests on suspensions of magnetite particles with solids contents typically foundin dense media indicated that:i. Magnetite suspensions exhibit bulk (hindered) rather than differential settlingproperties.ii. The bulk settling properties were characterized by the presence of four zones (fromtop to bottom): a supematant, a transition zone, a constant density zone and a sediment. Theconstant density zone has a solids content that is approximately equal to that of the initialsuspension.iii. The mudline settling rate of a magnetite suspension is very close to the settlingrate of the transition zone - constant density zone interface. Since the extent of the constantdensity zone and the rate at which it diminishes in size characterizes the medium stability, themudline settling rate provides a good indication of the settling stability.2. A rheometer fixture was developed to measure the rheological properties of settlingsuspensions. The fixture is a modified double gap concenthc cylinder cup and bob arrangementthat attaches to rotational viscometers. It was designed for suspensions exhibiting zone settlingproperties by positioning the bob in the constant density zone during the rheological293measurements. The design also accounts for typical measurement errors associated with wall slipand end effects and it is surrounded by a temperature controlled water jacket so that thesuspension temperature can be controlled. The fixture is an improvement over existing devicessince no undefined shearing is required to maintain a homogeneous suspension compositionduring rheological measurements.Measurement procedures were developed to account for non-Newtonian shear rate effects,bob inertia effects and high shear rate limitations due to turbulence. The new device was usedto characterize the rheological properties of magnetite suspensions and to study the effects ofsuspension variables on these rheological properties. More recently it has been used to measurethe rheological properties of quartz suspensions and of various sulphide mineral suspensions.3. Rheological measurements on magnetite suspensions with compositions found in densemedia indicated that:i. Magnetite dense media exhibits shear thinning flow properties with an apparentyield stress.ii. The Casson flow curve model, which is a simple two parameter equation, can beused to characterize the flow behaviour of magnetite suspensions. The model was found to fitthe flow curves better than other well known models including the Herschel Bulkley, Carreau andCross models.iii. Magnetite suspensions exhibit thixotropic properties that are enhanced bymagnetizing the suspension particles.iv. The apparent yield stress, the thixotropic properties and zone settling propertiesexhibited by magnetite suspensions suggest that a structure exists in these suspensions. The294structure is believed to result from particle aggregation that can be attributed to remnant particlemagnetism.v. The Bingham plastic equation could not fit the curvature of the flow curve dataat low shear rates and was therefore not considered to be a suitable model. The review of theliterature indicated that, because the Bingham equation cannot fit the curvature, exhibited bymany suspensions, at low shear rates the model over estimates the yield value. However, yieldvalues determined from the Casson equation compared well to those determined using directmeasurement procedures.4. From a statistically designed experimental program, the effects of physico-mechanicalparameters (magnetite solids content and particle size), physico-chemical parameters (pH, sodiumsilicate, carboxylmethyl cellulose and demagnetization) and contaminants (coal fines, kaoliniteand bentonite) on measured settling and rheological properties were investigated. For a diverseset of parameter conditions, the results of the experimental program revealed that:i. The suspensions exhibit thinning flow behaviours and have an apparent yieldstress.ii. The flow behaviours can be accurately modelled using the Casson equation whichwas found to provide a better fit to all twenty sets of flow curves than the Herschel Buildey,Carreau and Cross models.iii. The Casson yield stress was influenced significantly by most of the suspensionvariables while the Casson viscosity was affected by only a few of the parameters indicating thatthe yield stress term is the most controllable rheological property.iv. The Casson yield stress dominated the viscous properties of the suspension. In295particular, the contribution of the Casson yield stress to the apparent viscosity is significantlygreater than the contribution from the Casson viscosity term.v. The suspension parameters that influenced the yield stress term most, also had thegreatest effect on the mudline settling rate. It was revealed that the yield stress and the settlingrate are inversely related such that when the yield stress is high the setting rate is low and viceversa.vi. Based on the magnitudes of the effects on the measured responses, the magnetitesolids content, particle size and pH are the most significant parameters.vii. Increasing the solids content resulted in an increased Casson yield stress and adecreased settling rate while the Casson viscosity was not significantly affected. Increasing theparticle size decreased the Casson yield stress, increased the settling rate and had no effect onthe Casson viscosity. An interaction effect between solids content and particle size alsoinfluenced the yield stress and settling rate responses.viii. Since changes in pH did not alter the settling rates of pure magnetite suspensions,its effect on the suspensions in the experimental program was attributed to its influence on clayparticle coagulation and its interactions with sodium silicate and carboxylmethyl cellulose.ix. Increasing the pH decreased the Casson yield stress and increased both the settlingrate and Casson viscosity. The results can be explained as follows. In the acidic and neutral pHrange clay particles coagulate to form a structure that contributes to the yield stress and preventsparticle settling. In the basic pH range, the clay particles disperse resulting in a lower structuralstate which corresponds to a lower yield stress and allows particles to settle. In addition, withincreasing pH electrostatic repulsive forces between particles may enhance the contributions of296electroviscous effects to the Casson viscosity.x. At high pH, the dispersants, sodium silicate and carboxylmethyl cellulose, becamemore effective. The interaction effect between pH and the dispersing agents revealed that byjointly increasing the pH and dispersant dosages the Casson yield stress decreased and the settlingrate and Casson viscosity increased. The carboxylmethyl cellulose influenced the suspensionproperties more than the sodium silicate.xi. Demagnetization improves media properties by decreasing the Casson yield stressand increasing the settling rate but does not significantly influence the Casson viscosity.5. The effects of bimodal particle size distribution on the rheological and settling propertiesof magnetite suspensions were investigated using a statistically designed experimental program.The findings are as follows:i. The determined responses, Casson yield stress and settling rate are affected by theparticle size distribution parameters which include the ratio of mean particle sizes of the two sizefractions and the fraction of the solids that are fine particles. For the levels of the sizedistribution variables investigated, the Casson viscosity was influenced by the particle size ratiobut not by the fme fraction. The effects of size distribution on the rheological properties wasmore pronounced at a high solids content.ii. The Casson yield stress was modelled using a second order equation as a functionof the size ratio, the fine fraction and the solids content. The model revealed that a minimumapparent yield stress exists along a line of compositions corresponding to increasing size ratiosand fine fractions. The minimum is most pronounced over the size ratio range of 0.2 to 0.35.At a high suspension solids content, the effects of size distribution on the yield value are much297more pronounced.iii. The Casson viscosity was found to be affected by the size ratio and solids contentin a non-linear manner that was modelled using a second order equation. The model indicatedthat the viscosity term was a maximum along a line of composition corresponding to increasingsize ratio and solids content.iv. The mudline settling rate was modelled as a function of size ratio, fine fractionand solids content using a second order equation. The model revealed that the settling ratedecreased in a non-linear manner with increasing size ratio and fine fraction. The size ratio wasshown to be more significant than the fine fraction. In particular, the results indicated thatstability of bimodal suspensions can be improved by using a small fine fraction of particles witha very small size ratio or by using a much greater fine fraction of particles with slightly largersize ratio.v. From the results of the experimental program it was found that the Casson yieldstress and the settling rate are inversely in the same manner as was indicated from investigationsinto the effects of various parameters on the medium properties. Specifically, when thesuspension yield value is high the settling rate is low and vice versa. This result suggests thatthe relationship between media viscosity and stability that is referred to in the literature can bemore accurately attributed to the yield stress - settling rate relationship.29819.2 Recommendations For Further Work1. The test work carried out for this thesis is part of ongoing research in the Department ofMining and Mineral Process Engineering to study the dense media separation process. Theresults of this thesis should be applied to this research. Specifically, the results should be usedto develop models that relate separation performance to accurately characterized rheological andsettling properties. From models of this type, the medium properties that are important to theseparation performance could be assessed using bench scale test work. Once such relationshipsexist, the effects of various parameters (magnetite particle size, pH, etc.) on separationperformance can be assessed.2. From electrophoretic mobility (EPM) measurements, it was found that the magnetitesample exhibited an anomalous iso-electric point. Since surface chemical interactions with otherparticles and with various surfactants may be important to the medium rheology and stability, thisanomalous result should be investigated. Specifically, measurements were made using ungroundmaterial which may have been coated with precipitates produced from weathering. Therefore,EPM measurements should be made using a sample with freshly ground surfaces.3. It was found that magnetite suspensions exhibit zone settling properties characterized bythe existence of a constant density zone. While the solids content of this zone was constantthrough its vertical extent, tests were not performed to determine the size distribution at differentlevels. To confirm that differential settling does not occur, such a study should be carried out.4. To investigate the implications of the shear thinning flow properties and the apparent yieldstress to the dense medium separation process, there is a need to know how these properties299influence particle settling. Specifically, tests should be performed to determine if the apparentyield value affects particle settling through its contribution to the apparent viscosity or if it is ameasure of an additional stress that must be overcome before a particle can settle. Test thatrelates drag coefficients to the Casson model coefficients would be useful. Investigations shouldalso be carried out to provide better estimates of the effective shear rates experienced by coalparticles in the separator.5. Due to the potential implications of a yield stress on separation performance, test workshould be carried out to determine if magnetite dense media exhibits a true yield value. Thiscould be tested by using direct yield stress measurement procedures such as the vane method (seeSection 6.3).6. The inverse relationship between the Casson yield stress and the settling rate wasexplained by the presence of a structure that influence both medium properties. Test work shouldbe performed to provide more evidence of the structure. Direct measurements of the yield stressas recommended above would provide additional evidence.7. Results of the experimental test work indicated that the properties of magnetite densemedia can be controlled by manipulating various parameters. Further investigations into theeffects of many of these parameters (particle size, magnetization and the additions of dispersants)is warranted. Specifically:i. The addition of C.M.C. was found to decrease the settling rate of pure magnetitesuspensions; however, no experiments were performed to determine the effect of C.M.C. on therheological properties of pure magnetite suspensions.ii. The rheological and settling test results could be explained by the presence of a300structure resulting from magnetic aggregation of particles. Despite demagnetization, thesuspensions still exhibited an apparent yield stress, thixotropic properties and zone settlingproperties. The results indicated that demagnetization was not complete which was attributed tothe difficulties associated with demagnetizing fine magnetite particles. To confirm thisexplanation, it is recommended to investigate the effect of demagnetization on fine magnetiteparticles.iii. To achieve good stability and rheological properties in dense media, it has beenrecommended to use fine magnetite particles for low media densities and large particles for highmedia densities. This practice is supported by the experimental results which showed that mediaproperties are influenced by an interaction effect between solids content and particle size. Moredetailed information concerning this interaction effect may assist in determining optimum particlesizes for specific media densities.8. Experiments carried out to investigate the effect of particle size disthbution on mediaproperties indicated that the size distribution can be manipulated to optimize media properties.Further experiments are required to more accurately define particle size distributionscorresponding to optimum media properties.9. This work emphasizes the importance of accurately characterizing the rheologicalproperties of magnetite suspensions so that the effects of media parameters can be understood.The rheometer fixture developed to measure the rheological properties of settling suspensionscould also be used to characterize the rheological properties of other industrially importantunstable suspensions.301REFERENCESAarnio, A.A., Laapas, H.R., 1988, “Rheological Properties of Finely Ground Quartz and FeldsparSlurries”, Proc. 10th Tnt. Congr. on Rheol., 1, P.H. Uhiher, ed, Australian Society ofRheology, Sydney, 119-121.Ahuja, S.K., Isganitis, L., 1988, Viscoelasticity of Non-aqueous Suspensions”, Proc. 10th mt.Congr. on Rheol.,!, P.H. Uhiher, ed, Australian Society of Rheology, Sydney, 131-3.Al-Fariss, T., Pinder, K.L., 1987, “Flow Through Porous Media of a Shear-Thinning Liquid withYield Stress”, Can. J. Chem. Eng., 65, 391-406.Alderman, N.J., Ram Babu, D., Hughes, T.L., Maitland, G.C., 1988, “The Rheological Propertiesof Water-Based Drilling Fluids”, Proc. 10th Tnt. Congr. on Rheol., 1, P.H. Uhlher, ed,Australian Society of Rheology, Sydney, 140-2.Allen, T., 1990, Particle Size Measurement, 4th ed., Chapman and Hall, New York, 806.Alessandrini, A., Kikic, I., Lapasin, R., 1983, “Rheology of coal suspensions”, Rheol. Acta,500-4.Anon, 1985, “The Testing of Magnetite for Use in Coal Preparation”, Draft Proposal ISO/DP8833,22pp.Aplan, F.F., Spedden, H.R., 1964, “Viscosity Control in Heavy-Media Suspensions”, Proc. 7thTnt. Mm. Proc. Congr., N. Arbiter, ed, Gordon & Breach, New York, 103-113.Atlas, H., Casassa, E.Z., Parfitt, G.D., Rao, A.S., Toor, E.W., 1985, “The Stability and Rheologyof Coal/Water Slurries”, 10th Ann. Powder & Bulk Solids Conf. Proc., Rosemont, ill.,University of Microfilm International, Ann Arbor, Michigan, 77 1-8.Berg, R.H., 1958, “Electronic Size Analysis of Subsieve Particles by Flowing Through a SmallLiquid Resister”, Special Technical Publication, 234, Am. Soc. for Testing Materials.Berghofer, W., 1959, “Konsistenz und Schwertrubeaufbereitung”, Bergbauwissenschaffen, 6(20),493-504, 533-541.Boger, D.V., Sarmiento, G., Tiu, C., Uhlherr, P.H.T., 1978, “Flow of Mineral Slurries”, The Aus.1MM Conference, North Queensland, 29 1-8.Bradley, D., The Hydrocyclone, Pergamon Press, New YorkBrenner, H., 1972, “Suspension Rheology”, Progress in Heat and Mass Transfer, W. Schowalter,ed, Pergamon Press, New York, 89-129.302Brown, J.P., Pinder, K.L., 1971, “Time Dependent Rheology of Artificial Slurries”, Can. J. Chem.Eng., 49, 38-43.Burch, E, Stone, C, 1985, “Feeding to Zero: Island Creek’s Experience in Kentucky”, Coal Age,.L 66-70.Burt, R.O., 1984, Gravity Concentration Technology, Elsevier, Amsterdam, p. 567.Cann, R.M., 1979, Geochemistry of Magnetite and the Genesis of Magnetite-Apatite Lodes inthe Iron Mask Batholith, British Columbia, M.Sc Thesis, University of British Columbia.Carreau, P.J., 1972, “Rheological Equations from Molecular Network Theories”, Trans. Soc.Rheology, 16(1), 99-127.Carreau, P.J., De Kee, D., 1979a, “Review of Some Useful Rheological Equations”, Can. J.Chem. Eng., 57, 3-15.Carreau, P.J., De Kee, D., 1979b, “An Analysis of the Viscous Behaviour of PolymericSolutions”, Can. J. Chem. Eng., 57, 135-140.Castillo, C., Williams, M.C., 1979, “Rheology of Very Concentrated Coal Suspensions”, Chem.Eng. Commun., 3, 529-547.Casassa, E.Z., Parfitt, G.D., Rao, A.S., Toor, E.W., 1984, “The Effect of Surface ActiveAdditives on Coal/Water Slurry Rheology”, ASME Spec. Publ. 84-WA/HT-96, l0pp.Casson, N., 1959, “A Flow Equation for Pigment-oil Suspensions of the Printing Ink Type”,Rheology of Disperse Systems, C.C. Mill, ed, Pergamon Press, New York, 84-104.Chakravarti, A.K., Chattopadhyay, 3., Sarkar, G.G., Lahiri, A., 1958, “A Study of the Propertiesof Some Suspensions Suitable for Use in Dense Media Coal Washing”, md. Mi J., 6,1-11.Chance, T.M., 1924, “A New Method of Separating Materials of Different Specific Gravities”,Trans. AIME ,70,740-749.Chaston, R.R.M., Napier-Munn, T.J., 1974, “Design and Operation of Dense-medium CyclonePlants for the Recovery of Diamonds in Africa”, 3. S. Afr. Inst. Mm. Met., 75(1), 120-133.Chen, Z.Q., Xin, Y.Ch., Lu, Ch.X., 1988, “Negative thixotropic behaviour of montmorillonite andhydrolyzed polyacrylamide system”, Progress and Trends in Rheology II, Prague, H.Giesekus, ed, Springer-Verlag, New York, 328-9.303Cheng, D.C-H., 1971, “The Characterization of Thixotropic Behaviour”, Warren SpringLaboratory, LR 157(MH), 29pp.Cheng, D.C-H., Richmond, R.A., 1978, “Some observations on the rheological behaviour ofdense suspensions”, Rheol. Acta., 17, 446-453.Cheng, D.C-H., 1980a, “Sedimentation of suspensions and storage stability”, Chem. and Ind.,5,407-4 14.Cheng, D.C-H., 1980b, “Viscosity-concentration equations and flow curves for suspensions”,Chem.and Ind.,5 403-6.Cheng, D.C-H., 1984, “Further Observations of the Rheological Behaviour of DenseSuspensions”, Powder Tech., 37, 255-273.Cheng, D.C-H., 1985, “Yield Stress: A Time-dependent Property and How to Measure It”, NewTechniques in Experimental Rheology, Reading, England, Brit. Soc. of Rheol. Conf.,l4pp.Cheng, D.C-H., 1988, “High Shear Limitations in Viscometers”, Proc. 10th Tnt. Congr. onRheol., j, Sydney, P.H. Uhlherr, ed, Australian Society of Rheology, 250-3.Chong, J.S., Christiansen, E.B., Baer, A.D., 1971, “Rheology of Concentrated Suspensions”, LAppl. Polymer Sci., 15, 2007-2021.Clarke, B., 1967, Rheology of Coarse Setting Suspensions”, Trans. Inst. Chem. Eng., 45, T251-6.Collins, B., Napier-Munn, T.J., Sciarone, M., 1974, “The production, properties, and selection ofFerrosilicon powders for heavy-medium separation”, J. S. Afr. Inst. Mm. and Met., 12,103-119.Collins, D.N., Tumbull, P., Wright, R., Ngan, W., 1983 “Separation efficiency in dense mediacyclones”, Trans 1MM, 92, C38-C51.Cormode, D.A., White, G.A., 1988, “Heavy media separation studies at Cominco potash”, Proc.90th An. Meet. of the CIM, Edmonton, CIM, Montreal, 25pp.Cross, M.M., 1964, “Rheology of Non-Newtonian Fluids: A New Flow Equation forPseudoplastic Systems”, J. Coll. Sci., 90, 417-437.Cross, M.M., 1969, “Kinetic Interpretation of Non-Newtonian Flow”, J. Coll. Interf. Sci., 33(1),30-5.Czaban, S., Parzonka, W., Havlik, V., 1988, “Non-Newtonian behaviour of kaolin suspensions”,304Progress and Trends in Rheology II, Prague, H. Giesekus, ed, Springer-Verlag, New York,325-8.Davis, J.J., Lyman, G.J., 1983, “Magnetite Recovery Using a Wet Drum Separator”, Proc.Australas. Inst. Mm. Met., 7.., 51-60.Davis, J.J., 1987, “A Study of Coal Washing Dense Medium Cyclones”, PhD. Thesis, Universityof Queensland, Brisbane, ll3pp.Davis, 1.1., Wood, CJ., Lyman, G.J., 1985, “The Use of Density Tracers for the Determinationof Dense Medium Cyclone Partition Characteristics”, Coal Prep., 2, 107-125.Davis, J.J., Napier-Munn, T.J., 1987, “The Influence of Medium Viscosity on the Performanceof Dense Medium Cyclones in Coal Preparation”, Proc. 3rd mt. Conf. on Hydrocyclones,Oxford, P. Wood, ed, Elsevier, New York, 155-165.Davies, R.J., 1986, “Report on Survey of Magnetite-Medium Usage in Heavy Media CoalCleaning”, EMR Canmet.Davies, R.J., 1986, “Report on Plant Procedures and Magnetite Testing and Analysis”, EMRCanmet.Dedegil, M.Y., 1986, “Drag Coefficient and Settling Velocity of Particles in Non-NewtonianSuspensions”, ASME Fluids Engineering Division, , 9-15.Derjaguin, D.V., Landua, L.D., 1941,”Theory of the Stability of Strongly Charged LyophobicSols and of the Adhesion of Strongly Charged Particles in Solutions of Electrolytes:, ActaPhysiochim, 14, USSR, p. 633-622.Derjaguin, D.V., 1989, “Theory of stability of colloids and thin films”, Consultants Bureau, NewYork.Deurbrouck, A.W., Hudy, Jr., J., 1972, “Performance Characteristics of Coal-WashingEquipment: Dense-Medium Cyclones”, USBM RI-7673, 34pp.DeVaney, F.D., Shelton, S.M., 1940, “Properties of Suspension Mediums for Float-and-SinkConcentration”, USBM RT-3469R, 66pp.Doraiswamy, D., Tsao, I.L., Danforth, S.C., Beris, A.N., Metzner, A.B., 1988, “The Rheologyof Ceramic Suspensions”, Proc. 10th Tnt. Cong. on Rheol., 1, Sydney, P.H. Uhlherr, ed,Australian Society of Rheology, 300-2.Dreissen, H., Jennekens, H., 1982, “History of Coal Washing in Holland and Its Impact Abroad”,Proc. 9th Tnt. Coal Prep. Cong., New Delhi, S.R.R. Rao, ed, Indian Organizing305Committee for 9th Tnt. coal Prep. Congr., Calcutta, 73-8.Du Plessis, M.P., Ansley, R.W., 1967, “Settling Parameters in Solid Pipe Lining”, Proc. Am. Soc.Civ. Eng. J., 93, 1-17.Duty, R.L., Reid, W.H., 1964, “On the stability of viscous flow between rotating cylinders” jof Fluid Mech., 20(1), 8 1-94.Eilers, H., 1941, Kolloid Z.Z. Polymer, 97, p. 313.Einstein, A., 1905, Ann. Phys., 17, p. 459.Erten, M.H., 1964, “Investigations of the Effects of Magnetization and Demagnetization on theSettling Rate and Viscosity of Magnetite Dense Media used in Dense-Medium CoalWasheries”, Habilitation Thesis, Orta Dugo Teknik Universitesi, pp. 165.Everett, D.H., 1988, The Basic Principles of Colloid Science, The Royal Society of Chemistry,22lpp.Eveson, G.F., 1953, “Properties of Suspensions Used in Coal Cleaning”, J. Inst. Fuel, 26(152),139-145.Eveson, G.F., 1957, “The Viscosity of Stable Suspensions of Spheres at Low Rates of Shear”,Rheology of Disperse Systems, C.C.Mill, ed, Pergamon Press, New York, 61-9.Eveson, G.F., 1959, “A Rheological Approach to Certain Features of Dense-Medium Coal-Cleaning Plant Operation”, J. Oil Colour Chem., 42, 146-179.Farris, R.J., 1968, “Prediction of the Viscosity of Multimodal Suspensions from UnimodalViscosity Data”, Trans. Soc. Rheol., 12(2), 281-301.Fedors, R.F., 1973, “Relationships Between Viscosity and Concentration for NewtonianSuspensions”, J. Coll. Interf. Sci., 46(3), 545-7.Fedors, R.F., 1975, “Viscosity of Newtonian Suspensions”, Polymer, j, 305-6.Fedors, R.F., 1979a, “A Relationship between Maximum Packing of Particles and Particle Size”,Powder Tech., 23, 7 1-6.Fedors, R.F., Landel, R.F., 1979b, “Effect of Surface Adsorption and Agglomeration on thePacking of Particles”, Powder Tech., 23, 219-223.Fedors, R.F., Landel, R.F., 1979c, “An Empirical Method of Estimating the Void Fraction inMixtures of Uniform Particles of Different Size”, Powder Tech., 23, 225-231.306Fern, K.A., 1952, “The Cyclone as a Separating Tool in Mineral Dressing”, Trans Instn ChemEngrs,30, 82-86.Ferrara R.F., 1973, “Relationships Between Viscosity and Concentration for NewtonianSuspensions”, J. Coll. Interf. Sci., 46(3), 545-7.Ferrara, G., Schena, G.D., 1986, “Influence of contamination and type of ferrosilicon on viscosityand stability of dense media”, Trans 1MM, 95, C21 1-5.Ferrara, G., Schena, G.D., 1987, “Cycloning in Dense Media Separation”, Proc. 3rd Tnt. Conf.on Hydrocyclones, Oxford, P. Wood, ed, Elsevier, New York, 101-110.Ferrara, G., Schena, G.D., 1988, “Design Criteria and Control Strategies for Dynamic DenseMedia Separation Processes Treating Fine Ores”, Proc. 16th Tnt. Mm. Proc. Congr., ,E.Forsberg, ed, Elsevier, Amsterdam, 885-904.Ferrini, F., Ercolani, D., de Cindio, B., Nicoclemo, L., Nicolais, L., Ranaudo, S., 1979, “Shearviscosity of settling suspensions”, Rheol. Acta, 18(2), 289-296.Ferrini, F., Battarra, V., Donati, E., Piccinini, C., 1984, “Organization of Particle Grading forHigh Concentration Coal Slurry”, Hydrotransport 9, Rome, BHRA Fluid Engineering,75pp.Fidleris, V., Whitmore, R.N., 1961, Rheol. Acta., 1, 4-6.Firth, B.A., Hunter, R.J., 1976, “Flow Properties of Coagulated Colloidal Suspensions. III. TheElastic Floe Model”, J. Coll. Interf. Sci., 57, 266-275.Fourie, P.J.F., Van Der Walt, P.J., Falcon, L.M., 1980, “The beneficiation of fine coal by dense-medium cyclone”, J. S. Afr. 1MM, 80, 357-361.Frankel, N.A., Acrivos, A., 1967, “On the viscosity of a concentrated suspension of solidspheres”, Chem. Eng. Sci., 22, 847-853.Friend, J.P., Kitchener, J.A., 1973, “Some Physico-chemical Aspects of the Separation of FinelyDivided Minerals by Selective Flocculation”, Chem. En. Sci., 28, 107 1-1080.Furnas, C.C., 1931, “Grading Aggregates. I. Mathematical Relations for Beds of Broken Solidsof Maximum Density”, md. and Eng. Chem., 23(9), 1052-1064.Geer, M.R., Sokaski, M., West, J.M., Yancey, H.F., 1957, “The Role of Viscosity in DenseMedium Coal Cleaning”, USBM RI-5354, 2Spp.Gillespie, T., 1963, “The Effect of Size Distribution on the Rate Constants for Collisions in307Disperse Systems”, J. Coil. Sci., 18, 562-7.Goldsmith, H.L., Mason, S.G., 1967, “The Microrheology of Dispersions”, Proc. 4th Tnt. Congr.on Rheology, Providence, Rhode Island, F.R. Eirich, ed, John Wiley & Son, New York,85-250.Goodwin, J.W., 1981, “Some Uses of Rheology in Colloid Science”, Colloidal Dispersions, J.W.Goodwin (ed), Royal Society of Chemistry, London, 165-195.Govier, G.W., Shook, C.A., Lilge, E.O., 1957, “The Rheological Properties of Water Suspensionsof Finely Subdivided Magnetite, Galena and Ferrosiicon”, CIM Trans., , CIM pubi.,147-154.Graebel, W.P., 1964, “The Hydrodynamic Stability of a Bingham Fluid in Couette Flow”,Secondorder Effects in Elasticity, Plasticity and Fluid Dynamics,, M. Reiner, D. Abir, ed,Pergamon Press, Oxford, 636-649.Graham, C.C., Lamb, R., 1982, “Coal Preparation - Dense Media Rheology A Review ofMeasurement and Control”, ACIRL P.R.-82-3, 52pp.Graham, C.C., Lamp, R., 1983, “A Study of Dense Media Rheology”, Proc. 2nd Austr. CoalPrep. Conf., Rockhampton, 107-128.Greenspan, H.P., Ungarish, M., 1982, “On Hindered Settling of Particles of Different Sizes”, Tin.J. Multiphase Flow, 8(6), 587-604.Griskey, R.G., 1989, “How to Tame, Handle and Process Shear-Thickening Fluids; A VeryImportant but Poorly Understood Class of Non-newtonian Fluids”, ViscTech, Chicago,Omni Press 329-353.Hancock, K.D., 1988, Magnetite Occurrences in British Columbia, Prov. of B.C., Mm. of EnergyMines & Petrol Resources, pp.28.Hanks, R.W., 1981, “Hydraulic Design for Flow of Complex Fluids”, Course Notes, Society ofRheology, New York, 329pp.Harris, D.L., Reid, W.H., 1964, “On the stability of viscous flow between rotating cylinders.Part 2. Numerical analysis”, 3. Fluid Mech., 20(1), 95-101.Harris, J., 1977, Rheology and non-Newtonian Flow, Longman, New York.Hartig, H.E., Onstad, N.T., Foot, N.J., 1951, “Demagnetization of Magnetite”, Univ. of MinnesotaIC-No. 7, 22pp.308Helfricht, R., Schatz, J., 1989, “The Use of Dispersants in Kaolin Processing”, Proc. 2nd WorldCongress on Non-Metallic Minerals, Beijing, 735-740.Himmelblau, D.M., 1970, “Identification of the Best Models”, Process Analysis by StatisticalMethods, Wiley, New York, 208-283.Hocquart, R., Decruppe, J.P., Cressely, R., 1988, “Flow Birefringence of Solutions of RigidParticles Near the First Transition from Laminar Flow to Taylor Vortex Flow”, Proc. 10thmt. Cong. on Rheol., 1, P.H. Uhiher, ed, Australian Society of Rheology, Sydney, 410-2.Hone, M., Pinder, K.L., 1979, “Time-Dependent Shear Flow of Artificial Slurries in CoaxialCylinder Viscometer with a Wide Gap”, Can. J. Chem. Eng., 57, 125-134.Horsley, R.R., Snow, R.J., 1988, “The rheology of some Australian mine tailings”, Progress andTrends in Rheology II, Prague, H. Geisekus, ed, Springer-Verlag, New York, 344-6.Horsley, R.R., Allen, D.W., 1987, “The Effect of Yield Stress on Hydrocyclone Performance inthe Mining Industry”, Proc. 3rd Tnt. Conf. on Hydrocyclones, Oxford, P. Wood, ed,Elsevier, New York, 269-275.Hudy, J., 1968, “Performance Characteristics of Coal-Washing Equipment Dense-MediumCoarse-Coal Vessels”, USBM RI-7154, 29pp.Hunter, R.J., Firth, B.A., 1976, “Electrochemical Control of the Flow Behaviour of CoagulatedColloidal Sols”, Trends in Electrochemistry, J.O’M. Bockris, D.A.J. Rand, B.J.Welch, eds,Plenum Press, New York, 193-202.Hunter, R.J., 1985a, “Rheological and Sedimentation Behaviour of Strongly Interacting ColloidalSystems”, Modern Trends of Colloid Science in Chemistry and Biology, H.F. Eike, ed,Basel, Birkhauser Verlag, 184-202.Hunter, R.J., Everett, D.W., 1988, “The Elastic Behaviour of Coagulated Colloidal Dispersions”,Proc. 10th Tnt. Cong. on Rheology, 1, P.R. Uhlherr, Sydney, Australian Society ofRheology, 428-430.Iwasaki, I., Carlson, W.J., Parmerter, S.M., 1969, “The Use of Starches and Starch Derivativesas Depressants and Flocculants in Iron Ore Beneficiation”, Trans. AIME, 244, 88-98.Jones, R.L., Chandler, H.D., 1989, “The effect of drag-reducing additives on the rheologicalproperties of silica-water suspensions containing iron(llI) oxide and of a typical gold-mineslurry”, J. S. Afr. Inst. Mm. and Met., 89(6), 187-191.Jonker, L., 1984, “The Development of Standard Procedures for the Evaluation of Magnetite forUse in Heavy-Medium Separation”, MINTEK Report No. M144, 2lpp.309Kamiyama, S., Satoh, A., 1989, “Rheological Properties of Magnetic Fluids with the Formationof Clusters: Analysis of Simple Shear Flow in a Strong Magnetic Field”, J. Coll. Interf.Sci., 127(1), 173-188.Kelsall, D.F., 1952, “A Study of the Motion of Solid Particles in a Hydraulic Cyclone”, Trans.Inst. Chem. Eng., 30, 87-108.Kikkawa, H., Okiura, K., Arikawa, Y., 1984, “Development of Highly Loaded CWM PreparationSystem”, 921-932.Killmeyer, R.P., 1982, “Dense-Medium Cycloning of Fine Coal at Low Specific Gravities”, USDOEJPETC/TR-83/2, l3pp.King, R.P., Juckes, A.H., 1984, “Cleaning of Fine Coals by Dense-Medium Hydrocyclone”,Powder Tech., 40, 147-160.King, R.P., Juckes, A.H., 1988, “Performance of a Dense-Medium Cyclone When BeneficiatingFine Coal”, Coal Prep., 5, 185-210.Kirchberg, H., Topfer, E., Scheibe, W., 1975, “The effect of suspension properties on separatingefficiency of mechanical classifiers”, Proc. 11th mt. Mm. Proc. Cong., University ofCagliari, Italy, 219-244.Kitchener, J.A., 1969, “Colloidal Minerals: Chemical Aspects of their Dispersion, Flocculationand Filtration”, Filtr. and Sep., 6(5), 1-6.Kiassen, V.1., Litovko, V.1., Myasnikov, N.F., 1964, “Improvement of Physical and MechanicalProperties of Ferrosilicon Suspensions with Help of Reagents”, Proc. 7th Int. Mm. Proc.Cong.,i, N. Arbiter, Gordon and Breach, New York, 95-101.Klassen, V.1., Krasnov, G.D., Litovko, V.1., Blagova, Z.S., 1966, “New Methods of Preparation.Part I: Methods of Improving the Physical and Mechanical Properties of MagnetiteSuspensions”, 5th Int. Coal Prep. Conf., Pittsburgh, D.O.E., D5.Klein, B., Partridge, S.J., Laskowski, 1988, “Influence of Physicomechanical Properties on theRheology and Stability of Magnetite Dense Media”, mt. Symp. on the Prod. and Proc. ofFine Particles, Montreal, A.J. Plumpton, ed, Pergamon Press, Toronto, 397-407.Klein, B., Laskowski, J.S., Mular, A.L., 1990, “Rheology of Magnetite Dense Media: Modellingand Control”, Proc. 11th Int. Coal Prep. Congr., Tokyo, 5 1-56.Klembowski, 1986, “Continuous Measurements of Viscous Properties of Suspensions withSettling Particles”,Progress and Trends in Rheology II, Prague, H. Giesekus et. al., ed,Springer-Verlag, New York, 177-9.310Klima, M.S., Killmeyer, R.P., 1990, “Effect of Operating Conditions on Micronized-MagnetiteCycloning Performance”, Coal Prep’90, Cincinnati, l5pp.Krieger, I.M., Efrod, H., 1951, “Direct Determination of the Flow Curves of Non-NewtonianFluids. II. Shearing Rate in the Concentric Cylinder Viscometer”, J. Appl. Phys., 24(2),134-6.Krieger, I.M., Elrod, H., 1952, “Direct Determination of the Flow Curves of Non-NewtonianFluids. III. Standardized Treatment of Viscometric Data”, J. Appi. Phys., 25(1), 72-5.Krieger, I.M., Dougherty, T.J., 1959, “A Mechanism for Non-Newtonian Flow in Suspensionsof Rigid Spheres”, Trans. Soc. Rheol., ffl, 137-152.Krieger, I.M., 1968a, “Shear Rate in the Couette Viscometer”, Trans. Soc. Rheol., 12(1), 5-11.Krieger, I.M., 1968b, “Computation of Shear Rate in the Couette Viscometer”, Proc. 5th Tnt.Congr. on Rheol., Kyoto, S. Onagi, ed, University of Tokyo Press, Tokyo, 511-6.Krieger, I.M., 1971, “Rheology of Monodisperse Latices”, Advan. Coll. Tnterf. Sci., 3, 111-136.Krueger, ER., Gross, A., Di Prima, R.C., 1966, “On the relative importance of Taylor-vortex andnon-axisymmetric modes in flow between rotating cylinders”, J. Fliud Mech., 24(3), 521-538.Laapas, H., 1982, “Viscosity Measurement of Fast Settling Mineral Suspensions with a ModifiedCapillary Tube Viscometer”, Proc. 5th Tnt. Symp. on Powder Tech., Kyoto, HemispherePublications, 216-223.Laapas, H.R., 1985, “Rheology of Fast Settling Mineral Slurries”, Proc. 15th Tnt. Miii. Proc.Cong., Cannes, Soci&é de l’industrie minérale, Paris, 28-40.Lang, E.R., Rha, C-K., 1984, “Analysis and Estimation of the Yield Stress of Dispersions”,659-665.Lapasin, R., Ferrara, G., Ruscio, E., Schena, G.D., 1988, Rheological Characterization ofMagnetite Dense Media”, Coal Prep., , 167-183.Laskowski, J.S., Walters, A.D., 1987, “Coal Preparation”, Encycl. of Phys. Sci. & Tech.,Academic Press, 37-61.Laskowski, J.S., 1988, “Dispersing Agents in Mineral Processing”, Froth Flotation, S.H. Castro,J.A. Moisan, eds, Elsevier, 1-16.Laskowski, J.S., Pugh, R.J., 1992, “Dispersions Stability and Dispersing Agents”, Colloid311Chemistry in Mineral Processing, Chapter 4, J.S.Laskowski, J.Ralston (ed) Elsevier, 115-172.Lathioor, R.A., Osborne, D.G., 1984, “Dense Medium Cyclone Cleaning of Fine Coal”, Proc. 2ndTnt. Conf. on Hydrocyclones, Paper Gi, Bath, England, Elsevier, New York, 233-252.Lee, D.I., 1970, “Packing of Spheres and Its Effect on the Viscosity of Suspensions”, J. PaintTech., 42(550), 579-587.Leighton, D., Acrivos, A., 1987, “The shear-induced migration of particles in concentratedsuspensions”, J. Fluid Mech., 181, 415-439.Leja, 3., 1983, Surface Chemistry of Froth Flotation, Plenum Press, New York, pp 758.Leong, Y.K., Boger D.V., 1988, “Importance of Surface Chemistry in Concentrated SuspensionRheology”, Proc. 10th Tnt. Congr. on Rheol., 2, P.H. Uhlherr, ed, Australian Society ofRheology, Sydney, 85-87.Leong, Y.K., Boger, D.V., 1990, “Surface Chemistry Effects on Concentrated SuspensionRheology”, J. Coll. Interf. Sci., 136(1), 249-258.Lewis, T.B., Nielsen, L.E., 1968, “Viscosity of Dispersed and Aggregated Suspensions ofSpheres”, Trans. Soc. Rheol., 12(3), 421-443.Lilge, E.O., Fregren, T.E., Purdy, G.R., 1957, “Apparent Viscosities of Heavy Media and theDriessen Cone”, Trans. 1MM, 67, 229-249.Lin, K.F., Burdick, C.L., 1988, “Polymeric Depressants”, Surfactant Science Series, 27, 47 1-483.Lockyer, M.A., Davies, J.M., Jones, T.E.R., 1980, “The importance of rheology in thedetemination of the carrying capacity of oil-drilling fluids”, Proc. 8th Tnt. Congr. onRheol., Naples, Italy, G. Astarita et al, eds, Plenum Press, New York.Mannheimer, R.J., 1982, “Rheological Evaluation of Cement Slurries”, Southwest ResearchInstitute Final Report No. SwR-6836, Dallas, 4.Spp.Mannheimer, R.J., 1985, “Flow Characteristics of Slurries at Shear Stresses Near the YieldValue”, Proc. 10th mt. Conf. on Slurry Tech., G.H. Eatman, ed, Hydro Transport 10,BHRA Fluid Engineering, Lake Tahoe, Nevada, 123-133.McGeary, R.K., 1961, “Mechanical Packing of Spherical Particles”, J. Am. Cer. Soc., 44(10),513-522.Meagher, L., Farrow, J.B., Horsley, R.R., Warren, L.J., 1988, “The Effect of Dissolved Ions on312the Rheology of Concentrated Quartz Suspensions”, Proc. 10th Tnt. Congr. on Rheol., 2,P.H. Uhlherr, ed, Sydney, Australian Society of Rheology, 118-120.Meerman, P.G., 1958, “Geomagnetic Flocculation: An Explanation of the Rheological Behaviourof Suspended Magnetite”, Rheol. Acta, 1(2-3), 106-110.Mehta, R.V., Prabhakaran, P., Patel, H.I., 1983, “Thixotropy of Certain Diester Based MagneticFluids in a Magnetic Field”, J. Magnetism and Magnetic Mat., 39, 35-8.Mewis, J., Spaull, A.J.B., 1976, “Rheology of Concentrated Dispersions”, Adv. Coll. Interf. Sci.,6, 173-200.Michaels, A.S., Bolger, J.C., 1962, “Settling Rates and Sediment Volumes of Flocculated KaolinSuspensions”, I&EC Fundamentals, 1(1), 24-33.Mills, P., Snabre, P., 1988, “The fractal concept in the rheology of concentrated suspensions”,Progress and Trends in Rheology II, Prague, H. Giesekus, ed, Springer-Verlag, New York,105-8.Mooney, M., 1951, “The Viscosity of a Concentrated Suspension of Spherical Particles”, J. Coll.Sci.,6, 162-170.Moore, F., Davies, L.J., 1956, “A New Rotational Viscometer and Some Preliminary Results”,Trans. Brit. Cer. Soc., 55, 3 13-338.Mular, A.L., 1972, “Empirical Modelling and Optimization of Mineral Processes”, Minerals Sci.Engng., 4(3), 30-42.Mun, R.P., Boger, D.V., 1988, “Turbulent Pipe Flow of Yield Stress Fluids”, Proc. 10th Tnt.Congr. on Rheology, 2, P.H. Uhiher, ed, Australian Society of Rheology, Sydney, 145-7.Murray, W., 1990, private correspondence.Napier-Munn, T.J., 1980, “Influence of Medium Viscosity on the Density Separation of Mineralsin Cyclones”, Tnt. Conf. on Hydrocyclones, Paper 6, Cambridge, Elsevier, New York, 63-82.Napier-Munn, T.J., 1983, “The Mechanism of Separation in Dense Medium Cyclones”, Ph.D.Thesis, University of London, London.Napier-Munn, T.J., 1984, “The Mechanism of Separation in Dense Medium Cyclones”, 2nd Tnt.Conf. on Hydrocyclones, Paper G2 Bath, England, Elsevier, New York, 253-280.Napier-Munn, T.J., Reeves, T.J., Hansen, J.Y., 1989, “The Monitoring of Medium Rheology in313Dense Medium Cyclone Plants”, Aus 1MM Bull, and Proc., 294(3), 85-93.Napier-Munn, T.J., 1990, “The Effect of Dense Medium Viscosity on Separation Efficiency”,Coal Prep., 8, 145-165.Napier-Munn, T.J., Scott, l.A., 1990, “The Effect of Demagnetisation and Ore Contamination onthe Viscosity of the Medium in a Dense Medium Cyclone Plant”, Minerals Eng., 3(6),607-613.Nelder, J.A., Mead, R., 1965, “A Simplex Method for Function Minimization”, Comput. J.,7,308-313.Nguyen Q.D., 1983, “Rheology of Concentrated Bauxite Residue Suspensions”, PhD. Thesis,Monash University, 386pp.Nguyen, Q.D., Boger, D.V., 1983, “Yield Stress Measurement for Concentrated Suspensions”,J. Rheol., 27(4), 32 1-349.Nguyen, Q.D., Boger, D.V., 1984, “Exploiting the Rheology of Highly ConcentratedSuspensions”, Proc. 9th Tnt. Congr. on Rheol., ! Mexico City, B. Mena, ed, UniversidadNacional Autonoma De Mexico, Mexico City, 153-17 1.Nguyen, Q.D., Boger, D.V., 1985, “Direct Yield Stress Measurement with the Vane Method”,J. Rheol., 29(3), 335-347.Nguyen, Q.D., 1989, “Time-dependent Flow Behaviour of Concentrated Industrial Suspensions”,ViscTech, Chicago, Omni Press, 65-76.Nicol, S.K., Hunter, R.J., 1970, “Some Rheological and Electrokinetic Properties of KaoliniteSuspensions”, Austr. J. Chem., 2177-2186.Ogden, I.K., Rutter, P.R., 1984, “The Sedimentation Stability and Viscosity of Coal OilDispersions”, Colloids and Surf., 8, 249-259.Ohl, N., Gleissle, W., 1988, “Shear Flow Behaviour of Viscoelastic Suspensions: Prediction andMeasurement of Shear and Normal Stress”, Proc. 10th Tnt. Congr. on Rheol., 2, P.H.Uhlherr, ed, Australian Society of Rheology, Sydney, 154-6.Oldroyd, J.G., 1956, “Non-Newtonian Flow of Liquids and Solids”, Rheology: Theory andApplications, L F.R. Eirich, Academic Press, New York, 653-682.Onstad, N.T. et al, “1954, “Method and Apparatus for Demagnetizing Magnetic Ores Having HighCoercive Force”, US Patent No. 2,678,130, 8pp.314Osborne, D.G., 1988, “Dense-Medium Separation”, Coal Preparation Technology, 1, Graham &Trotman, London, 199-287.Overbeek, J.Th.G., 1952, “The interaction between colloidal particles”, Coil. Sci., 1, 245-277.Overend, I.J., Horsley, R.R., Jones, R.L., Vinycomb, R.K., 1984, “A New Method for theMeasurement of Rheological Properties of Settling Slurries”, Proc. 9th Tnt. Congr. onRheology,2, Mexico City, B. Mena et al, eds, Universidad Nacional Autonoma DeMexico, Mexico City, 583-590.Papenhuijzen, J.M.P., 1972, “The role of particle interactions in the rheology of dispersedsystems”, Rheol. Acta, 11, 73-88.Parkinson, C., Matsumoto, S., Sherman, P., 1970, “The Influence of Particle-Size Distribution onthe Apparent Viscosity of Non-Newtonian Dispersed Systems”, J. Coil. Interf. Sci., 33(1),150-160.Pinder, K.L., 1964, “Time Dependent Rheology of the Tetrahydrofuran Hydrogen Sulphide GasHydrate Slurry”, Can. J. Chem. Eng., 132-8.Plackett, R.L., Burman, J.P., 1946a, “The Design of Optimum Multifactorial Experiments”,Biometrika, 33, 305-325.Plackett, R.L., 1946b, “Some Generalizations in the Multifactorial Design”, Biometrika, 33, 328-332.Purohit, N.K., Roy, A.N., 1965, “Studies on the Rheological Properties of Rapidly SettlingSuspensions Including Minerals”, Proc. 8th Commonwealth Mi & Met. Congr. AIMM,(Paper 39), Aus. I.M.M. 455-466.Purohit, N.K., Roy, A.N., 1968, “Studies on the Rheological Properties of Rapidly SettlingSuspensions Including Minerals”, Trans. 1MM, C201-C208.Reeves, T.J., 1990, “On-Line Viscosity Measurement Under Industrial Conditions”, Coal Prep.,8, 1-9.Renehan, M.J., Pullum, L., Lambrianidis, J., Bhattacharya, S.N., 1988a, “Effects of CoarseParticle Size Fractions on Rheology of Coal Suspensions Containing Fine Particles”, Proc.10th Tnt. Congr. on Rheol., 2, P.H. Uhlherr, ed, Australian Society of Rheology, Sydney,207-10.Renehan, M.J., Snow, R.J., Bhattacharya, S.N., 1988b, “Factors Affecting the MaximumAllowable Volumetric Fraction of Mineral Slurry Systems”, Proc. 10th Tnt. Congr. onRheol., , Sydney, Australian Society of Rheology, 211-4.315Reynolds, P.A., Jones, T.E.R., 1989, “An Experimental Study of the Settling Velocities of SingleParticles in Non-Newtonian Fluids”, mt. J. Mm. Proc., 25, 47-77.Richardson, J.F., Zaki, W.N., 1954, Trans. Inst. Chem. Eng., 32, 35.Roscoe, R., 1952, “The viscosity of suspensions of rigid spheres”, Brit. J. Appl. Phys., 3, 267-9.Round, G.F., Hessari, A.R., 1984, “The Effect of Size Disthbution and pH on the Rheology ofCoal Slurries”, Hydrotransport 9, BHRA Fluid Engineering, 15 1-5.Rukin, E.I., Slivinskaya, 1.1., Delyagin, G.N., Isaev, V.V., 1977, “Influence of the Grain-sizeComposition of Coal on the Properties of Aqueous Coal Suspensions”, Solid Fuel Chem.,.11 54-9.Russel, W.B., 1980, “Review of the Role of Colloidal Forces in the Rheology of Suspensions”,J. Rheol., 24(3), 287-3 17.Rutgers, I.R., 1962a, “Relative Viscosity of Suspensions of Rigid Spheres in Newtonian Liquids”,Rheol. Acta, 2(3), 202-10.Rutgers, I.R., 1962b, “Relative Viscosity and Concentration”, Rheol. Acta, 2(3), 305-348.Sadowski, Z., Mager, J., and Laskowski, J., 1978, “Hindered Settling of CoagulatingSuspensions” ,Powder Tech., 21, 73-9.Sadowski, Z., and Laskowski, J., 1980, “Hindered Settling - A New Method of the i.e.p.Determination of Minerals”, Colloids and Surf.,j., 15 1-9.Saraf, D.N., Khullar, S.D., 1975, “Some Studies on the Viscosity of Settling Suspensions”, Can.3. Chem. Eng., 53, 449-452.Saunders, F.L., 1967, “Rheological Properties of Monodisperse Latex Systems: Flow Curves ofThickened Latexes”, 3. Coll. Interf. Sci. , 23, 230-6.Schlegel, D., 1988a, “A new method for determining the wall effects with a Couette viscometer”,Progress and Trends in Rheology II, Prague, H. Giesekus et al, ed, Springer-Verlag, NewYork, 172-4.Schlegel, D., 1988b, “Test of a New Two-gap Method for the Couette Viscometer withSuspensions of Glass Spheres in Oil”, Proc. 10th Int. Congr. on Rheol., 2, P.H. Uhlherr,ed, Australian Society of Rheology, Sydney, 248-250.Schlichting, H., 1979, Boundary Layer Theory, 7th Edition, New York, trans 3. Kestin, McGrawHill, New York, 5 10-542.316Schranz, H., 1954, “The Use of Heavy Media of high Density and reduced Consistency in Dense-Medium Washing”, Proc. 2nd Int. Coal Prep. Congr., Essen, 6pp.Schreuder, F.W.A.M., Stein, H.N., 1986, “Rheology of non-coagulating suspensions”, Progressand Trends in Rheology II, Prague, H. Giesekuse et al, ed, Springer-Verlag, New York,320-3.Scott, l.A., Davis, J.J., Manlapig, E.V., 1986, “A Methodology for Modelling Dense MediumCyclones”, Proc. 13th Cong. Council Mm. Met. Insts., Singapore, Aus. I.M.M., 67-76.Scott, l.A., Baguley, P.J., Napier-Munn, T.J., 1987, “The Influence of Medium Rheology on theSeparation of Minerals in Dense Medium Drums and Cyclones”, Dense MediumOperators’ Conference, Aus. I.M.M., Parkville, Victoria, Brisbane, 205-215.Scott, l.A., 1988, “A Dense Medium Cyclone Model Based on the Pivot Phenomenon”, PhDThesis, University of Queensland, Brisbane.Selim, M.S., Kothari, A.C., Turian, R.M., 1983, “Sedimentation of Multisized Particles inConcentrated Suspensions”, AIChE J., 29(6), 1029-1039.Seshadri, V., Sutera, S.P., 1970, “Apparent Viscosity of Coarse, Concentrated Suspensions inTube Flow”, Trans. Soc. Rheol., 14(3), 35 1-373.Sherman, P., 1965, “An Equation for the Newtonian Contribution to Pseudoplastic Flow inConcentrated Dispersions”, 4th Int. Congr. on Rheol., 4(3), E.H. Lee, John Wiley & Sons,New York, Providence, Rhode Island, 605-620.Shewchuk, M., 1983, The Craigmont Story, Hancock House, Surrey, B.C.Simha, R., 1952, “A Treatment of the Viscosity of Concentrated Suspensions”, J. App. Phys.,23(9), 1020-5.Smoluchowski, M. von, 1916, Physik Zeitschift, 17, 557-583.Speers, R.A., Holme, K.R., Tung, M.A., Williamson, W.T., 1987, “Drilling fluid shear stressovershoot behaviour”, Rheol. Acta, 26, 447-452.Speers, R.A., Durance, T.D., Tung, M.A., 1989, “Flow Behaviour of Commercial Brewing YeastSuspensions”, Rheology of Food, Pharmaceutical and Biological Materials, R.E. Carter,ed, Elsevier, Essex, England, 2’lpp.Steinour, H.H., “Rate of sedimentation: nonflocculated suspensions of uniform spheres,” Ind.Engng Chem.,36, 618-624.317Stoessner, R.D., 1987, “Selection of Dense Medium Cyclones for Low Gravity Fine CoalCleaning”, Proc. 3rd Tnt. Conf. on Hydrocyclones, Oxford, England, Elsevier, New York,111-9.Stokes, G.C., 1891, Mathematical and Physical Paper III, Cambridge.Street, N., 1956, Austr. J. Chem., 9, 467.Sun, Z-S., Denn, M.M., 1972, “Stability of Rotational Couette Flow of Polymer Solutions”,AIChE J., 18(5), 1010-5.Sweeny, K.H., Geckler, R.D., 1954, “The Rheology of Suspensions”, J. App. Phys., 25(9), 1135-1144.Tadros, Th.F., 1980, “Physical Stability of Suspension Concentrates”, Adv. Coil. and Interf. Sci.,12, 141-261.Tadros, Th.F., 1985, “Rheology of concentrated suspensions”, Chem. and md., ! 210-8.Tadros, Th.F., 1988, “Rheology of Concentrated Stable and Flocculated Suspensions”, Proc. ofthe Eng. Found. Conf., Palm Coast, Florida, Minerals, Metals & Materials Society, 43-87.Tadros, Th.F., Zsedanai, A., 1990, “Viscoelastic Properties of Aqueous Concentrated PesticidalSuspension Concentrates”, Colloids and Surf., 43, 95-103.Tam, K.C., Moussa, T., Tiu, C., 1988, “Comparison of Rheological Properties of Organic andAqueous Drag Reducing Solutions”, Proc. 10th Tnt. Cong. on Rheol., 2, P.H. Uhlherr, ed,Australian Society of Rheology, Sydney, 298-300.Taylor, G.m., 1923, “Stability of a viscous liquid contained between two rotating cylinders”,Trans. A223, 289-343.Thomas, D.G., 1965, “Transport Characteristics of Suspension: VII. A Note on the Viscosity ofNewtonian Suspensions of Uniform Spherical Particles”, J. Coil. Sci., 20, 267-277.Ting, A.P., Luebbers, R.H., 1957, “Viscosity of Suspensions of Spherical and OtherIsodimensional Particles in Liquids”, A.I.Ch.E., J., 3(1), 111-7.Tipler, P.A., 1976, Physics, Worth Publishers, New York, 953pp.Tsai, S.C., Knell, E.W., 1986, “Viscometry and rheology of coal water slurry”, Fuel, 66, 2-7.Tung, M.A., Speers, R.A., 1985, “Development of Yield Stress Measurement Methodology”,Literature Review, llpp.318Tung, M.A., Speers, R.A., Britt, I.J., Wilson, L.L., 1986a, “Development of Yield StressMeasurement Methodology”, Second Ouarter Report, l4pp.Tung, M.A., Speers, R.A., 1986b, “Development of Yield Stress Measurement Methodology”,Final Progress Report, 43pp.Tung, M.A., Speers, R.A., Britt, I.J., Owen, S.R., Wilson, L.L., 1989, “Yield StressCharacterization of Structured Foods”, Proc. 5th Tnt. Cong. Eng. and Food, Cologne,Elsevier, Amsterdam, lOpp.Valentilc, L., Whitmore, R.L., 1964, “Controlling the Performance of Dense-Medium Baths” Proc.7th Int. Mi Proc. Cong., N. Arbiter, ed, Gordon and Breach, New York. 87-93.Valentik, L., Whitmore, R.L,, 1965, “The terminal velocity of spheres in Bingham plastics”, Brit.J. Appl. Phys., 16, 1197-1203.Valentyik, L., 1971, “Instrumentation and Control of the Specific Gravity and the Rheology ofHeavy-Media Suspensions”, Mi Sci. Eng., 38-44.Valentik, L., 1972, “Rheological Properties of Heavy Media Suspensions Stabilized byPolymers”, Trans. Soc. Mi Eng., 252, 99-105.Valentik, L., Patton, J.T., 1976, “Rheological Properties of Heavy-Media Suspensions Stabilizedby Polymers and Bentonites”, Trans. Soc. Mi Eng., 260, 113-8.Van Der Walt, P.1., Fourie, A.M., 1957, “Determination of the Viscosity of Unstable IndustrialSuspensions with the Aid of a Stormer Viscometer”, J. S. Afr. Inst. Mi and Met., 709-723.Van Der Walt, P.J., Falcon, L.M., Fourie, P.J.F., 1981, “Dense Medium Separation of Minus0.5mm Coal Fines”, Proc. 1st Austr. Coal Prep. Conf., Paper El, Newcastle, CoalPreparation Societies of New South Wales and Queensland, 208-2 19.van de Ven, T.G.M., Hunter, R.J., 1977, “The energy dissipation in sheared coagulated sols”,Rheol. Acta, 16, 391-543.Van Wazer, J.R., Lyons, J.W., Kim, K.Y., Colwell, R.E., 1963, Viscosity and FlowMeasurement, John Wiley & Sons, New York, 389pp.Verwey, E.J.W., Overbeek, J.Th.G., 1948, Theory of Stability of Lyophobic Colloids, TheInteraction of Sol Particles Having an Electric Double Layer, Elsevier, Amsterdam, 199pp.Voet, A., Suriani, L.R., 1950, “Dielectrics and Rheology of Dispersed Magnetized Particles”,Trans. Soc. Rheol., 155-161.319Wein, 0., Tovchigrechko, V.V., Pokryvaylo, N.A., 1988, “Wall effects in Non-Newtonian fluids”,Progress and Trends in Rheology II, Prague, H. Giesekus et al, ed, Springer-Verlag, NewYork, 332-3.Westman, A.E.R., Hugill, H.R., 1930, “The Packing of Particles”, J. Am. Cer. Soc., 13(10), 767-779.White, G.A., Littman, C., Cormode, D.A., 1987, “Dense Media Separation of Potash Ore UsingTn-fib Dense Media Separation” Cominco Fertilizer, File 14SQ.23440-6-9 123.White, H.E., Walton, S.F., 1937, “Particle Packing and Particle Shape”, J. Am. Cer. Soc., 20(5),155-166.Whitmore, R.L, 1957a, “The Relationship of the Viscosity to the Settling Rate of Slurries”, LInst. of Fuel, 238-242.Whitmore, R.L., 1958, “Coal Preparation: The Separation Efficiency of Dense Medium Baths”J. Inst. of Fuel, 422-8.Whitmore, R.L., 1959, “The Viscous Flow of Disperse Suspensions in Tubes”, Rheology ofDisperse Systems, C.C. Mill, ed, Pergamon Press, New York, 49-60.Whitmore, R.L., 1968, “Drag Forces in Bingham Plastics”, Proc. 5th Tnt. Congr. on Rheol.,!,Kyoto, S. Onogi, ed, University of Tokyo Press, Tokyo, 353-360.Whorlow, R.W., 1980, Rheological Techniques, Ch-2, 60-111, Ch-3, Haisted Press, New York,131-191.Wildemuth, C.R., Williams, M.C., 1985, “A new interpretation of viscosity and yield stress indense slurries: coal and other irregular particles”, Rheol. Acm, 24, 75-9 1.Williams, E.J., Kloot, N.H., 1953, “Interpolation in a Series of Correlated Observations”, Austr.J. App. Sci., 4, 1-17.Williams, P.S., 1951, “Some Effects on the Flow of Concentrated Suspensions of Variations inParticle Size and Shape”, Faraday Soc. Disc., No. 11, 47-55.Williams, R.A., Amarasinghe, W.P.K., 1989, “Measurement and simulation of sedimentationbehaviour of concentrated polydisperse suspensions”, Trans 1MM, C68-C82.Williams, R.A., Xie, C.G., Bragg, R., Amarasinghe, W.P.K., 1990, “Experimental Techniques forMonitoring Sedimentation in Optically Opaque Suspensions”, Colloids and Surf., 43, 1-32.Windhab, E., 1986, “A new method for describing the time-dependent rheological behaviour of320concentrated suspensions”, Progress and Trends in Rheology II, Prague, H. Giesekus, ed,Springer-Verlag, New York, 317-320.Yancey, H.F., Geer, M.R., Sokaski, M., 1958, “Viscosity - Its Measurement and Importance inDense-Medium Cleaning of the Fine Sizes of Coal”, Proc. 3rd Tnt. Coal Prep. Conf.,Brussels 583-59 1.Yang, D.C., 1988, “Reagents in Iron Ore Processing”, Surfactant Sci. Ser., 27, 579-644.Yen, W.-T., 1968, “Surface Area and Viscosity Relationship for Minerals”, M.Sc. Thesis, McGillUniversity, Montreal, llOpp.Yopps, S.W., Spottiswood, D.J., Bull, W.R., Pillai, K.J., 1987, “A Study of the Effect of SlurryRheology on Hydrocyclone Performance”, Proc. 3rd Tnt. Conf. on Hydrocyclones, P.Wood, Oxford, England, Elsevier, New York, 59-63.Yoshimura, A., Prud’homme, R.K., 1988, “Wall Slip Corrections for Couette and Parallel DiskViscometers”, J. Rheol., 32(1), 53-67.Yucel, 0., Hughes, M.R., 1984, “Sensitivity of Pressure Drop to Particle Size Distribution andRelated Rheologic Characteristics of Hetero-Homogeneous Slurries”, Hydrotransport 9,Lake Tahoe, BHRA Fluid Engineering, 25 1-7.Zheng, R-z., Zeng, F., Hu, K-M., 1984, “Research on CWM Preparation Technique with ChineseCoals”, China Institute of Mining, 234-250.Zimmels, Y., 1985, “Accelerated and Steady Particle Flows in Newtonian Fluids”, Encyl. of FluidMech., 5, Cheremisinoff, N.P. (Ed), Gulf Publ. Col, Houston, 94-153.321APPENDIX IPublications Related to this Thesis322The following papers have been presented or published in support of this work:Klein, B., Partridge, S.J., Laskowski, J.S., 1988, “Physicomechanical and PhysicochemicalAspects of Magnetite Dense Medium Rheology”, 4th Austr. Coal Prep. Conf., GladstoneAustr., P. Holtman, ed, Coal Preparation Societies of New South Wales and Queensland,340-360.Klein, B., Partridge, S.J., Laskowski, 1988, “Influence of Physicomechanical Propertieson the Rheology and Stability of Magnetite Dense Media”, mt. Symp. on the Prod. andProc. of Fine Particles, Montreal, A.J. Plumpton, ed, Pergamon Press, Toronto, 397-407.Laskowski, J.S., Klein, B., Partridge, S.J., 1988, “Apparatus for the Determination of theRheological Properties of Settling Suspensions”, Canadian Letters Patent, Serial No.575,872.Laskowksi, J.S., Klein, B., Partridge, S.J., 1991, “Apparatus for the Determination of theRheological Properties of Settling Suspensions”, United States Patent, No. 5,056,358.Klein, B., Laskowski, J.S., Mular, A.L., 1990, “Rheology of Magnetite Dense Media:Modelling and Control”, Proc. 11th Int. Coal Prep. Congr., Tokyo, 5 1-56.Klein, B., Partridge, S.J., Laskowski, J.S., 1990, “Rheology of Unstable MineralSuspensions”, Coal Preparation, 8, 123-124.323APPENDIX IIProgram For Shear Rate Corrections324This program uses the method developed by Krieger (1968a, 1968b) to calculatethe shear rates for non-Newtonian fluids in the annular gap of a concentric cylinderviscometer. The program was written to read flow curve data from a file produced withthe Haake viscometer software. Each shear rate is recalculated and restored along withthe corresponding shear stress values. The mathematical formulae to calculate thecorrected shear rates are presented in Chapter 6. The program was written in thelanguage Basic.32510 ‘2030 ‘ THIS PROGRAM READS IN A HAAKE DATA FILE AND CORRECTS THE SHEAR40 RATES FOR NON—NEWTONIAN FLUID FLO’ BEHAVIOUR. THE HAAKE DATA FILE50 IS STORED UNDER A NEW FILE NAME WITH THE SHEAR RATES BEING REPLACED60 ‘ WITH THE CORRECTED VALUES.7080 ‘ APRIL 15, 1989 B. KLEIN90100110120 GOSUB 230 ‘DEFINE VARIABLES AND INITIALIZE VALUES130 GOSUB 800 ‘READ IN HAAKE DATA FILE140 GOSUB 1030 ‘CALCULATE ANGULAR VELOCITY OF SHEAR RATES150 GOSUB 1190 ‘CALCULATE SLOPES OF LOG(OMEGA) VS LOG(TAU)160 GOSUB 1350 ‘ CALCULATE D2(LOG(TAU))/D(LOG(OMEGA))2170 GOSUB 1510 ‘ CALCULATE T — TERMS WHERE T=2*N*LOG(S)180 GOSUB 1700 ‘ CALCULATE F(T)=F(2*N*LOG(S))190 GOSUB 1890 ‘ CALCULATE CORRECTION TERM200 GOSUB 2080 ‘CALCULATE CORRECTED SHEAR RATES210 GOSUB 2310 ‘SAVE DATA FILE WITH CORRECTED SHEAR RATES220 END230240 ‘ DEFINE VARIABLES AND INITIALIZE VALUES250260 ‘ A$ — INPUT FILENAME STRING270 ‘ Bi — B9 — STRING AND NUMERIC INPUT FROM LINE 1 OF DATA FILE280 ‘ Cl — C6 — NUMERIC INPUT FROM LINE 2 OF DATA FILE290 ‘ D(I.J) — DATA FILE APPARENT VISCOSITY300 ‘ TAU(I,J) — DATA FILE SHEAR STRESS310 ‘ GAMMA(I,J) - DATA FILE SHEAR RATE320 ‘ E(I,J) — DATA FILE TIME330 ‘ F(I,J) — DATA FILE TEMPERTATURE340 ‘ G$ - NUMERIC INPUT FROM LINE AFTER FIRST RAMP350 ‘ Hi — H6 - NUMERIC INPUT FROM LINE AFTER HOLD PERIOD360 ‘ L$ — FINAL LINE OF DATA FILE STRING370 ‘ OMEGA(I,J) - ROTATIONAL SPEED380 ‘ Ki — CONVERSION FACTOR FOR NEWTONIAN SHEAR STRESS TO ROTATIONAL SPEED390 ‘ N(I,J) — SLOPE OF LOG(OKEGA) Vs LOG(TAU)400 ‘ NP(I,J) - SLOPE OF LOG(OMEGA) VS N410 ‘ T1(I.J) — T — TERM FOR INNER GAP420 ‘ T2(I,J) - T - TERM FOR OUTER GAP430 ‘ FT1(I,J) — EVALUATED FUNCTION OF Ti TERM440 ‘ FT2(I,J) - EVALUATED FUNCTION OF T2 TERM450 ‘ CTI(I.J) - CORRECTION TERM FOR INNER GAP460 ‘ CT2(I,J) - CORRECTION TERM FOR OUTER GAP470 ‘ CGAM1(I.J) — CORRECTED SHEAR RATE FOR INNER GAP480 CGAM2( I. J) — CORRECTED SHEAR RATE FOR OUTER GAP190 ‘ CGAM(I.J) — CORRECTED TOTAL SHEAR RATE500 ‘ S — RADILS RATiO326510 PS — NAME OF CORRECTED DATA FILE520 DIMD(50.3), TAU(50,3), GAfrIMA(5O,3), EC50,3), F(50,3), OMEGA(50,3)530 DIMN(50,3), NP(50,3). T1(50,3). T2(50,3). FT1(50,3). FT2(50,3)540 DIM CTI(50,3), CT2(50,3), CGAM1(50,3), CGAM2(50,3), CGAM(50,3)550 FOR J=1 TO 3560 FOR 1=1 TO 50570 D(IJ)=O580 TAU(I,J)=0590 GAMMA(I,J)=O600 E(I,J)=O610 F(LJ)=0620 N(I,J)=0630 NP(I,J)=0640 T1(I,J)=0650 T2(I,J)0660 FTI(I,J)=0670 FT2(I,J)0680 CTI(I,J)=0690 CT2(I.J)O700 CGAM1(I,J)O710 CGAM2(I,J)0720 CGAM(I.J)O730 OKEGA(I.J)0740 ‘iEXT I750 NEXT J760 K1=.010678770 S1=1.0252780 S2=1,0189790 RETURN800810 ‘ READ IN HAAXE DATA FilE820830 LINE INPUT ‘FILE NAME 7 ‘AS840 OPEN A$ FOR INPUT AS #1850 INPUT #1, 81$, B2$, B3$. B45, 85, 86, B75, 88, B9860 INPUT #1. Cl. C2, C3, C4. C5, C6870 FOR 1=1 TO 50880 J189OINPUT#1, D(I,J),TAU(I,J),GAMMA(IJ), E(I,J), F(I,J)900 NEXT I910 INPUT #1, Gil 02, G3. G4. 05 ,G6920 FOR 1=1 TO 6930 J=2940 INPUT#1, D(I,J), TAL’(I,J),GAMMA(I,J), E(I,J), F(I,J)950 NEXT I960 INPUT #1 Hi , H2. 113. H4, 115 , 116970 FOR 1=1 TO 50980 J=3990 INPUT #1, 1)(I,J), TAU(T.J), GAMMA(I,J). E(I,J), F(I,J)1000 NEXT I3271010 INPUT #1. L$1020 RETURN10301040 CALCULATE ANGULAR VELOCITIES FROM SHEAR RATE DATA10501060 FOR 1=1 TO 501070 J=11080 OMEGA(I.J)GAMMA(LJ)*K11090 NEXT I1100 FOR 1=1 TO 61110 J=21120 OMEGA(IJ)=GAMMA(I.J)*Kl1130 NEXT I1140 FOR 1=1 TO 501150 J=31160 OMEGA( I, J)=GAMMA( I, J)*K11170 NEXT I1180 RETURN11901200 CALCULATE SLOPES OF LOG(OMEGA) VS LOG(TAU)12101220 FOR 1=1 TO 501230 J=11240 N(I,J)=LOG(TAU(I,J))/LOG(OMEGA(I ,J))1250 NEXT I1260 FOR 1=1 TO 61270 J=21280 N(I ,J)=LOG(TAU(I ,J))/LOG(OMEGA( I ,J))1290 NEXT I1300 FOR 1=1 TO 501310 J=31320 N(I,J)=LOG(TAU(I,J))/LOG(OMEGA(I J))1330 NEXT I1340 RETURN13501360 ‘ CALCULATE N—PRIME13701380 FOR 1=1 TO 501390 J=11400 NP(I,J)N(I,J)/LOG(OMEGA(I.J))1410 NEXT I1420 FOR 1=1 TO 61430 J=21440 NP(I J)N(I ,J)/LOG(OMEGA(LJ))1450 NEXT I1460 FOR 1=1 TO 501470 J=31480 NP(I,J)=N(I.J)/LOG(OMEGA(IJ))1490 NEXT I1500 RETURN32815101520 CALCULATE T - TERM15301540 FOR 1=1 TO 501550 J=11560 T1(I ,J)=2*N(I ,J)*LOG(S1)1570 T2(I,J)=2*N(I ,J)*LOG(S2)1580 NEXT I1590 FOR 1=1 TO 61600 J=21610 T1(I ,J)=2*N(I J)*LOG(51)1620 T2(I ,J)=2*N(I,J)*LOG(S2)1630 NEXT I1640 FOR 1=1 TO 501650 J=31660 T1(I,J)=2*N(IJ)*LOG(S11670 T2(1.J)2*N(I.J)*L0G(S2)1680 NEXT I1690 RETURN17001710 CALCULATE F(T) TERMS17201730 FOR 1=1 TO 501740 J=11750 FTI(I J)=((T1(IJ)2)/12)*(1-(T1(IJ)/2)+((T1(I,J)2)/15))1760 FT2(I,J)=((T2(I J)2)/12)*( 1—(T2(I,J)/2)+((T2(I ,J)’2)/15))1770 NEXT I1780 FOR 11 TO 61790 J=21800 FT1(I,J)=((T1(I ,J)2)/12)*(1—(T1(I,J)/2)+((T1(I,J)’2)/15))1810 FT2(IJ)=((T2(I ,J)2)!12)*(1—(T2(I ,J)/2)+((T2(I,J)2)/15))1820 NEXT I1830 FOR 1=1 TO 501840 J=31850 FT1(I,J)=((T1(I,J)2)/12)*( 1—(T1(I,J)/2)+((T1(I,J)2)/15))1860 FT2(I,J)=((T2(I.J)’2)/12)*(1—(T2(I,J)/2)+((T2(I ,J)2)/15)1870 NEXT I1880 RETURN18901900 CALCULATE CORRECTION TERMS19101920 FOR 1=1 TO 501930 J=11940 CT1(I,J)=(1+(NP(IJ)*FTI(I,J) )/(N(I,J)2))1950 CT2(IJ)=(1+(NP(I.J)*FT2U ,J))/(N(I.J)2))1960 NEXT I1970 FOR 1=1 TO 61980 J=21990 CTI(I,J)=(1+(NP(I,J)*FTI(I .J) )/(N(I,J)2))2000 CT2(I,J)(1+(NP(I,J)*FT2(I.J) )/(N(I.J)2))3292010 NEXT I2020 FOR 1=1 TO 502030 J=32040 CT1(I,J)=(1+(NP(I,J)*FTI(I,J) )/(N(I ,J)2))2050 CT2(I,J)=(1÷(NP(I,J)*FT2(I,J))/(N(I ,J)2))2060 NEXT I2070 RETURN208020902100 ‘ CALCULATE CORRECTED SHEAR RATES21102120 FOR 1=1 TO 502130 J=12140 CGAM1(I,J)=2*N(I ,J)*OMEGA(I ,J)*CT1(I .J)!(1—S1(—2*N(I,J)))2150 CGAM2(I,J)=2*N(I,J)*OMEGA(I,J)*CT2(I.J)/(1—S2(—2*N(I,J)))2160 CGAM(I,J)= CGAKI(I ,J)+CGAM2(I,J)2170 NEXT I2180 FOR 1=1 TO 62190 J22200 CGAM1(I,J)=2*N(I,J)*OMEGA(I.J)*CT1(I,J)/(1—S1’(—2*N(I,J)))2210 CGAM2(I,J)=2*N(I J)*OMEGA(I,J)*CT2(I .J)/(1—S2’(—2*N(I .J)))2220 CGAt1(IJ)= CGAMI(I,J)+CGAK2(I,J)2230 NEXT I2240 FOR 1=1 TO 502250 J=32260 CGAHI(I,J)=2*N(I .J)*Ot.IEGA(I,J)*CTI(I,J)/(1—5V(—2*N(I,J)))2270 CGAM2(I ,J)=2*N(I ,J)*O14EGA(J,J)*CT2(I ,J)/(1—S2(—2*N( I J)))2280 CGAM(I ,J)= CGAKI(I,J)+CGAK2(I,J)2290 NEXT I2300 RETURN2310 S2320 ‘ SAVE DATA FILE WITH THE CORRECTED SHEAR RATES23302340 LINE INPUT SAVE FILE AS: “;P$2350 OPEN P$ FOR OUTPUT AS #22360 WRITE #2, B1$, B2$, B3$, B4$, B5, B6, 117$, B8, B92370 WRITE #2, Cl. C2, C3, C4, C5, CO2380 FOR 1=1 TO 502390 J=12400 PRINT #2,USING”####”””; D(I,J), TAU(I,J), CGAM(LJ). E(I,J), F(I,J)2410 NEXT I2420 WRITE #2, 01, G2, G3, 04, 05, GO2430 FOR 1=1 TO 62440 J=22450 PRINT #2,USING’####”: D(I,J). TAU(I.J), CGAH(I,J), E(I.J), F(I.J)2460 NEXT I2470 WRITE #2, Hi H2. 113. 114 H5, HO2480 FOR 1=1 TO 502490 J=32500 PRINT #2.USING####”’”: D(I,J), TAU(I,J), CGAM(I,J), E(i,J). F(I,J)3302510 NEXT I2520 WRITE #2, L$2530 RETURN331APPENDIX IllSimplex Optimization Program for ModellingRheological Flow Curve Data332This program uses the simplex optimization regression method (Nelder and Mead,1954) to fit rheological flow curve models to flow curve data. A brief description of themethod can be found in Chapter 15. The program reads up to three sets of rheologicaldata with fifty points each. It then asks the user which model should be fit to the dataand the regression begins. The program ends when the objective function, residual sumof squares, reaches a limit which was set at 108 or after 1000 iterations. The programthen prints the residual sum of squares, the multiple index of determination and the flowcurve model coefficients. The program was written in the computer language BASIC.333102030 ‘**********************************************************************4050 ‘ SIMPOP2.BAS6070 THIS PROGRAM USES THE SIMPLEX OPTIMIZATION METHOD FOR MAXIMIZING80 OR MINIMIZING AN OBJECTIVE FUNCTION90 ‘ IT CAN FIT FIVE DIFFERENT MODELS TO RHEOLOGiCAL DATA PRODUCED BY THE100 ‘ HAAKE VISCOMETER. IT WILL READ IN UP TO THREE DATA SETS AND FIT THE110 ‘ EQUATIONS TO THEIR MEANS. THE EQUATIONS ARE THE HERSCHEL-BULKLEY. CASSON120 ‘ LOGARITHMIC, CARREAU AND CROSS MODELS. THE OUTPUT PROVIDES THE EQUATION130 ‘ COEFFICIENTS AND FIT CRITERION.140150 ‘ AUGUST 3, 1989 B. KLEIN160170180 ‘**********************************************************************190200 ‘ DEFINE VARIABLES -210220 N - NUMBER OF CONSTANTS IN EQUATION230 ‘ A — REFLECTION COEFFICIENT240 ‘ V - EXPANSION COEFFICIENT250 ‘ B — CONTRACTION COEFFICIENT260 ‘ C(1,J) — STARTING CONSTANT VALUES A,B,C270 * D(1,J) — STEP SIZES FOR CONSTANTS A,B,C280 M - NUMBER OF DATA POINTS TO BE READ290 * F(I) - SHEAR STRESS DATA300 * G(I) — SHEAR RATE DATA310 ‘ W(I) —WEIGHTING FACTOR320330 * SET DIMENSIONS OF MATRICES340345 DEFDBL X35ODIMD(1,1OLC(1,1O),X(11,IO),Z(1,1O),Y(11.1),Q(11.1O)360 DIM F(50).G(5OLW(5O),FI(5O.4). DUM1(50), DUM2(50), DUM3(50)370 GOTO 520380390 ‘ ASSIGN ZERO VALUES TO ALL MATRICES AND ARRAYS400410 FOR 1=1 TO 4420 FOR J=1 TO 3430 X(I,J)=O440 Y(I,l)O450 Q(I,J)0460 Z(1,J)O470 C(1.J)O480 D(1,J)O490 NEXT J500 NEXT I334510 RETURN520530 ‘ ASSIGN NUMBER OF DATA POINTS TO BE READ TO M -540 READ DATA FILE INTO G(I)—SHEAR RATE AND F(I)—SHEAR STRESS550560 INPUT NUMBER OF DATA SETS DS570 INPUT NUMBER OF DATA POINTS TO BE READ “;M580 FOR J=l TO DS590 LINE INPUT “FILE NAME ? “;F$600 OPEN F$ FOR INPUT AS #J610 INPUT #J, A1$, A2S, A3$. A4$. AS, A6, A7$, A8, A9620 INPUT #J, AlO, All, A12, A13, A14, A15630 FOR 1=1 TO M640 INPUT #J, DUM1(I). FI(1,J). G( [). DUM2(I), DUM3(I)650 NEXT I660 NEXT J670 ‘ INPUT TEST DESCRIPTION680 LPRINT CHR$(14):’FITTED EQUATIONS USING SIMPLEX OPTIMIZATION’690 LPRINT CHR$(14);”DATA SHEET”700 LPPINT710 ‘LINE INPUT “MODEL FILE NAME ?“ :AA$720 LINE INPUT TIME ?“ ;AQ$730 LINE INPUT “SOURCE FILES ?“ SF$740 LINE INPUT “MODEL ? ‘ ;MN$750760770 ‘ CALCULATE MEAN STRESS VALUES FROM DATA FILES780790 FOR 1=1 TO M800 F(I)=0810 FOR J=1 TO DS820 F(I)=F(I)÷FI(I ,J)830 NEXT J840 F(I)=F(I)/DS850 NEXT I860870 ‘ CALCULATE WEiGHTING FACTORS880890 IF DS=1 GOTO 990900 FOR 1=1 TO M910 TP=0920 FOR J=1 TO DS930 TP=TP+(ABS(F(I)—FI(I ,J)))2940 NEXT J950 TP=TP/(DS—l)960 W(I)=1/TP970 NEXT I980 GOTO 990 ‘540990 FOR 1=1 TO N1000 W(I)=13351010102010301040105010601070108010901110112011301140115011601170118011901200121012201230124012501260127012801290130013101320133013401350136013701380139014001410142014301440145014601470148014901500PRINTPRINTPRINTPRINTPRINTPRINTPR I NTPRINTPRINTGOTO 1230PRINT TRY AGAIN’INPUT “MODEL “; EIF E=O THEN 1310IF E=1 THEN 1380IF E=2 THEN 1500IF E=3 THEN 1610IF E=4 THEN 1710IF E=5 THEN 1840GOTO 1220FOR U=1 TO 5PRINT “U= “UE=UGOTO 1240N=3GOSUB 390C(l, 1)=.O01C(1 ,2)=.001C(1 ,3)=.08FOR J=1 TO ND(1 .J)=,1*C(1 ,J)NEXT JGOTO 1960CASSON MODELNEXT IU=5FOR 1=1 TO M ‘TEMPORARY PRINT STATEMENTS- STRESS VALUES, MEAN STRESS, W.FFOR J=1 TO DS‘PRINT FI(I,J),NEXT J‘PRINT F(I), W(I)NEXT I1100 ‘ SELECT MODELS FOR FITTING DATA‘SELECT MODEL(S)”O — ALL MODELS”1 — Y = A + BXC”2 — Y = (A”1/2 + (BX)1/2)23 — Y = A + BLOG(X)”4 — Y = AX/(1 +5 — Y = X(A + (B—A)/(1+CX2/3))”HERSCHEL-BULKLEY EQUATION33615101520 N=21530 GOSUB 3901540 C(11)=.011550 C(1,2)=.011560 FOR J=1 TO N1570 D(1 .J)=. J*(( •J)1580 NEXT J1590 GOTO 196016001610 ‘ LOGARITHMIC MODEL16201630 N=21640 GOSUB 3901650 C(1.1)=.011660 C(1,2)=.51670 FOR J=1 TO N1680 D(1J).1*C(1,J)1690 NEXT J1700 GOTO 196017101720 CARREAIJ MODEL17301740 N=31750 GOSUB 3901760 C(1,1)=11770 C(12)z.11780 C(1.3)z.11790 FOR J=1 TO N1800 D(1,J)=. 1*C(1 .J)1810 NEXT J1820 GOTO 196018301840 ‘ CROSS MODEL18501860 N=31870 GOSUB 3901880 C(1,1)11890 C(1,2)=.11900 C(1,3)=.11910 FOR J=l TO N1920 D(1 1*C(1 .J)1930 NEXT J1940 GOTO 196019501960 A=11970 V=21980 B=.519902000 SET UP INITIAL SIMPLEX WITH VERT ICES STORE!) LN X( I. J)33720102020 FOR J=1 TO N2030 FOR 1=1 TO N+12040 X(I.J)=C(1 ,J)—(2/(J+1))*D(1 ,J)2050 IF I=J+1 THEN 20702060 NEXT I2070 X(I.J)=C(1,J)±((2/(J+1))*D(1 •J))*J2080 FOR I=J÷2 TO N÷12090 X(I.J)=C(1.J)2100 NEXT I2110 NEXT J212021302140 Z7=O2150 Z8=02160 Z9=02170 T3=9.999999E+3521802190 ‘ DETERMINE VALUES OF OBJECTIVE FUNCTION AT EACH VERTICE OF SIMPLEX22002210 FOR 1=1 TO N÷12220 H=I2230 GOSUB 34402240 Y(I.1)=Y12250 NEXT I2260 GOSUB 3620 ‘ SORT VALUES SUBROUTINE22702280 ‘ DETERMINE STANDARD DEVIATION OF OBJECTIVE FUNCTION VALUES AT VERTICES22902300 T1=O2310 T2=02320 T4=02330 FOR 1=1 TO N+12340 T2=T2+Y(I1)2350 NEXT I2360 T1=T2/(N+1)2370 FOR 1=1 TO N+12380 T4=T4+(Y(L1)—T1)22390 NEXT I2400 T=SQR(T4!N)24102420 ‘ PROGRAM LIMITS AND OUTPUT24302440 IF T>1E—08 THEN 25802450 GOTO 24802460 PRINT CYCLE LIMIT = Z92470 PRINT “CONVERGENCE FUNCTION = T2480 GOSUB 3890 ‘PRINT FITS AND RESIDUALS SUBROUTINE2490 GOSUB 4050 ‘PRINT TEST DESCRIPTION2500 GOSUB 4190 ‘PRINT COEFFICIENTS SUBROUTINE3382510 GOSUB 4340 ‘CALCULATE AND PRINT INDEX OF DETERMINATION SUBROUTINE2520 GOSUB 4690 ‘CREATE DATA FILE WITH FITTED POINTS SUBROUTINE2530 IF U5 THEN 25502540 NEXT U2550 STOP256025702580 IF Z9>l000 THEN 24602590 IF TT3 THEN 26802600 T3=T2610 PRINT ITERATION’. ‘STD. DEV. ,‘LOW \TERTEX’ HIGH VERTEX’2620 PRINT Z9.INT(T*10000±,5)/10000.INT(Y(L,1)*10000÷.5)/10000,2630 PRINT INT(Y(H.1)*10000÷.5)/1000026402650 ‘ REFLECTION2660 ‘ DETERMINE CENTROID AND COORDINATES OF NEW \‘ERTICE26702680 FOR 1=1 TO N+l2690 FOR J=l TO N2700 Q(I,J)=X(I.J)2710 NEXT J2720 NEXT I2730 FOR J=1 TO N2740 P=02750 FOR 1=1 TO N+12760 IF I=H THEN 27802770 P=P+X(I.J)/N2780 NEXT I2790 Z( 1 ,J)=( 1+A)*P—A*X(H,J)2800 X(H,J)=Z(1,J)2810 D(1,J)=P2820 NEXT J283028402850 GOSUB 34402860 FOR 1=1 TO N+I2870 FOR J1 TO N2880 X(I,J)=Q(T,J)2890 NEXT J2900 NEXT I2910 YY12920 IF Y>=Y(L,1) THEN 305029302940 EXPANSION2950 ‘ EXPAND COORDINATES OF REFLECTED VERTICE AND DETERMINE THE VALUE2960 ‘ OF THE OBJECTI\T FUNCTION AT THIS POINT29702980 FOR J1 TO N2990 X(H.J)( 1+V)*Z( 1 ,J)—V*D( 1 ,,J)3000 NEXT J3393010 GOSUB 34403020 IF Y1>Y THEN 30603030 Y(H1)=Y13040 GOTO 22603050 IF Y>Y(S,1) THEN 31103060 Y(H1)=Y3070 FOR J=1 TO N3080 X(H,J)=Z(1.J)3090 NEXT J3100 GOTO 22603110 IF Y>Y(H,1) THEN 31903120 FOR J=1 TO N3130 X(H,J)=Z(1J)3140 NEXT J3150 Y(H.1)=Y31603170 * CONTRACTION31803190 FOR Ji TO N3200 X(H,J)=B*X(H,J)+(1—B)*D(1,J)3210 NEXT J3220 GOSUB 34403230 IF Y1>Y(H,1) THEN 32903240 Y(H.1)=Y13250 GOTO 226032603270 ‘ SHRINK32803290 FOR J=1 TO N3300 FOR 1=1 TO N+13310 X(I ,J)=(Q(I ,J)+Q(L,J))/23320 NEXT I3330 NEXT J3340 Z8Z8+1335033603370 PRINT3380 PRINT STEP CHANGE’ Z83390 PRINT3400 GOTO 221034103420 CALCULATE VALUE OF OBJECTiVE FUNCTION AT \:ER’FLCE34303440 S1=03450 S2=03460 FOR K=1 TO M3470 IF E=1 THEN 35203480 IF E=2 THEN 35303490 IF E=3 THEN 35403500 IF E=4 THEN 35503403510 S2G(K)*(X(H, 1)+(X(H,2)—X(H,1))/(1+X(H,3)*G(K)(2/3))):GOTO 35603520 S2=X(H.1)+X(H,2)*G(KrX(H.3):GOTO 35603530 S2=(SQR(ABS(X(H, 1)))+SQR(ABS(X(H,2))*G(K)))2:GOTO 35603540 S2=ABS(X(H,1))+ABS(X(H,2))*LOG(G(K)):GOTO 35603550 S2=ABS(X(H,1))*G(K/(1÷(ABS(X(H.2))*G(K)r2)ABS(X(H,3)):GOTO 35603560 S1=S1+W(K)*(F(K)—S2) 23570 NEXT K3580 Y1=S13590 Z9=Z9+13600 RETURN36103620 ‘ SORT VALUES AT VERTICES AND RETURN THE COORDINATES OF THE3630 ‘ HIGHEST. SECOND HIGHEST AND LOWEST W.F{.T. OBJECTIVE FUNCTION3640 ‘ VALUES36503660 L=13670 H=13680 S=13690 FOR 1=2 TO N+13700 IF Y(I.1)>Y(H.1) THEN 37403710 IF Y(I.1)Y(L1) THEN 37603720 NEXT I3730 GOTO 37803740 11=13750 GOTO 37103760 L=I3770 GOTO 37203780 R=Y(H,1)3790 Y(H,1)03800 FOR 1=2 TO N+13810 IF Y(I,1)>Y(S,1) THEN 38403820 NEXT I3830 GOTO 38603840 S=I3850 GOTO 38203860 Y(H,1)=P3870 RETURN3880 END3890 ‘PROGRAM OUTPUT3900 PRINT “CONVERGENCE”3910 ‘ PRINT FITS AND RESIDUALS3920 H=L3930 PRINT ‘MEAS. Y ,‘PRED. V’ ,“RESIDUALS” ,% DIFF”3940 FOR 1=1 TO M3950 GAM=G(I)3960 IF E1 THEN GOSUB 5010: GOTO 40103970 IF E=2 THEN GOSUB 5030: GOTO 40103980 IF E3 THEN GOSUB 5050: GOT() 10103990 IF E4 THEN GOSUB 5070: GOTO 40104000 GOSUB 5(3903414010 PRINT PCI), INT(G2*1000±,5)/1000,INT(CF(I)—G2)*1000+.5)/1000,4020 PRINT INT(( (F(I)—G2)/F(I))*1000±.5)/10004030 NEXT I4040 RETURN4050 ‘PRINT TEST DESCRIPTION4060 LINE INPUT “FILE NAME ? “;AA$4070 LPRINT FILE NAME:”AAS,4080 LPRINT “DATE:”.A7$4090 LPRINT4100 LPRINT “MEASURING SYSTEM: “;A4S.4110 LPRINT “SENSOR:” .A3$4120 LPFIINT4130 LPRINT “SOURCE FILES: ,SFS4140 LPRINT ‘SAMPLE:’,AI$,4150 LPRINT ‘DESCRIPTION:”.A2$4160 LPRINT4170 RETURN41804190 ‘PRINT EQUATIONS AND COEFFICIENTS4200 LPRINT “MODEL:”,MN$4210 LPPINT4220 IF E1 THEN LPRINT “YA+B*XC’: GOTO 42704230 IF E=2 THEN LPRINT “Y(A.5+(B*Xr.5)2”: GOTO 42704240 IF E3 THEN LPRINT ‘YA+B*LOG(X)”: GOTO 42704250 IF E=4 THEN LPRINT “Y=A*X/(1+(B*X)”2)”C”: GOTO 42704260 LPRINT “YX(A+(B—A)/(1+CX2/3))”4270 LPRINT4280 LPRINT “A’ ;INT(ABS(X(H,1)*10000÷.5))/I00004285 LPRINT ‘B”: USING “#.######“ABS(X(H.2))4290 ‘LPRINT ‘B”;INT(ABS(X(H,2)*I0000+.5))/100004300 IF XCH,3)0 THEN LPRINT ‘C”;INT(ABS(X(H,3)*10000+.5))/100004310 LPRINT4320 RETURN43304340 ‘CALCULATE AND PRINT INDEX OF DETERMINATION4350 YBAR=04360 R104370 R2=04380 R304390 CO1O4400 CO3=04410 ‘ CALCULATE MEAN STRESS YBAR4420 FOR 1=1 TO K4430 YBAR=YBAR+F(I)4440 NEXT I4450 YBARYBAR/M4460 FOR 11 TO K4470 GAMG(I)4480 IF E1 THEN GOSUB 5010: GOTO 45304490 IF E=2 THEN GOSUB 5030: GOTO 45304500 IF E=3 THEN c;OsUB 5050: GOTO 45303424510 IF E4 THEN GOSUB 5070: GOTO 45304520 GOSUB 50904530 R1=R1+(G2—YBAR)’24540 P2=R2+(F(I)—YBAR)”24550 CO1=CO1+(F(I)—G2)24560 NEXT I4570 R3R2/R14580 C03=1—(CO1/R1)4590 LPRINT ‘INDEX OF DETERMINATION. P2 = : R34600 LPRINT “COEFFICIENT OF DETERMINATION, r2 ‘:CO34610 LPRINT RESIDUAL SUM OF SQUARES. SS :514620 IF E2 THEN DV48: GOTO 46404630 DV=474640 LPRINT “VARIANCE OF FITTED EQUATION, \1AR. = “;Sl/DV4650 LPRINT NUMBER OF ITERATIONS, N = “:Z94660 RETURN467046804690 CT=E+24700 CT=CT+14710 GAM=..14720 C5=254730 A5=1004740 C9=3/5O4750 C4=04760 OPEN AA$ FOR OUTPUT AS #CT4770 WRITE #CT,A1$,A2$,A3$,A4$ ,A5,A6,A7$,A8 A94780 WRITE #CT,A1O,A11 ,A12,A13,A14,A154790 IF GAM>=G(5O) GOTO 48204800 GOSUB 49104810 GOTO 47904820 All=04830 A14=34840 A15=04850 WRITE #CT AlO ,All . A12 .Al 3, A14 ,Al 54860 AIOO4870 A1414880 WRITE #CT,A1O All .A12 ,A13 ,A14 , A154890 WRITE #CT.AQ$4900 RETURN4910 IF E1 THEN GOSUB 5010: GOTO 49604920 IF E=2 THEN GOSUB 5030: GOTO 49604930 IF E=3 THEN GOSUB 5050: GOTO 49604940 IF E=4 THEN GOSUB 5070: GOTO 49604950 GOSUB 50904960 C1=G2/GAM4970 C4=C4+C94980 PRINT #CT,USING”####””;Cl,G2GAM,C4,C54990 GAK=GAM+(G(5O)/50)5000 RETURN3435010 G2X(H. 1)÷X(H2)*GAMX(H.3)5020 GOTO 51005030 G2=(SQR(ABS(X(H.1)))÷SQR(ABS(X(H.2))*GAM))’25040 GOTO 51005050 G2=ABS(X(H1))-l-ABS(X(H,2))*LOG(GAH)5060 GOTO 51005070 G2=ABS(X(H. 1))*GAK/(1+(ABS(X(H2))*GAM)2)ABS(X(H,3))5080 GOTO 51005090 G2=GAM*(X(H, 1)±(X(H,2)—X(H,1))/(1+X(H,3)*GAM(2/3)))5100 RETURN344APPENDIX IVModel Discrimination Program to CompareFits of Rheological Flow Curve Models345This program was written to compare the fits of two flow curve models to theflow curve data. The model discrimination procedure developed by Williams and Klootwas used. The program reads in information about the two models to be compared andthe flow curve data. A slope is calculated which if negative means that model one fitsthe data better and if positive it means that model two fits the data better. Details of theprocedure have been presented in Chapter 15. The program was written in the computerlanguage Basic.346102030 ‘**********************************************************************405060 THIS PROGRAM USES THE WILLIAMS AND KLOOT METHOD OF MODEL70 * DISCRIMINATION TO DISTINGUISH WHICH IS THE BETTER OF TWO MODELS.80 ‘ THE MODELS HAVE BEEN FITTED TO RHEOLOGICAL FLOW CURVE DATA.90100 AUGUST 11. 1989 B. KLEIN110120130 ‘**********************************************************************140150 GOSUB 460 ‘DEFINE AND INITIALIZE VARIABLES160 GOSUB 630 ‘READ IN DATA FILES170 GOSUB 800 ‘ CALCULATE MEAN STRESS VALUES180 GOSUB 910 ‘SELECT MODELS TO COMPARE190 MN=M1200 PRINT ‘ENTER COEFFICIENTS FOR MODEL 1210 GOSUB 1020 ‘ENTER VALUES OF COEFFICIENTS FOR MODEL 1220 MN=M2230 PRINT ‘ENTER COEFFICIENTS FOR MODEL 2240 GOSUB 1020 ‘ENTER VALUES OF COEFFICIENTS FOR MODEL 2250 MN=M1260 GOSUB 1260 ‘CALCULATE STRESS VALUES FOR MODEL 1270 MN=M2280 GOSUB 1260 ‘CALCULATE STRESS VALUES FOR MODEL 2290 PRINT “MEAN STRESS’ ,“MODI STRESS” ,MOD2 STRESS’300 PRINT305 FOR 1= 1 TO M310 PRINT F(I).YF(M1,I),YF(M2,I)320 NEXT I330 LPRINT *340 PRINT350 GOSUB 1350 ‘ CALCULATE Z VALUES360 GOSUB 1390 ‘ CALCULATE STRESS DIFFERENCE370 PRINT “Z-VALUE” . “X—VALUE’380 FOR 1=1 TO M390 PRINT USING400 NEXT I410 PRINT420 PRINT430 GOSUB 1440 * CALCULATE LEAST SQUARES COEFFICIENT440 GOSUB 1510 ‘ PROGRAM OUTPUT450 STOP460470 ‘ M - NUMBER OF DATA POINTS TO BE READ480 * FI(I,J) - SHEAR STRESS DATA490 ‘ G(I) - SHEAR RATE DATA500 * F(I) — MEAN SHEAR STRESS VALUE347510 YM(I)— SHEAR STRESS CALCULATED FROM MODEL520 ‘ YF(MN,I)- MODEL I AND MODEL 2 SHEAR STRESS VALUES530540 ‘ SET DIMENSIONS OF MATRICES550560 DIM F(50), G(50). FI(50,3), D1(50). D2(50), D3(50)570 DIM YM(50), YF(4.50). Z(50), X(50)580 AA=0590 BB=0600 CC=0610 RETURN620630 ‘ READ IN DATA FILES640 ASSIGN NUMBER OF DATA POINTS TO BE READ TO— N -650 READ DATA FILE INTO G(I)-SHEAR RATE AND F(I)—SHEAR STRESS660670 INPUT NUMBER OF DATA SETS : DS680 INPUT NUMBER OF DATA POINTS TO BE READ “;M690 FOR J=1 TO DS700 LINE INPUT “FILE NAME ? “;FS$710 OPEN FSS FOR INPUT AS #J720 INPUT #J, A1$, A2$. A3$. A4$, A5, A6, A7$, A8, A9730 INPUT #J, AlO, All, A12, A13, A14, A15740 FOR 1=1 TO M750 INPUT #J, D1(I), FI(I,J), G(I), D2(I), D3(I)760 NEXT I770 NEXT J780 RETURN790800 CALCULATE MEAN STRESS VALUES FROM DATA FILES810820 FOR 1=1 TO M830 F(I)0840 FOR J=1 TO DS850 F(I)=F(I)+FI(I ,J)860 NEXT J870 F(I)F(I)/DS880 NEXT I890 RETURN900910 ‘SELECT MODELS TO COMPARE920925 INPUT RUN NUMBER IS: “:NUM930 PRINT “ 1- HERSCHEL BULKLEY EQUATION940 PRINT “ 2 - CASSON EQUATION950 PRINT “ 3 - CARREAU MODEL960 PRINT “ 4— CROSS MODEL970 INPUT “SELECT FIRST MODEL Ml980 INPUT “FIRST MODEL NAME IS: “;MODI$990 INPUT “SELECT SECOND MODEL’ M21000 INPUT ‘SECOND MODEL NAME IS: “:MOD2$348VALUES OF COEFFICIENTSTHEN GOTO 1070THEN GOTO 1120THEN GOTO 1160THEN GOTO 1210Y = A + BxC“ENTER VALUE “;C1“ENTER VALUE ‘ : C2“ENTER VALUE ‘ : C31250Y = (A’1/2“ENTER VALUE“ENTER VALUE‘C51250Y = AX/(l+(BXr2)CENTER VALUE OF COEFFICIENT A: “;C6ENTER \TALUE OF COEFFICIENT B: ‘:C7“ENTER VALUE OF COEFFICIENT C: “:C81200 GOTO 12501210 PRINT1220 INPUT : C91230 INPUT co1240 INPUT CII1250 RETURN1260 ‘ CALCULATE STRESS1270 FOR 1=1 TO K1280 IF MN=1 THEN1290 IF MN=2 THEN1300 IF MN=3 THEN1310 IF MN=4 THEN1320 YF(MN,I)=YM(I)1330 NEXT I1340 RETURN1350 ‘CALCULATE Z VALUES1360 FOR 1=1 TO M1370 Z(I)=F(I)—.5*(YF(M1,I)+YFU12,I))1380 NEXT I1390 ‘ CALCULATE STRESS DIFFERENCE1400 FOR 1= 1 TO K1410 X(I)=YF(M2,I)—YF(M1 .1)1420 NEXT I1430 RETURN1440 ‘CALCULATE LEAST SQUARES1450 FOR 1=1 TO K1460 AAAA+X(I)*Z(I)1470 BB=BB+(X(I))21480 NEXT I1490 CC=AA/BB1500 RETURNRETURNENTERIF KN=1IF MN=2IF KN=3IF MN=41010102010301040105010601070108010901100111011201130114011501160117011801190PRINTINPUTINPUTINPUTGOTOPRINTINPUTINPUTGOTOPRINTINPUTINPUTINPUTOF COEFFICIENT A:OF COEFFICIENT B:OF COEFFICIENT C:+ BX1/2)’2OF COEFFICIENT A:OF COEFFICIENT B:Y = X(A+(B—A)/(1+CX2/3)“ENTER VALUE OF COEFFICIENT A:“ENTER VALUE OF COEFFiCIENT B:“ENTER VALUE OF COEFFICIENT B:VALUES FOR MODELSGOSUBGOSUBGOSUBGO S U B1560159016201650COEFFIC LENT3491510 PROGRAM OUTPUT1520 LPRINT RUN #“:NUM.MOD1 “;MODI$,”MOD2 = “:MOD2$.LAMDA”:CC1530 LPRINT *1540 RETURN15501560 HERSCHEL BULKLEY EQUATION1570 YM(I)C1+C2*G(I)C31580 RETURN1590 ‘ CASSON EQUATION1600 YM(I)=(SQR(C4)÷.SQR(C5*G(I)))’21610 RETURN1620 ‘ CAPREAU MODEL1630 YM(I)=(C6*G(I))/((14-(C7*G(I) )2)’C8)1640 RETURN1650 * CROSS MODEL1660 YM(I)=G(I)*(C9+(C10--C9)/( 1+C11*(G(I)2/3))1670 RETURN350APPENDIX VSettling Curves and Modelled RheologicalFlow Curves for Investigations into theEffects of Various Parameters on Media Properties351Run #1: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.50Particle Passing Size (j.im): 15.0Solids Volume Fraction: 0.20Magnetization: DemagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.75pH: 10.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.753028_________________________. . ._ . . . . . .26242220j 18, 14C-,12ci,- 1086420 I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.1 Settling curve interface height as a function of time for experimentalRun #1.352j:c.+++f+ ++ ++++++++++++ ++7• Hex’schej Bulkley+++ ++++++ ++++++++++++ +++++ +++ + ++ ÷ ÷: : + ++++ +++++++ +++++++ ++++ +:+++ +÷ + ++ +++ ++++4:2.5e ide 2d0 3O2’[i/s]b.4++++++++++++++ +++++++ ++++++++++++++Casson+++++ +++++4-f- +++++++ ++++++ ++++++ ++ +++++++++++++ ++ ++ +++++ +++2.52d0 3øflt/s]Figure AV.2 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #1.353Figure AV.3354Rheological flow. curve with fitted a) Carreau and b) Cross models forexperimental Run #1.Run 2: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 0.50Particle Passing Size (jim): 15.0Solids Volume Fraction: 0.20Magnetization: DemagnetizedSodium Silicate (kg T’): 0.05Kaolinite (% w/v): 0.75pH: 4.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.253°i28- a U2624222018ci)JE 1412- 1086420 I I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.4 Settling curve interface height as a function of time for experimentalRun #2.355Figure AV.5 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #2.b.‘Ct/s)356c.b.Figure AV.6 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #2.3e0,Ct/s)357Run #3: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 1.50Particle Passing Size (jim): 45.0Solids Volume Fraction: 0.20Magnetization: DemagnetizedSodium Silicate (kg r’): 0.05Kaolinite (% w/v): 0.25pH: 10.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.253028264—w222OEJ 18ci)14C)12E 10864-20— I I I I I H0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.7 Settling curve interface height as a function of time for experimentalRun #3.358utPa]++ ++++1-+i-++ ,.V+ ÷ —+ ++ +-+ _4+++Herschel Bulkley4’+ 4 +_r +— ++ + +4*.2’- + +44 ++++* +1.+/+1*1’+10 20 300?Ll/s]rEPa)+b.+ ÷÷--++ 1-l-_#— *+ ,4+3++Casson4: ++ +++..,-.-.+ +*1*20 300fll/s]Figure AV.8 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #3.359b.Figure AV.9 Rheological flow curveexperimental Run #3.with fitted a) Carreau and b) Cross models foree‘C1/sJ360Run #4: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 0.50Particle Passing Size (pm): 45.0Solids Volume Fraction: 0.20Magnetization: DemagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.25pH: 4.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.75302826 • • •—— •24-2220j 18• 1612- 108-6-42-0 I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.1O Settling curve interface height as a function of time for experimentalRun #4.3610.bFigure AV.11 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #4.362a.b.Figure AV.12 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #4.‘C1/s]363Run #5: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.50Particle Passing Size (jim): 15.0Solids Volume Fraction: 0.10Magnetization: DemagnetizedSodium Silicate (kg T’): 0.05Kaolinite (% w/v): 0.25pH: 4.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.2530T28-• • _ • • • •26 -24-2220Ej 18C)C) 14L)12C)- 108642I I I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.13 Settling curve interface height as a function of time for experimentalRun #5.364a-b.Figure AV.14 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #5.365a-.b.Figure AV.15 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #5.366Run #6: Suspension Composition________Carboxylmethyl Cellulose (kg T’): 0.50Particle Passing Size (pm): 15.0Solids Volume Fraction: 0.10Magnetization: DemagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.25pH: 10.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.753028E—2O18a)14-12-- 1086420 I0 1 2 3 4 5 6 7 8 9 10Setthng lime (mm)Figure AV.16 Settling curve interface height as a function of time for experimentalRun #6.367a-.b.300flt/s]Figure AV.17 Rheological flow curve with fitted a) Herschel Buildey and b) Cassonmodels for experimental Run #6.368ttPa]++++ js-* +4’ +Caxr’eau _.4’+ ++++ ++7r+ ±./ ++*ide 2ê0 300[1/s]T[Pa)b.+++1 5+ +_-.4 +Cross__4 ++++ +++ 4’+ ++ ++ * //0 ido 2d0 300‘C1/s]Figure AV.18 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #6.369Run #7: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 1.50Particle Passing Size (1m): 45.0Solids Volume Fraction: 0.10Magnetization: DemagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.75pH: 4.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.7530282018161412E 1086420 I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.19 Settling curve interface height as a function of time for experimentalRun #7.370a-.b.Figure AV.20 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #7.7’[l/s]371Figure AV.21 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #7.b.fll/s]fll/s]372Run 8: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 0.50Particle Passing Size (jim): 45.0Solids Volume Fraction: 0.10Magnetization: DemagnetizedSodium Silicate (kg T’): 0.05Kaolinite (% w/v): 0.75pH: 10.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.253028Settling Time (mm)Figure AV.22 Settling curve interface height as a function of time for experimentalRun #8.373Figure AV.23 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #8.b.300374a-.b.Figure AV.24 Rheological flow curveexperimental Run #8.with fitted a) Carreau and b) Cross models forfll/sJ375Run #9: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 1.50Particle Passing Size (jim): 15.0Solids Volume Fraction: 0.20Magnetization: MagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.25pH: 4.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.25302826 • • U U U •24222018161412ci)- 10864-2-0 I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.25 Settling curve interface height as a function of time for experimentalRun #9.376a.b.Figure AV.26 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #9.fll/s)377a-.b.Figure AV.27 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #9.fll/s)378Run #10: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 0.50Particle Passing Size (tim): 15.0Solids Volume Fraction: 0.20Magnetization: MagnetizedSodium Silicate (kg T1): 0.05Kaolinite (% w/v): 0.25pH: 10.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.7530-[28. • • • • • . i .26-24-2220()j 18.2 1614l2-E 1086420• I I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.28 Settling curve interface height as a function of time for experimentalRun #10.379Figure AV.29 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #10.b.nt/sJ3809r[Fa]0.4+++7+++++++++ +1**.+ ++++ +++6++ +++++++4+ +++++++ +++ Carr’eau+++1Ø 2e‘[1/s]b.4++7 +++++++ •*++ +++++++++++++ ++++++ +4f+++ ++ Cross+ ++++4 ++44.2ø 3@8‘[1/s]Figure AV.30 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #10.381Run #11: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 1.50Particle Passing Size (pm): 45.0Solids Volume Fraction: 0.20Magnetization: MagnetizedSodium Silicate (kg T’): 0.05Kaolinite (% w/v): 0.75pH: 4.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.7524—222018a)14C)-129 1086420 I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.31 Settling curve interface height as a function of time for experimentalRun #11.382Figure AV.32 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #11.b.fll/s]3830.b.Figure AV.33 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #11.384Run #12: Suspension CompositionCarboxylmethyl Cellulose (kg T1): 0.50Particle Passing Size (jim): 45.0Solids Volume Fraction: 0.20Magnetization: MagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.75pH: 10.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.2514L)12E 10864-20 I I I0 1 2 3 4 5 6 7 8 9 10Setthng Time (mm)Figure AV.34 Settling curve interface height as a function of time for experimentalRun #12.385c.b.Figure AV.34 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #12.386Q-.b.Figure AV.36 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #12.C1/s]‘[1/s]387Run #13: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.50Particle Passing Size (jim): 15.0Solids Volume Fraction: 0.10Magnetization: MagnetizedSodium Silicate (kg T’): 0.05Kaolinite (% w/v): 0.75pH: 10.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.753012ci,- 108642-0 I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.37 Settling curve interface height as a function of time for experimentalRun #13.3880..b.Figure AV.38 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #13.‘C1/sJ389b.Figure AV.39fll/s]Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #13.390Run #14: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 0.50Particle Passing Size (pm): 15.0Solids Volume Fraction: 0.10Magnetization: MagnetizedSodium Silicate (kg Tj: 0.15Kaolinite (% w/v): 0.75pH: 4.0Bentonite (% w/v): 0.75Fine Coal (% w/v): 0.25302826- • . . .24U2220j 18ci)14()12— 108642I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.40 Settling curve interface height as a function of time for experimentalRun #14.39135u[Pa]0..4 ++++ ++ +++++++++++ +++++2.5+++++++++++++++++++++++*++Hesche1Bu120 300TEPa]b.+1- ++++ ++ ++++++ +2.5 ÷+ ++++÷÷÷++++++ ++ + -pf++ + +::+ +1 + Cassonide 20 300‘U/s]Figure AV.41 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #14.392a.b.3e0fll/s]Figure AV.42 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #14.393Run #15: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.50Particle Passing Size (tim): 45.0Solids Volume Fraction: 0.10Magnetization: MagnetizedSodium Silicate (kg T’): 0.15Kaolinite (% w/v): 0.25pH: 10.00.750.25Bentonite (% w/v):Fine Coal (% w/v):30282624222018‘ 161412ci)- 10864200 1 2 3 4 5 6Settling Time (mm)Figure AV.43 Settling curve interfaceRun #15.height as a function of time for experimentalI7 8 9 10394a.b.2’Cl/s]‘[1/s]Figure AV.44 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #15.395a.b.fll/s]Figure AV.45 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #15.396Run #16: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 0.50Particle Passing Size (urn): 45.0Solids Volume Fraction: 0.10Magnetization: MagnetizedSodium Silicate (kg T’): 0.05Kaolinite (% w/v): 0.25pH: 4.0Bentonite (% w/v): 0.25Fine Coal (% w/v): 0.7526c, 14(.)12- 10864200 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.46 Settling curve interface height as a function of time for experimentalRun #16.39705.Figure AV.47fll/s]30gfll/s]Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #16.3980.b.300‘C1/s)Figure AV.48 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #16.399Run #17: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.00Particle Passing Size (pm): 30.0Solids Volume Fraction: 0.15Magnetization: DemagnetizedSodium Silicate (kg T’): 0.10Kaolinite (% w/v): 0.50pH: 7.0Bentonite (% w/v): 0.50Fine Coal (% w/v): 0.503028262220j 1814- 10864-2-0 I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.49 Settling curve interface height as a function of time for experimentalRun #17.400a.b.Figure AV.5O Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #18.‘E1/s)401ck-.30e2’[l/s)Figure AV.51 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #17.6.402Run #18: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.00Particle Passing Size (jim): 30.0Solids Volume Fraction: 0.15Magnetization: DemagnetizedSodium Silicate (kg T1): 0.10Kaolinite (% w/v): 0.50pH: 7.0Bentonite (% w/v): 0.50Fine Coal (% w/v): 0.503028E—20j18‘161412E 108642I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.52 Settling curve interface height as a function of time for experimentalRun #18.4032.5+ + -4++++ ++ -44++ ++ ++ +++++++ ++ 4+ +++ +*+Herschel Bulkley + ++ +1.5+++ +++++++ ++ ++ + ++ +++++ +4- ++++ ÷: ++ + +++ +4-+++++++0.5 4-300E1/s]2.5b.+ + 4-4-+++ ++ +-4+2+ + +++++++ ++ 4+ +++ +*+Casson + ++++ + +1.5 +++ 44+++++ ++ ++ ++++ +- +÷+ + +++ +lI+++++ +++4:4:*0.52 3ØØ‘Et/s)Figure AV.53 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #18.4042.51]0.+ +4-++++ ++2 ++++ ++++++++++ ++ 4+ +++ ++Car’peau + ++ + +1.5 +++ 444*++ ++ ++ + +++++++ ++ +++ + +++ *+++*0.5 +ide 20 300fll/s]75 [Pa].b.+ ÷ +4-+++ ++ -4-4+2 +++ + +++++++ ++ 4+ +++ +*+Cr’oss + ++ + +1.5++++++ ++ ++ +++++ +++4-f++++++ *+++ •1+ *+++0.5ide 2d0 300‘[17s)Figure AV.54 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #18.405Run #19: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.00Particle Passing Size (pm): 30.0Solids Volume Fraction: 0.15Magnetization: MagnetizedSodium Silicate (kg T’): 0.10Kaolinite (% w/v): 0.50pH: 7.0Bentonite (% w/v): 0.50Fine Coal (% w/v): 0.502218a), 14C-)12- 108-6-4-2-0 I I I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.55 Settling curve interface height as a function of time for experimentalRun #19.406c..b.Figure AV.56 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #19.4072.5++++++++ ++++ ++ +++Carz’eau ++ ++ + +++++++ ++++++ ++++ + ++ + +++- + ++++++ +++.f + + +++++++++++ + +++++++++++++++++ +++++ ++ + ++++ ++ ++++ ++++0.520 300‘E1/s]2.5 rCPa]b.++++++ ++ ++ +++ +++ +++ ++ ++ +Cross ++ ++ + ++++++ ++ +++++ ++++ + ++ + ÷++- + +++++ +4+++ +++++ + +++ ++ ++++1-++++ ++++++++ +++ ++++ +++++ ++ + ++++ ++ +++++ +++e10 20 300fll/s)Figure AV.57 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #19.408Run 2O: Suspension CompositionCarboxylmethyl Cellulose (kg T’): 1.00Particle Passing Size (jim): 30.0Solids Volume Fraction: 0.15Magnetization: MagnetizedSodium Silicate (kg T’): 0.10Kaolinite (% w/v): 0.50pH: 7.0Bentonite (% w/v): 0.50Fine Coal (% w/v): 0.50302812- 1086420 I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AV.58 Settling curve interface height as a function of time for experimentalRun #20.4090--b.Figure AV.59 Rheological flow curve with fitted a) Herschel Bulkley and b) Cassonmodels for experimental Run #20.fll/s]410rEPa]Figure AV.60 Rheological flow curve with fitted a) Carreau and b) Cross models forexperimental Run #20.b.E1/s]411APPENDIX VISettling Curves and Modelled RheologicalFlow Curves for Investigations into theEffects of Particle Size Distribution on Media Properties41225CL. 120C-)15ci,ci)C-)5I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)uEPaJb.++4 * +++4+*4+4*2* +++ ++4*++++++*e 2 300ci‘E1/s)Figure AVI.1 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #1 (Ø=O.25, Øf=O.40, dJd1=O.39, pH=8.08).413b050 I I I I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)‘u[PaJb.++++ ++2O‘E1/s)Figure AVI.2 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #2 (=O.25, =O.4O, dJd1=O.13, pH=8.33).4142520!151050 I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)4[Pa]b.+3 ++++++*+++ +2 +++ ++++++ ++ +++ ++++++++2ø 300Figure AVI.3 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #3 (Ø=O.25,p1=O.25 cLJd1=O.39, pH=8.38).41525 -5Figure AVI.4 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #4 (Ø=O.25, =O.25, cLJd1=O.13, pH=8.21).20EC-)15cC)b.00 1 2 3 4 5 6 7 8 9 10Settling Time (mm)‘[1/s]416a. 25201050b.417EC)- 15DIci-)C)a)....0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)Figure AVI.5 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #5 (=O.15, =O.4O, dJd1=O.39, pH=8.17).25c.20EC-)•-:: 15ci)ci)C-)a)1050Figure AVI.6 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #6 (=O.15, Ø=O.4O, cLJd1=O.13, pH8.78).4180 1 2 3 4 5 6 7 8 9 10Settling Time (mm)fll/s)2520E:: 15a)JIa)b050t:.Figure AVI.7 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #7 (=O.l5, =O.25, dJd1=O.39, pH=8.42).419...0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)fll/s]25bFigure AVI.8 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #8 (=O.15, Ø=0.25, dJd1=0.13, pH=8.85).42020EL)EJ 15ci)ci)50.I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)‘E1/s)2505.. U • U • U U0 1 2 3 4 5 6Settling Time (mm)7 8 9 1020EC-)15a)a)C-)10a)0b.Figure AVI.9 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #9 (Ø=O.2O, Ø=O.325, dJd1=O.67, pH=8.25).421‘C1/s)2520 -c)15a)C-)10. I • • U U U U U50 I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm),rEPa) ++ +++ ++++ ++++3++++++2.5 +++ +++++#++++++++4: ++ ++++ ++++ +2 ++++ +++r + + ++++++++ +++ +++1.5++++0.520 300rCl/sJFigure AVI.1O a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #10 (Ø=0.2O, 4=O.325, d/d1=O.09, pH=8.63).42225Settling Time (mm)b.3ttPa)—++++++ t_—+4.+_4 11. 4++++*‘4/*7Figure AVI.11 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #11 (=O.2O, Ø=O.451, dJd=O.22, pH=8.35).42325Settling Time (mm)2b. ++ +++++++++ —+7-+ +_z7 ++/ +sk4’:f *+ +,— ++±4 + +/4+++V 4-++ ,+4,7e ze 3Figure AVI.12 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #12 (Ø=O.2O, Ø=O. 199, dJd1=O.22, pH=8.29).42425 ISettling Time (mm)5t[PaJ+++++++ +++ ++44 +z. $+ ÷+-2+,v++.J1e 2ø‘E1/s]Figure AVI.13 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #13 (Ø=O.284, =O.325, d/d1=O.22, pH=8.27).42520j 15ci)ci)0I.ci,.U U. U U U0 I I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)1t[Pa)b..pf +++ +e7 ++ + +++ + +__-‘:f+ +* +÷—+ ++44 iV++ +÷_:fr $ +++ + *+++%O25A2ä 3[1/sJFigure AVI.14 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #14 (=O.116, =O.325, dJd1=O.22, pH=8.41).4265I I I0 1 2 3 4 5 6 7 8 9 10Settling Time (mm)k ++6+_/‘ *+,4+4 ++++e 2ø 380C1/s)Figure AVI.15 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #15 (Ø=O.2O, Ø=O.325, dJd1=O.22, pH=8.42).4272520EC-)15a)a)C-)b050b.Figure AVL16 a) Settling curve and b) fitted (Casson model) flow curve forexperimental Run #16 (Ø=O.2O, Ø=O.325, d/d1=O.22, pH=8.94).4280 1 2 3 4 5 6 7 8 9 10Settling Time (mm)t1/s]APPENDIX VIIStatistical Analyses ofModelled Media Properties429TableVII.1StatisticalanalysisofthemodelfortheCassonyieldstressasafunctionofparticlesizedistributionparameters.VariableCoefficientStandardErrorT-statisticProbability(2-Tail)Solids-9.532.20-4.330.001FinesxSolids28.35.485.150.000Ratio26.121.514.060.002Solids231.06.754.590.001RatioxFinesxSolids-87.716.5-5.320.000MultipleIndex,R2:0.894AnalysisofVariance•SourceSumofSquaresDegreesofFreedomMeanSquareF-ratioProbabilityRegression3.9950.79718.50.000Residual0.474110.043TableVII.2StatisticalanalysisofthemodelfortheCassonviscosityasafunctionofparticlesizedistributionparameters.VariableCoefficientStandardErrorT-statisticProbability(2-Tail)MultipleIndex,R2:0.964AnalysisofVarianceSourceSumofSquaresDegreesofFreedomMeanSquareF-ratioProbabilityRegression331.7482.979.20.000_Residual12.6121,05Ratio-45.69.85-4.630.00Solids75.614.85.100.00RatioxSolids26148.45.410.00Solids2-30366.7-4.540.00TableVII.3Statisticalanalysisofthemodelforsettlingvelocityasafunctionofparticlesizedistributionparameters.-j.-..—_______________VariableCoefficientStandardErrorT-statisticProbability(2-Tail)Constant7.841.993.930.003Ratio32.54.507.220.000iFines-3.111.25-2.490.034Solids-76.117.3-4.410.002RatioxSolids-97.119.1-5.080.001Ratio2-10.43.25-3.200.011Solids2188.641.34.660.001MultipleIndex,R2:0.973________________AnalysisofVarianceSourceSumofSquares,DegreesofFreedomMeanSquareF-ratioProbabilityRegression38.866.4754.10.000Residual1.0890.1 19

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