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The effects of rheology and stability of magnetite dense media on the performance of dense medium cyclones He, Ying Bin 1994

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THE EFFECTS OF RHEOLOGY AND STABILITY OF MAGNETITE DENSE MEDIA ON THE PERFORMANCE OF DENSE MEDIUM CYCLONES by YINGBIN HE B.A.Sc., Heilongjiang Inst, of Mining and Tech., 1982 M.A.SC., The University of British Columbia, 1989 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Mining and Mineral Process Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1994 © Yingbin He, 1994 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholaRLy purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of Mining and Mineral Process Engineering The University of British Columbia Vancouver, Canada Date June 23, 1994 DE-6 (2/88) ABSTRACT The main objective of this thesis is to investigate the effect of the stability and non-Newtonian rheological properties of magnetite dense medium on the performance of dense medium cyclone (DMC). In addition, the DMC separation mechanism, the rheology of magnetite dense medium, and the hydrodynamics of particle movement in non-Newtonian fluids are also studied. The tests, carried out on a 150 mm pilot scale DMC loop with density tracers as the cyclone feed, reveal that the 0/U flowrate ratio is the fundamental operating parameter directly related to the DMC performance, other operating parameters influence the DMC performance through, or partially through the OAJ flowrate ratio. The medium rheology and stability exert opposite influences on DMC performance. In addition, the separation of fine feed particles (<0.5 mm) is more sensitive to the effect of medium rheology, while the separation of coarse feed particles (>2.0 mm) is more strongly affected by medium stability. As a consequence, contradicting results are observed depending on which of these factors is predominant. A DMC separation mechanism based on a modified equilibrium orbital hypothesis by taking into account the medium density gradient and medium inward radial flow was proposed. Based on this hypothesis, a theoretical model is derived to predict the DMC separation density and cutpoint shift behaviour: i i o-„-p„=a(rn-rj+ ( ^—) 50 H« vo c^ iSn^dr^L v/l+e)' where the first term represents the influence of medium stability and the second term reflects the influence of medium rheology. The rheological studies reveal that the non-Newtonian magnetite suspensions are best described by the Casson equation. The Casson yield stress is the principal rheological parameter and responds to the changing medium properties in a well defined pattern. On the other hand, the Casson viscosity is a subordinate rheological parameter which can be treated as a constant for coarse (commercial) and intermediate magnetite suspensions, or can be ignored for very fine magnetite suspensions. To interpret the influences of the non-Newtonian medium rheology on DMC performance, a theoretical framework of particle movement in non-Newtonian fluids is established. A shear rate equation bridging the hydrodynamic and rheology theories is derived: ^ 2M (l+9.06//Je*/V It is further derived that the general form of Reynolds number applicable to any rheological fluid types is: For magnetite suspensions conforming to the Casson equation, the modified Reynolds number is: i i i Thus the influences of the viscosity and yield stress on DMC performance can be interpreted via the general relationship between drag coefficient and the modified Reynolds number: The yield stress not only determines the threshold drag on particles before particle-to-fluid relative movement is achieved, more importantly, it also determines the viscous drag during the particle-to-fluid relative movement. Since the Casson yield stress value is much greater than the corresponding Casson viscosity value, the DMC separation of fine particles is mainly determined by the Casson yield stress. This postulation is verified by the experimental evidence obtained from the DMC separation tests and the rheological measurements. iv TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS v LIST OF TABLES viii LIST OF FIGURES ix LIST OF SYMBOLS xiii ACKNOWLEDGMENTS xv 1. INTRODUCTION 1 2. RESEARCH OBJECTIVES AND SCOPE 5 3. LITERATURE REVIEW 8 3.1 Theory of Dense Medium Cyclone (DMC) 8 3.1.1 Dense medium and particle movement inside a cyclone . . . . 8 3.1.2 Dense medium cyclone performance evaluation 11 3.2 Effect of Medium Properties on DMC Performance 14 3.2.1 Effect of medium rheology on DMC performance 14 3.2.2 Effect of medium stability on DMC performance 16 3.2.3 Joint effects of medium rheology and medium stability 18 3.3 Effect of Operating Conditions on DMC Performance 20 3.4 Summary 25 4. EXPERIMENTAL PROGRAM 26 4.1 Materials 26 4.1.1 Magnetite samples 26 4.1.2 Density tracers 27 4.2 Equipment 29 4.2.1 Pilot scale DMC circuit 29 4.2.2 Equipment for preparation and characterization of magnetite samples 32 4.2.3 Rheometer 32 4.3 Experimental 34 V 4.3.1 Operation of the DMC circuit 34 4.3.2 Rheological measurement 35 5. EFFECT OF OPERATING CONDITIONS ON DMC PERFORMANCE 37 5.1 Introduction 37 5.2 Results 39 5.2.1 Control of O/U flowrate ratio 39 5.2.2 Effect of O/U flowrate ratio on cutpoint shift 39 5.2.3 Effect of O/U flowrate ratio on separation efficiency 51 5.2.4 Effect of O/U flowrate ratio on medium stability 57 5.3 Discussion 63 5.3.1 Control range for O/U flowrate ratio 63 5.3.2 Applications of the O/U flowrate ratio control 66 5.3.3 The mechanism of density separation in DMC 70 5.4 Summary 81 6. THE EFFECT OF MEDIUM COMPOSITION ON DMC PERFORMANCE . . 83 6.1 Introduction 83 6.2 Experimental 85 6.3 Results and Discussions 86 6.3.1 Effect of feed particle size on DMC performance 86 6.3.2 Control of cyclone operating conditions 86 6.3.3 Dense medium stability 90 6.3.4 Separation efficiency 92 6.3.5 Cutpoint and cutpoint shift 99 6.4 Summary 105 7. RHEOLOGY OF MAGNETITE SUSPENSIONS 107 7.1 Introduction 107 7.1.1 Theory of rheology 108 7.1.2 Rheological properties of magnetite suspensions I l l 7.2 Flow Curve Type and Modelling 114 7.2.1 Flow curve type 114 7.2.2 Modelling of rheological flow curves 118 7.2.3 Casson yield stress and Casson viscosity 125 7.3 Effect of Magnetite Particle Size Distribution 136 7.3.1 Theory 136 7.3.2 Relative hydrodynamic volume factor 139 7.4 Effect of Temperature 145 7.4.1 Introduction 145 7.4.2 Results and discussions 145 7.5 Summary 152 8. PARTICLE MOVEMENT IN NON-NEWTONIAN FLUIDS 154 V I 8.1 Introduction 154 8.2 Particle Reynolds Number in Non-Newtonian Fluids 157 8.3 Shear Rate and Shear Rate Constant 162 8.4 Stokes' Equation for Non-Newtonian Fluids 167 8.5 The Effect of Yield Stress on Particle Movement 170 8.6 Application of Apparent Viscosity 175 8.7 Summary 177 9. THE EFFECT OF DENSE MEDIUM RHEOLOGY ON DMC PERFORMANCE 179 9.1 Introduction 179 9.2 Results 181 9.2.1 The effect of medium rheology on medium stability 181 9.2.2 The effect of medium rheology on DMC performance . . . . 184 9.2.3 DMC separation using bimodal magnetite dense medium . . 191 9.3 Discussion 200 9.3.1 The influence of medium rheology on DMC performance . . 200 9.3.2 The characteristic shear rate in a DMC 203 9.4 Summary 207 10 CONCLUSIONS 209 11 RECOMMENDATION FOR FUTURE WORK 216 12 REFERENCES 219 V l l LIST OF TABLES Table Page 4.1 RRB size and distribution moduli of the magnetite samples 26 4.2 (a) Specifications of density tracers - set one 27 4.2 (b) Specifications of density tracers - set two 28 5.1 BOC dense medium cyclone separation tests using density tracers 49 7.1 The rheological models tested 119 8.1 Particle shear rate (D) and R value (x<,d/T|^ u) in the magnetite suspensions at medium density of 1.45 g/cm^ 172 V l l l LIST OF FIGURES Figure Page 1.1 Dense medium cyclone 1 2.1 A schematic diagram of research approach 6 3.1 A partition curve 12 4.1 (a) Layout of the 150 mm DMC circuit 30 4.1 (b) Flow sheet of the 150 mm DMC circuit 31 5.1 (a) Effect of medium density and magnetite particle size on O/U flowrate ratio 40 5.1 (b) Effect of vortex finder diameter on O/U flowrate rat 40 5.2 (a) The relationship between cutpoint shift and vortex finder diameter 42 5.2 (b) The relationship between cutpoint shift and spigot diameter 42 5.3 (a) The relationship between cutpoint shift and cone ratio 43 5.3 (b) The relationship between cutpoint shift and O/U flowrate ratio 43 5.4 The relationship between cutpoint shift and O/U flowrate ratio as affected by the medium density 44 5.5 A summary of the results in 5.4 46 5.6 The relationship between cutpoint shift and O/U flowrate ratio as affected by the medium density 46 5.7 The relationship between cutpoint shift and cone ratio as affected by the medium density 47 5.8 The relationship between cutpoint shift and O/U flowrate ratio obtained on full scale DMC circuit using density tracers 49 5.9 (a) B.O.C. full scale DMC test using 19.3 cm vortex finder 50 5.9 (b) B.O.C. full scale DMC test using 30.5 cm vortex finder 50 5.10 (a) Effect of spigot expansion due to wear on the clean coal loss in the tailings 52 5.10 (b) Effect of cyclone throughput on the cumulative clean coal loss in the tailings 52 5.11 (a) The relationship between Ep value and cone ratio 53 5.11 (b) The relationship between Ep value and O/U flowrate ratio 53 5.12 Effect of vortex finder diameter on Ep value 55 5.13 Effect of magnetite particle size on Ep value 55 5.14 The relationship between Ep value and O/U flowrate ratio i x 5.15 5.16 (a) 5.16(b) 5.17 (a) 5.17 (b) 5.18 (a) 5.18 (b) 5.19 5.20 (a) 5.20 (b) 5.21 (a) 5.21 (b) 6.1 6.2 (a) 6.2 (b) 6.3 6.4 6.5 6.6 6.7 (a) 6.7 (b) 6.8 as affected by medium density 56 The overflow and underflow medium densities as a function of O/U flowrate ratio 58 The relationship between density differential and cone ratio for Mag#4 59 The relationship between density differential and O/U flowrate ratio for Mag#4 59 The relationship between density differential and cone ratio for Mag#2 60 The relationship between density differential and O/U flowrate ratio for Mag#2 60 The effect of magnetite particle size on relationship between density differential and O/U flowrate ratio 62 The effect of medium density on relationship between density differential and O/U flowrate ratio 62 By-passing of the low density feed particles at low O/U ratio 64 A typical parallel layout of two DMCs to form a bank 68 A reduced overall separation efficiency due to the variation in cutpoint 68 The relationship between cutpoint and underflow medium density 72 The relationship between cutpoint and overflow medium density 72 The relationship between Ep value and feed particle size as affected by operating condition and medium properties 87 DMC O/U flowrate ratio as affected by the medium composition 89 DMC medium flowrate as affected by the medium composition 89 The effect of magnetite particle size on overflow and underflow medium densities 91 Density differential as a function of magnetite particle size and medium density 91 DMC separation efficiency as affected by medium density and magnetite particle size 93 DMC separation efficiency as affected by magnetite particle size and medium density 95 Separation cutpoint as a function of magnetite particle size and medium density 100 Cutpoint shift as a function of magnetite particle size and medium density 100 Cutpoint shift as a function of feed particle size and medium density 102 7.1 Types of rheological flow curves 109 7.2 (a-d) The flow curves of magnetite suspensions 115 7.3 (a-d) The apparent viscosity as a function of shear rate 117 7.4 The correlation coefficient of the three rheological models 121 7.5 (a-d) Curve fitting of the three rheological models to the flow curves of the magnetite suspensions 122 7.6 (a-d) Curve fitting of the Bingham model over the higher shear rate region 123 7.7 (a-d) Comparison of the yield stress as estimated from the three rheological models 126 7.8 The effect of magnetite particle size and medium solid content on Casson yield stress 127 7.9 The effect of magnetite particle size and medium solid content on Casson yield stress 129 7.10 The relationship between Casson viscosity and Casson yield stress 132 7.11 (a-d) The relationship between apparent viscosity and Casson yield stress 134 7.12 The relationship between Casson yield stress and relative hydrodynamic volume concentration (% vol.) 141 7.13 The relationship between Casson viscosity and relative hydrodynamic volume concentration (% vol.) 143 7.14 Relative hydrodynamic volume factor as a function of specific surface area 144 7.15 Effect of temperature on medium rheology at different medium density and magnetite particle size distribution 146 7.16 Effect of temperature on Casson yield stress 148 7.17 Effect of temperature on Casson viscosity 149 7.18 Effect of temperature on water viscosity (after P.W. Atkins, 1981) 149 7.19 (a) Effect of temperature on apparent viscosity (Mag#2 suspensions) 151 7.19 (b) Effect of temperature on apparent viscosity (Mag#5 suspensions) 151 8.1 (a) The correlation between drag coefficient and Reynolds number calculated without taking into account of yield stress (Data adapted by Dedegil, 1987 from the experimental results of Valentyik and Whitmore, 1965) 161 8.1 (b) The correlation between drag coefficient and Reynolds number calculated by taking into account of yield stress (Data adapted by Dedegil, 1987 from the experimental results of Valentyik and Whitmore, 1965) 161 8.2 A schematic diagram for shear rate derivation 163 X I 8.3 Shear rate constant as a function of Reynolds number 163 9.1 The effect of Casson yield stress on medium stability 182 9.2 The relationship between density differential and Casson viscosity 183 9.3 The relationship between settling rate and yield stress (after B.Klein et al, 1990) 185 9.4 The effect of Casson yield stress on separation efficiency 187 9.5 The relationship between Ep value and Casson viscosity 188 9.6 Effect of Casson yield stress on cutpoint shift 190 9.7 The relationship between cutpoint shift and Casson viscosity 192 9.8 (a) Apparent viscosity of bimodal coal-water slurry (after F. Ferrini et al, 1984) 193 9.8 (b) Relative viscosity of bimodal poly spheres suspension in Nujol (after C. Parkinson et al, 1970) 193 9.9 The rheological properties of bimodal suspensions 194 9.10 Separation efficiency as affected by the proportion of fines in the bimodal dense medium 194 9.11 (a) Effect of fine magnetite content on bimodal dense medium stability 197 9.11 (b) Effect of fine magnetite content on overflow and underflow medium densities 197 9.12 Effect of fine magnetite content in the bimodal suspension on cutpoint shift 199 X l l LIST OF SYMBOLS A Particle surface area B A constant c A constant Cj Dry solid volume content CD Fluid drag coefficient Ch Hydrodynamic volume content d' Particle diameter d Particle hydrodynamic diameter do Threshold particle diameter D Shear rate D^ Diameter of cyclone DQ Cyclone vortex finder diameter D„ Cyclone spigot diameter Ep Ecart probable used to evaluate density separation efficiency FQ Threshold viscous drag Fj Fluid drag on particles Fc Centrifugal force g Gravitational acceleration K Fluid consistency index in Ostwald and Herschel-Bulkley models k Shear rate constant L Length of the imaginary cylindrical envelope formed by the loci of zero axial velocity m A constant n Flow behaviour index in Ostwald and Herschel-Bulkley models P Cyclone inlet pressure Q Feed medium flow rate Qo/f Overflow medium flow rate Qu/f Underflow medium flow rate r Radial distance from cyclone axis rg Radius of the locus of zero axial velocity r^  Radius of constant medium density zone in a DMC r^ Radius of cyclone wall r^  Radius of air cone in a cyclone Re Reynolds number RCn, Modified Reynolds number u Particle movement velocity relative to its surrounding fluid V( Tangential velocity of the dense medium in a cyclone X l l l Vn, Inward radial velocity of the medium Vf Particle radial velocity relative to cyclone wall a Density gradient of the medium in a D M C P A constant <y Boundary layer thickness CQ A constant 6 Mineral particle density 650 Separation density e A constant T| Viscosity r|a Apparent viscosity r\^ Casson viscosity T|p, Plastic viscosity p Fluid or medium density p„ Feed medium density po Medium density at the locus of zero axial velocity T Shear stress; To Real yield stress x^ Casson yield stress as estimated by the Casson equation Tp, Plastic yield stress as estimated by the Bingham equation 0 Cyclone overflow to underflow flowrate ratio O Hydrodynamic volume factor (j) Relative hydrodynamic volume factor X I V ACKNOWLEDGMENTS I would like to express my deepest gratitude to my supervisor, Prof. Janusz S. Laskovv'ski, who provided thorough and invaluable guidance and support in every aspect of my research work. The immense influence he presented in shaping my research approach and attitude can never be overestimated. I benefited from many useful discussions with experts in the fields of hydrocyclone and medium rheology. I would like to thank particularly Dr. R.P. King of University of Utah, Dr. C. Wood, and Dr. G.J. Lyman of University of Queensland, Dr. L.R. Plitt of University of Alberta, and Dr. B. Klein of Process Research Associates Ltd. for their comments and suggestions. I would also like to express my gratitude to Dr. John Meech, Dr. George Poling, Prof. Andy Mular, and Dr. Ken Pinder of The University of British Columbia for their kind encouragement in both my academic and research work and for their valuable advice in my thesis work. My sincere thanks are due to Mr. Frank Schmidiger, Mrs. Sally Finora, and Mr. Pius Lo for their kind and reliable technical assistance. I would like to acknowledge the enthusiastic support by Mr. Ken Wong, Process Engineer of Fording Coal Ltd. This fruitful co-operation was suddenly interrupted by Ken's tragic death. Some of his measurement results, which he kindly provided, are used in this thesis (Figures 5.10 (a) and (h)). I would also like to thank Mr. Lumir Bakota, Senior Process Engineer, and Mr. Mark Benardt, Plant Superintendent, of BuUmoose Operating Corp. for allowing me to conduct full scale dense medium cyclone tests on their facilities and for providing personnel assistance. The financial support for the research by the Science Council of British Columbia is gratefully acknowledged. Finally, I must thank my wife, Ying, for her support and care throughout my student years, and my son, David, who gives me great joy and homework. X V 1. INTRODUCTION The dense medium cyclone (DMC), developed in 1942 by the Dutch State Mines, is a cylindro-conical separation unit with an included cone angle of about 20 degrees (Figure 1.1). During its operation, the mixture of dense medium and coal (or mineral) par-ticles is injected tan-gentially into the cylindrical section of the unit. A vortex flow is created with a central air-core due to the centrifugal force induced by the rotating medium. Heavy par-ticles move down along the wall of the cyclone and out of the FEED Vortex finder FLOATS Spigot SINKS cyclone through the F i g . 1.1 Dense medium cyclone spigot. The low-density particles are carried by the medium toward the central air core and exit from the cyclone through the vortex finder. The motive force for the separation is centrifugal rather than gravitational. The acceleration applied to feed mineral particles 2 is increased by a factor of up to 40 or more. As a result, the separation efficiency for fine particles is greatly improved and the bottom size of the coal particles that can be treated in the DMC has been decreased by an order of magnitude compared to static separators. The DMC has become the most important separation equipment in modern coal preparation industry due to its high efficiency and high capacity for upgrading medium-sized coals, its ease of operational adjustment, and its capability of treating oxidized and difficult-to-clean coals. It has also been increasingly utilized for gravity concentration of a variety of minerals such as diamond (Nesbitt and Weavind, 1960; Chaston and Napier-Munn, 1974), iron ores (Voges, 1975; Napier-Munn, 1980), tin ores (Brien and Pommier, 1964; Collins et al, 1983), magnesite (Klassen et ai, 1964), uranium, cassiterite, fluorspar, lead-zinc sulphide ore, and sylvite-hahte (Fontein and Dijksman, 1953). Like all gravity separation methods, the performance of a DMC is highly dependent on feed particle size. As the feed particle size falls below 2 mm (Driessen, 1947), separation efficiency and separation density become increasingly sensitive to the influences of cyclone operating conditions and dense medium rheological properties which not only affect DMC performance directly by exerting viscous resistance to the movement of feed particles but also indirectly through changing the medium stability. A decrease in feed particle size leads to a drastic decrease in separation efficiency. Currently, the process is applied in coal preparation mainly for processing particles larger than approximately 0.5 mm. With an increasing proportion of coal fines being processed due to the mechanization of mining methods, the depletion of easy-to-clean coals, and the strict environmental regulations on sulphur reduction, it becomes imperative to improve DMC 3 separation performance of fine particles and to lower the feed size limit cleanable in the process. Obviously, these objectives can only be achieved by a better understanding of the effects of medium rheology and cyclone operating conditions on DMC performance and of the separation mechanism in dense medium cyclone. For these reasons, processing fine coals using the DMC has generated great interest both in industrial operations (Deurbrouck, 1974; Mengelers and Dogge, 1979; Chedgy and Gunos, 1985; Kempnich, 1993) and in basic research (King and Juckes, 1984 and 1988, Lathioor and Osborne, 1984; Scott et al. 1987, Klima et al, 1990). A great improvement in its understanding has been achieved. However, the DMC separation of fines is a much more complicated process, which is affected by cyclone operating conditions, medium stability and rheological properties. The interactions among these factors and the non-Newtonian nature of the medium rheology have greatly complicated the issue and hampered the progress toward its understanding. The theory of particle movement in non-Newtonian fluids is in its early stage of development and this creates problems in interpreting and modelling the density separation in non-Newtonian dense medium. Inconsistent results were often reported in literature over the effects of medium properties and operating conditions on DMC performance. Many of the factors which contribute to DMC performance are not well understood. The design procedures, operational control and modelling of the process are more often empirical. A systematic fundamental study is very much overdue. This is partly because conventional float-sink tests are expensive, time consuming, and involve toxic chemicals. It is prohibitive to conduct extensive DMC tests with real coal fines. In addition, the non-Newtonian 4 behaviour and rapid settling properties of the magnetite dense medium create great difficulties for systematic study with the use of conventional rheometer sensor systems. The newly developed density tracer technology for density separation analysis (Davis et ah, 1985), and the recent modification of the rheometer sensor system for the rheological characterization of fast-settling suspensions (Laskowski et ah, 1988; Klein, 1992) have solved these technical problems and have paved the way for future research work. 2. RESEARCH OBJECTIVES AND SCOPE The objective of this research is to improve the understanding of the effects of medium rheological properties and cyclone operating conditions on DMC performance. A schematic diagram delineating the research approach to fulfil this objective is given in Figure 2.1. The schematic diagram also reveals the research subjects to be conducted in this thesis and their inter-relationships. According to Figure 2.1, the scope of investigation can be detailed as follows: 1. To identify the major DMC operating parameters, to determine their effects on DMC performance, and to optimize these operating parameters; 2. To investigate the effects of medium composition on DMC performance, to examine the joint effects of medium properties and cyclone operating conditions on DMC performance, and to determine the optimum dense medium characteristics for DMC separation; 3. To study systematically the rheological properties of magnetite dense medium as affected by the medium composition, and to identify the rheological models and rheological parameters to characterize the non-Newtonian properties of magnetite dense medium; 4. To develop the hydrodynamic theory of particle movement in non-Newtonian fluids establishing a theoretical basis for interpreting the influences of the non-Newtonian rheological parameters on particle movement in non-Newtonian fluids Dense IViedium Composition Dense IViedium Rheoiogy and Stability \ Hydrodynamics of Particle Movement in Non-Newtonian fluids DMC Operating Conditions DMC Separation Mechanism Figure 2.1 A schematic diagram of the research approach 7 and on DMC performance. 5. To postulate the DMC separation mechanism, and to utilize the postulated theory to interpret the DMC separation data and phenomena; 6. To correlate the DMC performance with the non-Newtonian rheological parameters, and to interpret such a correlation based on the rheological theory of magnetite suspensions and the hydrodynamic theory of particle movement in non-Newtonian fluids. 3. LITERATURE REVIEW 3.1 Theory of Dense Medium Cyclone (DMC) 3.1.1 Dense medium and particle movement inside a cyclone The medium movement inside a cyclone is a three-dimensional flow consisting of mainly two vortices rotating in the same direction. The outer vortex spirals down to the apex and the inner one swirls upward to the vortex finder forming the overflow. Based on an ideal non-viscous potential flow, for which the fluid layers can be imagined to slide over one another without energy loss due to friction (angular momentum is constant), it was derived by Driessen (1947) that the tangential velocity in the 2-dimensional vortex flow conforms to the following equation: vj=k 3.1 where v, is the medium tangential velocity, r the radial distance from the cyclone axis, and k a constant. The above equation indicates that the tangential velocity increases when approaching the air core and reaches maximum at the surface of air core. For a viscous fluid, Driessen (1947) derived the following equation: r -T v-r=k-—^ 3.2 r -r ' w ' a where r^ is the radius of cyclone wall, r^  is the radius of air cone, and x is a constant. According to Equation 3.2, the maximum tangential velocity occurs at certain radius, r^ ,: ^ K - ^ ) ^ 3.3 r l-x a For water, the influence of the viscosity is negligible; the ratio TJT^ approaches one. For fluids with very high viscosities, the ratio rjr^ is 2.718. This was experimentally verified by Kelsall (1953) in the actual measurement of the fluid velocity distribution in a 3" cyclone. He proposed the following relationship between V; and r: vj"=k 3.4 where n=l for a non-viscous (or free) vortex, and n=-l for a force vortex in which the fluid rotates as a solid body (annular velocity constant). This equation applies for r values ranging from r,^  to approximately r^S (r^S is greater than r j . When the r value further decreases from r,^ /8 to r^ , Vj drops rapidly. The n value in the above equation decreases with increasing fluid viscosity. Measurements using a variety of techniques have suggested values for n in the range of 0.4 to 0.9 (Kelsall, 1952; Bradley, 1965). For the purpose of determining the medium apparent viscosity, the shear rate due to the vortex flow velocity distribution can be obtained from the derivative of Equation 3.4: ^ = -«-A:r-(i-) 3.5 dr According to the measurements of Kelsall (1953) and Lilge (1957), the shear rates of vortex flow are about zero at the cyclone wall, rising to a maximum at a point near the axis of the cyclone. The principal separating zone of the cyclone is normally in the 10 annular area between the cyclone wall and vortex finder within which the shear rate, as * measured by Collins et at (1957) on two 10" DSM and Vorsyl dense medium cyclones, is around 50 s ' . Since the shear rate is a function of cyclone diameter, inlet pressure, and medium composition, it may vary from one system to another. As a result, a different shear rate of 200 sec"' has been arrived at by Graham and Lamb (1983). As will be discussed in Chapters 8 and 9, two types of shear exist in DMC separation process. One is due to cyclone vortex flow, and another is induced by particle-to-fluid relative movement. The latter one is more fundamentally related to DMC separation. The average radial velocity of the medium, v„, in a cyclone is (Driessen, 1947): V r = — ^ 3.6 1%L where Q is the medium flow rate through a cyclone, L the height in the cyclone axial direction at radius r. Kelsall (1953) found that the radial velocity decreases with decreasing radius and becomes zero in the vicinity of the air cone/water interface. The vertical velocity of the medium in a cyclone varies as a function of the distance from the cyclone axis. The largest downward velocities occur near the conical wall. As the radial distance from the cyclone axis decreases, the downward vertical velocity decreases to zero at certain point. Then, it becomes upward increasing to a maximum near the air cone/fluid interface. Thus, an "envelope" is formed by the locus of zero vertical velocity. All fluid outside this envelope moves downwards and all fluid inside moves upwards. While the particle movement in a cyclone is also three-dimensional, the density 11 separation is mainly achieved by the relative radial movements of different density particles. The radial movement within a cyclone is determined by a balance between two forces: F^, the radial force due to centrifugal acceleration; and F^, the radial drag force. The following equations are most often used to calculate these forces (Kelly and Spottiswood, 1982; Napier-Munn, 1990): 6 r 17 1 2 . The radial terminal velocity is obtained by equating F^ with F^: 3.8 "'H 4</(5-p)vf 3.9 3 C^p r where 6 and p are the particle and fluid densities, respectively and d is the particle diameter. As will be discussed in Chapter 5, Equation 3.8 must be used with care due to existence of an inward radial medium velocity in a DMC. 3.1.2 Dense medium cyclone performance evaluation The DMC separation performance is evaluated with the use of a partition curve (or Tromp curve) which gives the percentage of any narrow density fraction of the feed reporting to the cyclone overflow (Figure 3.1). From the partition curve, two principal performance parameters can be obtained cutpoint, 650, and Ecart probable, Ep. The density of the feed particles which have equal probabilities of reporting to overflow and underflow is called the cutpoint, 650. The Ecart probable, Ep, reflects the sharpness of the 12 100 80 75 S5 60 H n E 3 C C o 50 ig 40 OS Q. 25 20 " " ' " l - - - ^ — S :N -5.5 ,1 \ \ \ \ \ \ \ (0 c 0) T3E 3 • D 0 } E r t 1 Perfect separation \ ^ \ j \ 1 \ Normal separation 1 \> ! \ j \ , 1 r\ j i \ ! \ 1 6 50 * N j N. 1/ ,'- "•"---. L /L 1..J. -1 :•-^~ 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Specific gravity Figure 3.1 A partition curve 13 separation. It is defined as: £--^25~^75 3.10 2 where 875 and 825 are the feed particle densities with 75% and 25% probabilities of report-ing to overflow, respectively. Obviously, a higher Ep value indicates a lower separation efficiency. With perfect separation, where all the mineral particles with densities lower than 850 report to the overflow and those higher than 850 to the underflow, the Ep value is zero. In DMC separation, the cutpoint is normally higher than the medium density, p^,. The difference, 850-Pn,, is called cutpoint shift, A850. As will be discussed later, both the Ep value and cutpoint shift are functions of feed particle size, medium properties and cyclone operating conditions. 14 3.2 Effect of Medium Properties on DMC Performance 3.2.1 Effect of medium rheology on DMC performance The study on the effect of medium rheology on dense medium performance is complicated due to the non-Newtonian properties of the medium. Whitmore and co-workers (Whitmore, 1958; Valentik and Whitmore, 1964) suggested that the separation efficiency of coal washing baths is a function of medium plastic viscosity. Napier-Munn (1980), who used a heavy liquid as a medium and modified the medium viscosity by using fine quartz particles, also found that with increasing medium plastic viscosity, the separation efficiency decreased, while the cutpoint increased. Since medium yield stress is a measure of the rigidity of the dense medium before movement is achieved, Whitmore (1958) claimed that dense medium separation is unlikely to be affected by the yield stress due to the constant shear created by the medium flow in dense medium bath or DMC. Although the importance of the yield stress in dense medium separation has been suggested by several researchers (Geer et al, 1957; Napier-Munn, 1980; Klein, 1992), no experimental data have been available. Napier-Munn (1980) speculated that since the near-density materials are more likely to be "locked" in the medium, the effect of the yield stress will lead to the establishment of a horizontal plateau region on the partition curve centred around feed medium density. Apparent viscosity has more often been used to characterize medium rheology and to correlate with DMC performance (Collins et al, 1974; Davis and Napier-Munn, 1989; Scott et al, 1987). In a series of DMC separation tests, Davis and Napier-Munn (1987) found that the separation performance of the coal washing cyclone was severely affected by increased medium apparent viscosity resulting from clay contamination. Since the 15 value of apparent viscosity for a non-Newtonian fluid varies with the shear rate, the use of an arbitrary shear rate to determine the apparent viscosity may not be appropriate because it does not necessarily reflect the real shear experienced by particles of different sizes. Since the medium rheology is determined by the medium composition, researchers more often interpret the effect of medium properties on DMC performance in terms of the medium composition. Morrimoto (1952) claimed that changing the medium density, which results in a change in medium properties, does not have any effect on DMC performance. The investigation results by King and Juckes (1984) indicate, however, that this is true only when the partition curves are normalized by plotting the partition number against the reduced specific gravity defined as 6"=specific density/cutpoint. Thus, the absolute Ep value increases proportionally with medium density. The effect of ferrosilicon particle size was studied by Collins et al. (1974) when working at high medium densities in iron ore separation. They observed that the sharpness of separation declined when a finer grade of ferrosilicon was used. They advocated the use of spherical medium particles to reduce viscosity and showed that the use of atomized (spherical) ferrosilicon resulted in a higher separation efficiency than the use of ground, irregular shaped particles. These results were apparently attributed to the lower medium viscosities associated with media composed of coarse or rounded particles. An opposite trend was observed by Fourie et al. (1980) and Chedgy et al. (1986). They claimed that with progressively finer magnetite, an improved separation efficiency was observed. Fourie et al. (1980) recommended that for a sharp separation of coal, at least 50 percent of the magnetite be finer than 10 microns. This is apparently in 16 disagreement with the general assumption that a decrease in medium particle size will increase medium viscosity and reduce the separation efficiency. As will be discussed in the next section, these phenomena are due to the effect of another medium property parameter, the stability. Sehgal et al. (1982) and Davis and Napier-Munn (1987) found that increasing the slime content resulted in a decreased fine coal washing efficiency. This is apparently due to a change in medium rheology. It has been shown that (Davies et al, 1963; Collins et al, 1983; Napier-Munn, 1984) the separation cutpoint, 650, is normally higher than the feed medium density, 5n,; the 850 for finer treated particles is always higher than that for coarser ones. At a constant 5„, the 850 decreases when the medium viscosity is increased by adding clay to the medium (Davis and Napier-Munn, 1987), or by reducing the magnetite particle size (Cohen and Isherwood, 1960). At very high medium viscosities, the 650 approaches 5^. Collins et al (1983) and later Davis and Napier-Munn (1987) examined the overflow and underflow medium densities and the separation cutpoint as affected by the apparent medium viscosity and found that the 650 corresponded to the underflow medium density, 6„, under normal operating conditions. They concluded that the medium viscosity influences the separation cutpoint through changing the underflow medium density since increasing medium viscosity, while keeping the feed medium density constant, results in a higher overflow density and a lower underflow density. 3.2.2 Effect of medium stability on DMC performance Collins et al {191 A) found that, compared to a stable medium, an unstable medium 17 of the same density resulted in a lower separating efficiency and a higher cutpoint shift. It is beUeved that (Stas, 1957; Davies et al, 1963; Davis, 1989) the separation is most efficient when the density differential between cyclone overflow and underflow is small, since the chances of a particle reporting to the correct stream are improved due to the recirculation of near-density particles. A high density differential was found to have an adverse effect on separation performance (Driessen, 1975; Baston and Jeunelcens, 1980). It has been recommended by Collins et al. (1983) and Scott et al. (1985) that for a satisfactory separation the density differential be maintained between 0.2 and 0.5 g/cm^. Under normal cyclone operating conditions, an air cone along the cyclone axis exists, and a spraying discharge pattern for underflow should be observed. A phenomenon of intermittent flow pattern was widely reported (Sokaski and Geer, 1963; Deurbrouck and Hudy, 1972; Driessen, 1975; Baston and Jenneken, 1980; and Davis, 1989). The normal spraying discharge was periodically interrupted by a rope-like discharge flow pattern. Sokaski and Geer (1963) explained that the near-density particles, which cannot penetrate the high-density downward-flow medium, migrate towards the axis of the cyclone into the upward-flowing medium. While being too heavy to be carried away by the low-density upward-flow medium, these particles become entrapped in the eddy current adjacent to the spigot until a sufficient amount is accumulated to interfere with the normal flow pattern in the cyclone. The internal pressure then forces the accumulated near-density materials out of the spigot causing cyclone roping (or surging) followed by the re-establishment of the cyclone flow pattern, and the whole process re-starts again. Thus, an intermittent cyclone flow pattern is observed. A similar explanation was given later by Driessen (1975). 18 It was noted by Davis and Napier-Munn (1987) in a full scale DMC test that the intermittent flow pattern was particularly prevalent when a large proportion of feed particles was in a near-density range and when the density differential exceeded 0.4 g/cm^. After stabilizing the medium by using finer magnetite (Sokaski and Geer, 1963), or by adding clay to the medium (Davis, 1989), the intermittent flow pattern disappeared indicating its close relationship with medium stability. The medium stability also influences the cyclone performance by changing the cutpoint shift. Fontein and Dijksman (1953), in studying sylvite/halite separation in a medium of fine magnetite and a saturated solution of NaCl/KCl, found that pure (heavy) liquids or stable media produced zero cutpoint shift. Davis (1989) in the DMC separation of coal also observed that, at a constant medium density, cutpoint shift decreased with increasing medium stability and became zero when medium was highly stabilized. 3.2.3 Joint effects of medium rlieology and medium stability The medium rheology and stability are inter-related (Whitmore, 1957; Apian et al, 1965; Collins et al, 1974; Govier et al, 1957; Klassen, 1964 and 1966; Valentik et al, 1965 and 1976; Klein, 1992). Stabihzing the dense medium by reducing the magnetite particle size or by adding clay into the suspension can substantially increase the medium viscosity. Davies et al (1963) indicated that although the separation efficiency could be improved by reducing the density differential, the separation might deteriorate if this was achieved at the expense of high medium viscosity. This can be illustrated by the results of Collins et al (1983) obtained in the DMC separation of tin ore; they found that there was a gradual increase in the separation efficiency as the density differential decreased 19 from 0.85 to 0.41 g/cm ,^ and when the density differential decreased further from 0.41 to 0.10 g/cm^, the separation efficiency deteriorated. This is obviously attributed to an elevated medium viscosity. The most efficient operation was obtained with density differential around 0.40 g/cm .^ The opposing influences of medium stability and medium rheology can be further illustrated by the different conclusions arrived at by various researchers. Sokaski and Geer (1963), in evaluating the performance of a 250 mm DMC in separation of coal, found that the fine magnetite medium provided sharper separation than the coarse one. A similar finding was also reported by Fourie et al. (1980) and Chedgy et al. (1986). They attributed this to the higher medium stability associated with finer magnetite. However, an opposite conclusion was obtained by Stoessner (1987) in studying the effect of magnetite particle size on DMC performance and by Collins et al. (1974) when working with ferrosihcon medium in iron ore separation. They reported that the fine magnetite (or ferrosihcon) does not perform as well as coarse commercial magnetite (or ferrosihcon) and attributed this to the deleterious effect of viscosity on the DMC performance when fine magnetite (or ferrosihcon) was used. Obviously, the DMC performance is determined not only by the medium properties (or composition), but also by the cyclone operating conditions. The optimum magnetite particle size distribution which gives reasonable stability and low viscosity in one operation can become an inferior one in another operation when medium density or cyclone operating condition (e.g. inlet pressure) is changed. 20 3.3 Effect of Operating Conditions on DMC Performance Major cyclone operating variables include feed particle size, cyclone inlet pressure, cyclone design parameters, and coal to medium volume ratio. The above contradicting conclusions concerning the effect of magnetite particle size distribution on DMC performance obtained by different researchers implies that the effect of medium properties on DMC performance is also interrelated with the cyclone operating conditions. Different combinations of medium properties and cyclone operating conditions will yield different separation results. This can be further illustrated by the following opposite trends observed by different researchers. When using a commercial grade of magnetite at low medium densities, Chedgy et al. (1986) found that the separation efficiency deteriorated when the cyclone inlet pressure was raised, and that the performance of small diameter cyclones at high feed pressures was inferior to that of large diameter cyclones tested under similar conditions. This finding contradicts the general presumption of the beneficial effect of increased centrifugal acceleration associated with higher inlet pressures in a smaller cyclone. Obviously, with the coarse commercial magnetite the adverse effect of increased medium segregation more than offsets the beneficial effect of higher centrifugal acceleration achieved with elevated inlet pressures and smaller cyclone diameters. Quite a different phenomenon was reported by Klima and Killmeyer (1990), who used micronized magnetite (90% <5)im) in the separation of fine coal and observed that when the feed pressure was increased from 35 to 372 kPa, the separation efficiency was significantly improved. Apparently, the very stable micronized-magnetite medium allows the use of high centrifugal acceleration without inducing an unduly high density 21 differential. The cyclone inlet pressure has twofold influences on DMC performance. On one hand, an increased inlet pressure increases the centrifugal acceleration in a cyclone, and may consequently improve the separation efficiency. On the other hand, it also increases the segregation of the medium which may lead to the deterioration of the separation efficiency. Apparently, the separation efficiency increases with inlet pressure up to a certain pressure point, and then falls off due to excessive magnetite segregation. This explains why with increasing inlet pressure, an increase in separation efficiency was observed by Klima and Killmeyer (1990) when using a micronized-magnetite dense medium, while an opposite trend was observed by Chedge et al. (1986) when using a commercial magnetite. Dense medium cyclones employed for cleaning coals usually operate at a minimum feed pressure head of nine times the cyclone diameter in meters of liquid column. Mengelers (1982) pointed out that larger diameter cyclones treating coals of wider size ranges (-50+0.5 mm) may require higher feed pressure than 9Dc in order to perform as well as original DSM 500 to 600 mm diameter cyclones treating -10+0.5 mm coals. In the separation tests of fine coal (-0.6+0.038 mm), a much higher inlet pressure of 35 to 375 kPa was used by Klima and Killmeyer (1990). This pressure is equivalent to 17 to 180 times the cyclone diameter. The performance of a DMC, like all gravity separators, is strongly affected by the feed particle size. In an early work, Driessen (1947) found that for coal feed particle sizes below 2 mm, the separation efficiency deteriorates and cutpoint shift increases drastically with decreasing particle size. These results were later confirmed by Davies et al. (1963) 22 in the DMC separation of fine ores. With decreasing coal particle size, the moving velocity of the coal particles relative to the medium decreases and an increasing proportion of coal particles is unable to report to the designated products within the cyclone residence time. As a result, the treatment of fine coal necessitates the use of high centrifugal acceleration achieved either by increasing inlet pressure or by reducing the cyclone diameter (Deurbrouck, 1974). Correspondingly, the ultra-fine magnetite has to be used to prepare the medium since the commercial magnetite currently in use experiences severe classification under high centrifugal acceleration. Efforts have been made by many researchers (Mengelers, 1982; King and Juckes, 1984 and 1988; Klima et al, 1990; and Klima and Killmeyer, 1990) to investigate the treatment of fine coal below 0.5 mm using DMC. The process has been demonstrated at a number of commercial coal preparation plants (Clybum, "1980; Fourie, 1980; Osborne et al, 1984; Stoessner, 1987). A successful operation in Australia was recently reported by Kempnich et al. (1993). Driessen (1975) and Baston and Jenneckens (1980) claimed that considerable load variation did not influence DMC performance provided that the designed raw coal feed rate was not exceeded. Davis (1989) and Klima and Killmeyer (1990) recommended that the raw coal feed rate as expressed by the coal-to-medium ratio be kept below 1:4 to 1:5 beyond which the separation deteriorates with increased misplacement of dense material to the overflow due to spigot crowding. It was also noted by Davis (1989) that when the cyclone was operating from 0 to full load at low density differential (0.3 s.g) the cutpoint and Ep only changed slightly. Similar results were also reported by Klima and Killmeyer 23 (1990) on the separation of fine coal. They found that the Ep value was only slightly affected when the coal-to-medium ratio varied from 1:10 to 1:5 even with the finest feed size fraction (0.075x0.038 mm). The main cyclone design parameters are the cone angle, and the diameters of the cyclone inlet, vortex finder, and spigot. Belugou and de Chawlowski (1950) studied the performance of 150, 350 and 500 mm cyclones in separating coal using barite and shale medium and found that under "normal" operating conditions the inlet diameter and cone angle, which is normally fixed at about 20°, had no effect on cyclone performance except in determining the capacity. Napier-Munn (1984) later observed, however, that the effect of cyclone inlet diameter is significant; the separation cutpoint shift at a given pressure increases with inlet diameter. He attributed this to changes in the momentum supplied to the rotating medium in the cyclone, the larger inlet diameter experiences less tangential velocity drop as the medium enter the body of the cyclone. Deurbrouck and Hudy (1972) claimed that the variations in orifice diameters did not affect the cyclone performance. The results obtained by other researchers, however, proved otherwise. It was observed that by decreasing the spigot diameter the separation efficiency (Olajide and Cho, 1989) and cutpoint shift (Belugou and de Chawlowski, 1950; Matoney, 1962) were significantly increased. Sokaski etal. (1979) advised that the spigot diameter be used as a coarse adjustment to the cutpoint. Such an idea has been employed by the Krebs Engineers (Moorhead, 1991) in an attempt to build a DMC with pneumatically controlled rubber-bladder spigot for cutpoint control. The above investigators treated the cyclone vortex finder and spigot diameters as independent variables. The two variables, as shown by Stas (1957), are interrelated; the 24 cyclone performance is related to their diameter ratio, DJD„, which is also called the cone ratio. He concluded that above cone ratio of 1.0, the underflow medium density and separation cutpoint increased rapidly. This conclusion was later confirmed by Brien and Pommier (1964). In general, the medium properties and cyclone operating conditions are inter-related. They jointly determine the DMC performance. Different combinations of the medium properties (or composition) and the cyclone operating conditions will result in different DMC performance results. The study of the effect of medium properties on cyclone performance must be carried out in the context of optimized cyclone operating conditions; satisfactory DMC performance can be achieved only with the combination of the optimized medium properties and the cyclone operating conditions. 25 3.4 Summary As reviewed above, the dense medium separation is a very complicated process. Its performance is subject to the effects of medium rheology, medium stability, and cyclone operating conditions. The major issues that are still unclear or in controversy can be summarized as follow: (1) The effect of medium yield stress on dense medium separation. (2) The joint effects of medium rheology and medium stability on dense medium separation. (3) The effect of medium composition including magnetite (or ferrosilicon) particle size distribution and medium density on dense medium separation. (4) The joint effects of cyclone operating conditions and medium properties on dense medium separation. In order to address these issues, a systematic investigation as delineated in Chapter 2 will be carried out in this thesis. 26 4. EXPERIMENTAL PROGRAM 4.1 Materials 4.1.1 Magnetite samples To study the effect of magnetite particle size on the stability and rheology of magnetite dense medium, and on the cyclone separation performance, six magnetite samples (Mag#l to Mag#6) have been prepared. Their particle size distributions are well represented by the Rosin-Rammler-Bennett (RRB) distribution: F(d)=100[l-exp( *63.2 -)'"] 4.1 The RRB size (dgjz) and distribution (m) moduli of these samples are given in Table 4.1. Table 4.1. RRB size and distribution moduli of the magnetite samples Sample Mag#l Mag#2 Mag#3 Mag#4 Mag#5 Mag#6 d63.2(Mni) 30.5 18.0 33.0 4.3 2.7 35.0 m 3.2 1.6 4.1 1.9 2.5 3.9 Mag#l is the commercial magnetite used by the coal producers in Western Canada, which was kindly provided by Craigmont Mines, B.C., Canada. Mag#2 was 27 prepared by grinding Mag#l in a 500 mm diameter ball mill. Mag#3 and Mag#6 were obtained by rejecting fines from Mag#l in a 7.4 cm classifying cyclone. Mag#4 and Mag#5 are micronized-magnetite (70%<5 |am and 90%<5 |mi, respectively) kindly provided by the U.S. Department of Energy, Pittsburgh. 4.1.2 Density tracers The conventional sink-float technique for the derivation of partition curves is expensive and time consuming, and usually involves the use of toxic chemicals. The accuracy of the results is often affected by the sampling representativeness and reproducibility, and by the coal particle degradation. In the case of fine coal, the accuracy of the traditional float-sink procedure is usually poor. This has lead to the development of density tracer techniques. The density tracers developed by Davis et al. (1985) are plastic particles dosed with heavy metal salts to known specific gravities and colour-coded for identification. The use of density tracers allows rapid analysis of DMC performance. Two series of fine density tracers were acquired from Partition Enterprise Pty Ltd., Australia. Their specifications are given in Tables 4.2 (a) and (b). Table 4.2 (a). Specifications of density tracers - series one Nominal density 1.20 1.25 1.30 1.35 1.40 1.45 Colour Black white Yellow lime green Red blue Real density 4x2 mm 1.190 1.256 1.300 1.340 1.400 1.452 1x0.71 mm 1.210 1.262 1.315 1.340 1.400 1.440 .5x.355 mm 1.210 1.265 1.310 1.366 1.420 1.459 28 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.90 Blue purple Orange grey Green white Pink yellow 1.480 1.550 1.590 1.650 1.690 1.750 1.790 1.888 1.490 1.555 1.600 1.650 1.715 1.750 1.810 1.911 1.520 1.570 1.630 1.655 1.740 1.755 1.820 1.912 Table 4.2 (b). Specifications of density tracers - series two Nominal density 1.30 1.32 1.34 1.36 1.38 1.40 1.52 1.54 1.56 1.58 1.62 1.64 1.66 1.68 Colour yellow pink white purple lime green dark blue grey yellow pink white purple light blue lime green grey Real density 4x2 mm 1.30 1.32 1.34 1.36 1.38 1.40 1.52 1.54 1.56 1.58 1.62 1.64 1.66 1.68 1x0.71 mm 1.30 1.32 1.34 1.36 1.38 1.40 29 4.2 Equipment 4.2.1 Pilot scale DMC circuit In this investigation, a pilot scale DMC circuit has been designed by the author and constructed by the technicians in Department of Mining and Mineral Process Engineering of UBC. The circuit layout and flowsheet are shown in Figures 4.1 (a) and (b), respectively. The 150 mm (6 inch) cyclone (model D6B-12°-S287) obtained from Krebs Engineers International, California, is placed on a supporting frame which is suspended on four 19.1 mm Ready rods. The cyclone is positioned at a pressure head of ten times the cyclone diameter (1.52 m). The cyclone is incHned at 15 degrees to the horizontal in accordance with industrial practice. The cyclone has changeable apex and vortex finder assemblies. Nine apex diameters (2.54, 3.18, 3.81, 4.45, 5.08, 5.64, 6.10, 6.35 and 7.62 cm) and three vortex finder diameters (3.81, 6.35 and 7.62 cm) are available. The head-box with a fluid-level control mechanism is positioned above the cyclone to provide a constant liquid head level. It is connected to the cyclone with a flexible hose to allow the adjustment of cyclone height. Two sampling boxes: one for cyclone overflow and another for underflow are designed both for sampling and for flowrate measurements. They are supported on rails inside the feed sump and thus movable to facilitate the sampling operation. Each sampling box has a 200 mm diameter opening in the bottom and a screen socket below the opening. During sampling, a 150 mesh screen is attached to the socket. The product particles are retained on the screen while the carrying medium passes through the screen back to the pump sump. During flow rate measurement, the opening is closed. The time required to fill up the sampling box and volume of the 30 headbox 6" DMC, sampling box. pump sump-THIRD FLOOR SECOITO FLOOR •y///77//////y/A •• •/ '///7//>/////'/y/'^y/y/'^// MAIN FLOOR Figure 4.1 (a). Layout of the 150 mm DMC circuit 31 Feed dense medium \ H e a d b o x Bypassing dense medium Pump Figure 4.1 (b) Flow sheet of the 150 mm DIVIC circuit 32 sampling box (23 litres) are used to calculate flow rate. The densities of the medium streams are monitored using a Marcy pulp density gauge. 4.2.2 Equipment for preparation and characterization of magnetite samples Classifying cyclone circuit. A 73.4 mm classifying cyclone circuit was employed to prepare the narrow-sized coarse magnetite samples, Mag#3 and Mag#6, in a batch mode operation. The feed magnetite (Mag#l) slurry was pumped to the classifying cyclone at a pressure of 78 kPa. The cyclone overflow was directed to an ENVIRO deep-cone-thickener, while the underflow was returned to the feed sump and recycled. The outgoing water to the deep-cone-thickener was made up by feeding clean water into the sump to keep the water level constant. After the cyclone overflow became clear, the cyclone underflow (Mag#3 or Mag#6) was discharged into a bucket. The same procedure was repeated until required amount of sample was produced. Ball mill. A ball mill of 450 nmi in diameter was set up and used to prepare the Mag#2 magnetite sample from the commercial magnetite Mag#l in a batch mode operation. In each run, about 40 kg of the Mag#l and 27 litres of water (60 percent pulp solid content) were loaded into the mill. The grinding time for each batch run was arbitrarily set at one hour. Particle size analyzer. An Elzone 280 PC particle size analyzer was used to determine the particle size distribution of the magnetite samples. The measurement generates a histogram of volume size, d^ , versus particle population. 4.2.3 Rheometer Rheological characterization of magnetite dense media was carried out using a 33 HAAKE Rotovisco RV20 rheometer. This is a rotational Searly-type rheometer in which the bob rotates inside a cup containing the suspension. The shear stress is determined from the torque exerted on the bob from the suspension. The shear rate versus time can be programmed on the PC computer interfaced with the rheometer; during measurement, the shear stress is monitored and the data recorded by the computer. An elongated sensor system (ESSP) specially designed and built in this laboratory (Laskowski et al, 1988; Klein, 1992) for rheological measurements on rapidly settling suspensions was employed. It consists of an elongated cup and inner cylinder with a bob attached to an elongated shaft. It is arranged so that the bob is positioned in the constant density zone of the suspension to avoid the effect of magnetite settling during the measurement. 34 4.3 Experimental 4.3.1 Operation of tiie DMC circuit The total volume of the magnetite dense medium charged into the sump is about 280 litres. Prior to testing, the pump is turned on and kept running to circulate the dense medium in the circuit for at least 20 minutes in order to homogenize the medium. Since the medium flow rate is affected by the medium properties and cyclone operating conditions, the pump speed and head-box bypassing valve need to be adjusted prior to testing to maintain a constant medium flowrate over the weir inside the head-box which controls the fluid level in the head-box. The densities and flow rates of the feed, overflow and underflow media are monitored throughout the testing using a Marcy pulp density gauge. To measure the overflow and underflow medium flow rate, the screen socket opening on the bottom of sampling box is closed. The time span for filling up the box is used to calculate the flow rate. The medium temperature is monitored using a thermo-couple. For a 6-hour continuous run on a 1.5 g/cm^ dense medium, a temperature increase of 4°C has been observed. A deliberate temperature control is thus not needed. During separation tests, the density tracers of different densities are always kept separate. Each time, only one density fraction is introduced into the cyclone loop from the head box; the minimum weight for each density fraction which includes three size fractions is about 100 grams. The tracer particles reporting to overflow and underflow are recovered on the screens mounted on the bottom of the sampling boxes, while the carrying media pass through the two screens back to the sump and are recycled. Approximately 25 minutes is required to recover all the introduced tracer particles in the 35 circuit. The tracer particles in the two products are washed, dried and weighed separately. From the weights, one partition number can be calculated. The whole process is repeated with different density fractions in order to get enough data points for constructing a partition curve. To check the accuracy, a duplicate data point for each tracer density close to the separation cutpoint is produced. During testing, the medium in the sump is continuously stirred and mixed by the back-flowing bypassing medium from the head-box to prevent the magnetite from settling in the sump. 4.3.2 Rheological measurement The rheological measurements on magnetite suspensions are complicated due to the instability caused by settling. The ESSP sensor system (Laskowski et al, 1988; Klein, 1992) makes use of the zoning properties of the hindered settling by positioning the bob in the constant density zone of the settling column. Obviously there is a measurement time limit due to the decrease and eventual disappearance of the constant density zone; the time limit is mainly a function of magnetite particle size and medium density. The measurement time period of 2 minutes has been used by Klein (1992) for a magnetite solids content above 15% by volume. In order to make measurements on the less stable magnetite suspensions with solid content below 15%, a shorter measurement time period is required. For fine magnetite samples (Mag#2, Mag#4 and Mag#5), the measurement time period of 1 minute was found appropriate, while for coarse magnetite (Mag#l), a measurement time period of 30 seconds was used. To obtain a complete flow curve, the shear rate was programmed to increase linearly from 0 to 300 s"' within the predetermined time period. The effect of bob inertia in the process of angular acceleration was 36 determined from the background running test without suspension in the cup. It was found that such an effect can be neglected even when using a time period as short as 15 seconds. The medium solids content was varied from 5 to 30 percent by volume which corresponds to medium density range from about 1.19 to 2.1 g/cm^ Each measurement requires 350 ml of magnetite suspension. Suspensions were prepared by mixing the correct amount of magnetite and water in a high-speed blender to ensure breakup of all magnetite aggregates. The suspension was then discharged into a volumetric cylinder and demagnetized by using a demagnetizing coil. It was found that without using high-speed blending, erratic data points with very high shear stress value were constantly observed on the flow curves at low shear rates. The phenomenon was especially significant at high medium densities; the measurement data became meaningless. This is apparently due to the additional stress required to break up the magnetite aggregates which cannot be dispersed by shaking or low-shear mixing. In the process of high-shear blending, air may be blended into the suspension (especially the fine magnetite suspensions at high solid contents). The particulate structure of the suspensions can trap the tiny air bubbles and, consequently, change the suspension rheology. This problem can be easily solved in the process of demagnetization. When the volumetric cylinder containing the magnetite suspensions slowly moves through the demagnetizing coil, the particulate structure is completely destroyed. In the alternating magnetic field, the magnetite particles form fibrous aggregates which vary in shape, orientation, and size with the moving magnetic field. Such a process can effectively expel the air bubbles out of the suspensions. 37 5. EFFECT OF OPERATING CONDITIONS ON DMC PERFORMANCE 5.1 Introduction The DMC performance is affected by both the medium properties and the cyclone operating conditions. In studying the effect of medium properties on DMC performance, the cyclone operating conditions must first be optimized and maintained constant. This requires a good understanding of the effect of the cyclone operating conditions on DMC performance, and of the interactions between medium properties and cyclone operating conditions. This chapter addresses the first part of this whole investigation: the effect of operating conditions on DMC performance. The main operating parameters include: cyclone inlet pressure, vortex finder and spigot diameters. The DMC inlet pressure in liquid column height commonly used by coal industry is 9 times the cyclone diameter. The recommended cyclone orifice diameters relative to the diameter of the cyclone have been given by Deurbrouck and Hudy (1972) as follows: Cylindrical diameter = Dc Inlet = 0.20DC Underflow = 0.32Dc Overflow = 0.40Dc 38 As reviewed in Chapter 3, when optimizing cyclone performance, it is more common to stipulate the cyclone orifice diameters with respect to the cyclone diameter and to manipulate the orifice diameters individually in search of the optimum geometry (Belugou and de Chawlowski, 1950; Matoney, 1962; Sokaski et al., 1979; Olajide and Cho, 1989), although it has long been recognized (Stas, 1957) that the cone ratio, DyDy, is more closely related to medium flow pattern and cyclone performance. Because of the very limited data available in the literature, the effects of cyclone vortex finder diameter, spigot diameters and inlet pressure on DMC performance and their inter-relationship are still unclear. Obviously, the knowledge of such inter-relationships is critical in the DMC optimization and control. It is found in this study that the overflow to underflow flowrate ratio (O/U flowrate ratio) is a fundamental operating parameter closely related to the DMC performance, while the cyclone design parameters and inlet pressure affect the DMC performance indirectly through changing the O/U flowrate ratio. To interpret these results, a theoretical model is derived laying the groundwork on the part of DMC operating conditions for further investigation into the effect of medium rheological properties on DMC performance. 39 5.2 Results 5.2.1 Control of O/U flowrate ratio The O/U flowrate ratio can be altered either by changing the vortex finder and spigot diameters or by changing the cyclone inlet pressure. In this work, the O/U flowrate ratio is controlled by changing the vortex finder and spigot diameters. The following vortex finder and spigot diameters were used: Vortex finders: 2.54, 3.18, 3.81, 4.45, 5.08, 5.64, 6.10, 6.35 and 7.62 cm. Spigots: 3.81, 6.35 and 7.62 cm. This gave a total of 27 different vortex finder versus spigot diameter combinations. The tests were conducted on two magnetite samples: Mag#2 and Mag#4 at two different medium densities: 1.36 and 1.60 g/cm^ in order to determine the additional role played by the medium properties in interacting with cyclone operating conditions and in influencing DMC performance. At a fixed inlet pressure (150 cm), the relationship between the O/U flowrate ratio and cone ratio (defined as the cyclone vortex finder to spigot diameter ratio) is independent of medium properties over the tested range as the data obtained on the three magnetite dense media fall on the same curve, Figure 5.1 (a). The relationship is, however, sensitive to the combination of vortex finder and spigot diameters. At any given cone ratio, a smaller vortex finder will result in a higher O/U flowrate ratio. Figure 5.1 (b). 5.2.2 Effect of O/U flowrate ratio on outpoint shift The DMC cutpoint, 850 , is essentially determined by the medium density. At a 40 o 13 l U U 10 1 0.1 n^ / 6 1 1 ^ ^ ^ - ' " ' A Vortex finder 6.35 cm medium used • IV1ag#4,1.36g/cm3 0 IVIag#2,1.36g/cm^ A Mag#2,1.60g/cm^ 1 1 0.5 1.5 2 Cone ratio 2.5 Figure 5.1 (a) Effect of medium density and magnetite particle size on O/U flowrate ratio 100 10 o 0.1 0.01 vortex finder 3.81 cm 0.5 vortex finder 7.62cm vortex finder 6.35cm medium used IVIag#4,1.36 g/cm Mag#2,1.36g/cm^ Mag#2,1.60 g/cm' 1.5 2 Cone ratio 2.5 Figure 5.1 (b) Effect of vortex finder diameter on O/U flowrate ratio 41 constant medium density, however, the 850 also varies with cyclone operating parameters. Because of this, the cutpoint shift must also be used to characterize the DMC performance. When cyclone vortex finder and spigot diameters are treated as independent variables by correlating them individually with cutpoint shift, no correlations can be identified (see Figure 5.2). When the two orifice diameters were combined to form a single parameter, the cone ratio, and to correlate with 650 in Figure 5.3 (a), a significant improvement in their correlation was observed. However, such a correlation was still not well defined; a band, instead of clearly defined curves, was obtained. It is speculated that the DMC performance should be more fundamentally related to the dense medium partition between cyclone overflow and underflow (or OAJ flowrate ratio as called in this study) since the O/U flowrate ratio more directly reflects the hydrodynamic conditions inside a cyclone. To verify this supposition, the data in Figure 5.3 (a) are plotted versus the corresponding O/U flowrate ratio. As shown in Figure 5.3 (b), the curves for different size fractions can be clearly identified. At a constant medium density, the separation density increases linearly with O/U flowrate ratio on a semi-log plot. The relationship is independent of the orifice diameters that were used to adjust the O/U flowrate ratio values. The results shown in Figure 5.3 serve as preliminary evidence of the fundamental properties of the O/U flowrate ratio, but only for a fixed medium density of 1.36 g/cm^. The relationship between cutpoint and O/U ratio may also be influenced by the medium properties. To test this, the medium properties were first modified by increasing the medium density to 1.60 g/cm^. The results in Figure 5.4 reveal that the relationship between the cutpoint shift, A650, and O/U flowrate ratio is virtually unaffected by the 42 E CO •s o 0.4 0.3 0.2 0.1 -0.1 Mag#2 at medium density 1.36 g/cm ^  -A D o A e a 0 0 D 1 Feed size 4x2 mm 1x0.71 mm 0.5x0.355 mm 1 A A D A O O a 8 1 A O A fl O A 8 8 8 6 a 1 5 6 7 Vortex finder diameter (cm) Figure 5.2 (b) The relationship between cutpoint shift and vortex finder diameter 0.4 0.3 i 0.2 CO .1 °-'' O -0.1 A O D A O D A O n A O A A 8 a A o D IVIag#2 at medium density 1.36 g/cm ^  A A H D A § B A A 8 i D o A A O D Feed size 4x2 mm 1x0.71 mm 0.5x0.355 mm A A e 4 5 6 Spigot diameter (cm) Figure 5.2 (b) The relationship between cutpoint shift and spigot diameter 43 0.4 0.3 Mag#2, at medium density 1.36 g/cm ^  Feed size * 4x2mm o 1x.71mm • .5x.355mm 1.5 2 Cone ratio Figure 5.3 (a) The relationship between cutpoint shift and cone ratio 0.4 0.3 I .1 0.1 o -0.1 Mag#2, at medium density 1.36 g/cm -Tracer 4x2mm Tracer 1x.71 mm Tracer .5x,355mm 0.1 10 100 O/U flowrate ratio Figure 5.3 (b) The relationship between cutpoint shift and O/U flowrate ratio 44 U.£3 0.2 C ^ 1 0.15 :^ i*^  ^. £ 0.1 CO t 8.0.05 3 o 0 -0.05 --« medium density 1.36 g/cm ^  o medium density 1.60 g/cm ^  Feed size: 4.0x2.0mm * * o o * . •* - . ^ - - - ^ - " ^ XJ . <» 0 • o *o • • 0.1 0.25 0.2 ;a 0.15 O 0.05 0.1 0.4 0.3 -: i 0.2 I I 0.1 0.1 0/U flowrate ratio 0/U flowrate ratio ^° 1 10 0/U flowrate ratio 100 _ -• medium density 1.36 g/cm ^  o medium density 1.60 g/cm ^  Feed size: 1.0x0.71 mm O c ^ 0 • «» • • • • o • O • i • • i K> • 100 ---• medium density 1.36 g/cm ^  o medium density 1.60 g/cm ^  Feed size: 0.5x0.355mm o °* o °* * o , o • • • o. • • 1 1 .° • 100 Figure 5.4 The relationship between outpoint shift and 0/U flowrate ratio as affected by the medium density 45 medium density over the range from 1.36 to 1.60 g/cm\ which covers the normal range employed by the coal industry. The three graphs in Figure 5.4 are summarized in Figure 5.5 to show that there is a significant influence of feed particle size on cutpoint shift. The effect of medium properties on the relationship between cutpoint shift and O/U flowrate ratio was also tested by changing the magnetite particle size. As shown in Figure 5.6, the relationship between A55o and O/U flowrate ratio is very sensitive to magnetite particle size; the slope of the curve with the less stable Mag#2 dense medium is much higher than that with the highly stable Mag#4 dense medium. For comparison, the cutpoint shift data from Figure 5.4 are also plotted against the corresponding cone ratio in Figure 5.7; no individual curves can be differentiated. The results in Figures 5.2 to 5.7 reveal that the cutpoint shift plotted on a semi-log graph gives a linear relationship with the O/U flowrate ratio irrespective of the combination of vortex finder and spigot diameters being used. At any given O/U flowrate ratio, the cutpoint shift increases with decreasing feed particle size, and the cutpoint shift for the coarse feed particles (4x2 mm) approaches zero at an O/U flowrate ratio of one. These properties, which will be further discussed in Section 5.3.1, have a great bearing on DMC design, operation control, and process modelling (Section 5.3.3). These results prove that the cyclone performance is more fundamentally related to O/U flowrate ratio, and that the individual orifice diameters or the cone ratio only influence the DMC performance indirectly through changing the O/U flowrate ratio. The results also provide experimental basis on which the mathematical models developed by Plitt (1976) for classifying cyclone may be adapted to DMC. The above conclusions were reached while working with a pilot scale 150 mm 46 E CO O 0.4 0.3 0.2 0.1 -0.1 Medium density • 1.36g/cm Feed size: <0.355mm mm 0.1 size: 4x2mm 1 10 O/U flowrate ratio 100 Figure 5.5 A summary of the results in Figure 5.4 0.1 1 10 O/U flowrate ratio Figure 5.6 The relationship between outpoint shift and O/U flowrate ratio as affected by the medium stability o 0.25 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -• medium density 1.36 g/cm ^  o medium density 1.60 g/cm ^  Feed size: 4.0x2.0mm • • o * . . * Q « O 0 • • • o o • 47 0.5 E o 0.25 0.2 0.15 0.1 0.05 0 -0.05 0.5 0.4 0.3 S 0.2 I 5 0.1 o -0.1. 0.5 1.5 2 Cone ratio 1.5 2 Cone ratio • medium density 1.36 g/cm' o medium density 1.60 g/cm' Feed size: 0.5x0.355mm 1.5 2 Cone ratio 2.5 -• medium density 1.36 g/cm ^  o medium density 1.60 g/cm ^  Feed size: 1.0x0.71 mm • • o 8 8 -o a" ° • • • 8 • 0 « • t • • 0 1 • , 2.5 2.5 Figure 5.7 The relationship between outpoint shift and cone ratio as affected by the medium density 48 DMC circuit under idealized conditions where the feed to medium ratio was close to zero. A verification by full scale tests is, therefore, needed. Two series of full scale tests were conducted on a 680 mm Krebs DMC circuit at BuUmoose Operating Corp. (BOC) located in north eastern B.C. In the first test series, density tracers were used as the cyclone feed in the absence of coal; the second test series was conducted with real coal feed under normal operating conditions and the partition curves were obtained by sink-float tests. The conditions for the first test series are given in Table 5.1; the vortex finder diameter was varied to alter the 0/U flowrate ratio. As shown in Figure 5.8, the relationship between cutpoint shift and O/U flowrate ratio obtained on the full scale DMC circuit with density tracers is in agreement with those in Figure 5.4 obtained in the pilot scale investigation. In the second test series, normal production was carried out on two dense medium cyclones installed respectively with the 19.3 and 30.8 cm vortex finders. In the process, simultaneous sampling was conducted on the feed, clean coal and refuse streams. The partition curves were calculated from the sink-float test data for the three samples and were plotted in Figure 5.9. With the 19.3 cm vortex finder, the separation densities for different feed particle sizes ranged from 1.50 to 1.53 g/cm .^ When a larger 30.5 cm vortex finder diameter was used, the separation densities were increased substantially to around 1.6 g/cm^. The plant operating data provided by K. Wong (1990) of Fording Coal Ltd, are also analyzed in this chapter. As observed by K. Wong in the production process, the DMC spigot diameter experienced a continuous expansion due to wear. According to 49 Table 5.1 BOC dense medium cyclone separation tests using density tracers Parameter Dimension (cm) Vortex finder Apex Length Cone ratio 3 IVIedlum density (g/cm ) Feed Overflow Underflow Density differential O/U flowrate ratio set one 25.4 18.1 41.9 1.40 1.54 1.47 1.86 0.39 4.59 set two 19.3 18.1 44.5 1.07 1.54 1.41 1.63 0.22 0.71 set three 30.5 18.1 44.5 1.68 1.54 1.49 1.97 0.48 7.86 0.25 1 2 O/U flowrate ratio 10 Figure 5.8 The relationship between outpoint shift and O/U flowrate ratio obtained on full scale DMC circuit using density tracers 50 100 ^ 80 o o S3 60 n E c I ^ t: ra Q. B.O.C. full scale operation test 20 Feed size (mm) o +9.5 A -9.5+2.36 D -2.36 T,T T medium: 1.54 g/cm^ vortex: 19.3 cm spigot: 18.0 cm O/U ratio: 0.71 1.2 1.3 1.4 1.5 1.6 1.7 1.8 specific gravity (g/cm ) Figure 5.9 (a) B.O.C full scale DMC test using 19.3 cm vortex finder 100 80 f & 60 (0 JQ E 3 C C o 'S ce a. 40 20 B.O.C. full scale operation test Feed size (mm) o +9.5 A -9.5+2.36 D -2.36 medium: 1.54 g/cm' vortex: 30.5 cm spigot: 18.0 cm O/U ratio: 7.86 1.2 1.3 1.4 1.5 1.6 1.7 1.8 specific gravity (g/cm ) Figure 5.9 (b) B.O.C full scale DMC test using 30.5 cm vortex finder 51 Figures 5.1 and 5.3, the increase in apex diameter should reduce the cone ratio and O/U flowrate ratio, and consequently, the separation cutpoint should decrease, too. As shown in Figure 5.10 (a), the decrease in separation cutpoint with increasing spigot diameter is manifested by the increasing misplacement of the -1.6 g/cm^ clean coal fraction to the tailings. As mentioned earUer, the O/U flowrate ratio can also be adjusted by changing the cyclone inlet pressure. An elevated inlet pressure, as observed in our pilot plant investigation, will divert more dense medium to the overflow and, consequently, will increase the O/U flowrate ratio and separation cutpoint. This is confirmed by the measurements carried out by K. Wong, Fording Coal Ltd., under industrial conditions. As shown in Figure 5.10 (b), when the cyclone throughput was increased from 500 t/h to 800 t/h by increasing the inlet pressure, the cumulative clean coal loss in tailings showed a substantial decrease due to an increased separation cutpoint. 5.2.3 Effect of O/U flowrate ratio on separation efficiency To determine the effect of cyclone operating conditions on separation efficiency, the Ep value is first correlated with the cone ratio. Figure 5.11 (a). The data points are substantially scattered. The correlation is considerably improved when the Ep values are plotted against O/U flowrate ratio. Figure 5.11 (b). In comparison with the correlation between cutpoint shift and O/U flowrate ratio in Figure 5.3 (b), the correlation between Ep value and O/U flowrate ratio in Figure 5.11 (b) exhibit substantial scattering, since separation efficiency is not only a function of O/U flowrate ratio, it is also sensitive to the vortex finder diameter. The influence of vortex 52 CO D) c % •a o o E I. Fording Coal Ltd. full scale operation test 800 t/h 1200t/h 51 52 53 54 55 56 57 58 59 60 61 62 63 Spigot diameter (cm) Figure 5.10 (a) Effect of spigot expansion due to wear on the clean coal loss in the tailings 1.25 1.3 1.35 1.4 1.45 1.5 Density (g/cm^) 1.55 1.6 1.65 1.7 Figure 5.10 (b) Effect of cyclone throughput on the cumulative clean coal loss in the tailings 53 0.09 0.08 0.07 0.06 S 0.05 1 o. 0.03 0.02 0.01 -----A • A A A ^ 2 o OO • A A A O 0 A O • 9 • • Mag#2 at A A 0 o" • medium d A A O 0 • ensity 1.36 g/cm ^ Feed size • 4x2mm o 1.x.71mm A .5x.355mm A O • 0.5 1.5 2 Cone ratio 2.5 Figure 5.11 (a) The relationship between Ep value and cone ratio 0.09 0.08 0.07 0.06 S 0.05 3 a. 0.03 0.02 0.01 0.1 --: ^ --\ ^ \ s ^ \ *^^ \ , A ^ ^ ^ , o O 1 A O • IVIag#2 at medium A * A O O A • o A A O O • ' 1 density 1.36 g/cm Feed size • 4x2mm o 1 .X.71 mm A .5x.355mm 3 • ^ 1 10 0/U flowrate ratio 100 Figure 5.11 (b) The relationship between Ep value and 0/U flowrate ratio 54 finder diameter on separation efficiency is shown in Figure 5.12. At any given O/U flowrate ratio, a lower Ep value is obtained with smaller vortex finder diameter. Obviously, it is beneficial to use a combination of smaller vortex finder and spigot diameters; the increased residence time of feed particles improves their chance of reporting to the correct product streams. Any attempt to increase DMC throughput by using a combination of larger vortex finder and spigot diameters will result in a lower separation efficiency. The influence of the medium properties on the relationship between Ep value and O/U flowrate ratio was also investigated by changing the medium density and magnetite particle size distribution. At any given O/U flowrate ratio and a constant medium density, the magnetite particle size distribution does not affect the general relationship between Ep value and O/U flowrate ratio; the curve only shifts slightly to a higher position when Mag#4 dense medium is employed (see Figure 5.13). A considerable increase in Ep value occurs only when the O/U flowrate ratio is below one, which, as will be discussed in section 5.3.2, is out of the normal O/U flowrate ratio operation range. The general relationship between Ep value and O/U flowrate ratio is not affected by a change in medium density either (see Figure 5.14); an increase in medium density from 1.35 to 1.60 g/cm^ only shifts the curves up to higher locations. The results shown in Figures 5.11 to 5.14 indicate that the separation efficiency improves with increasing O/U flowrate ratio. The results of Olajide and Cho (1989), which indicate that the separation efficiency of DMC improves with a smaller spigot diameter, are apparently due to an increased O/U flowrate ratio (see Figure 5.1). 55 0.14 0.12 0.1 ® 0.08 m 0.06 IVIag #4, at 1.36 g/cm^, tracer 1 .x.71 mm 0.04 0.02 3.81 cm / vortex finder 7.62 cm 6.35 cm / ' 0.1 1 10 0/U flowrate ratio 100 Figure 5.12 Effect of vortex finder diameter on Ep value 0.14 0.12 0.1 § 0.08 lu 0.06 0.04 0.02 Vortex=6.35cm, tracerl .0x0.71 mm, at 1.36 g/cm^ 0.1 M a g # 2 ^ 1 10 0/U flowrate ratio 100 Figure 5.13 Effect of magnetite particle size on Ep value 0.05 0.04 56 UJ 0.03 -0.02 0.01 -M a g # 2 Tracer size: 4.0x2.0 mm • 1 Medium density o 1.60 g/cm^ , 1.36 g/cm^ • 1 0.1 3 a LU 0.1 0.08 0.06 0.04 0.02 0.1 0.15 0.1 ffi 3 1 Q. LU 0.05 0.1 1 10 O/U flowrate ratio 1 10 O/U flowrate ratio M a g # 2 Tracer size: 0.5x0.355 mm Medium density o 1.60 g/cm^ • 1.36 g/cm^ 1 ., - 10 O/U flowrate ratio 100 -_ ---M a g # 2 Tracer size: 1.0x0.71 mm Medium density o 1.60 g/cm^ , 1.36 g/cm^ \ ^ ^ ^ ^ ^ - ^ - _ _ o ^ J ^ * o . 0^ ^ ^ ^ ^ * ^ ^ ^ ^ - ^ ^ - ^ ^ ^ • -—-^ ^_^^  1 1 100 100 Figure 5.14 The relationship between Ep value and O/U flowrate ratio as affected by medium density 57 5.2.4 Effect of O/U flowrate ratio on medium stability At a constant feed medium density, the cyclone overflow and underflow medium densities are determined by the O/U flowrate ratio. While the underflow medium densities show a continuous increase with O/U flowrate ratio in Figure 5.15, the overflow medium density of Mag#4 dense medium as shown in Figure 5.15 (a) is hardly affected. A minor change in the overflow medium density of Mag#2 dense medium is observed (see Figure 5.15 b and c); it reaches a minimum at an O/U flowrate ratio of one. Apparently, with the elevated O/U flowrate ratio, an increasing proportion of dense medium is diverted to the overflow, only the highly concentrated dense medium close to cyclone wall reports to underflow making the underflow density higher. The relationship between O/U flowrate ratio and overflow and underflow medium densities in Figure 5.15 is practically independent of vortex finder and spigot diameters when the orifice diameters are varied over a limited range; the variation in magnetite particle size distribution or in medium density does not change the general pattern of the relationship. Density differential, defined as the difference between underflow and overflow medium densities, is often used as a measure of dense medium stability. A high density differential is generally considered to be unfavourable to DMC performance and may result in a poor separation efficiency. The density differential of Mag#4 dense medium is plotted separately against the cone ratio and O/U flowrate ratio in Figure 5.16 (a) and (b), respectively. Apparently, the density differential is more closely correlated with the O/U flowrate ratio than with the cone ratio. The same is true with the Mag#2 dense medium (see Figure 5.17). I •D E E 1 1.6 1.55 1.5 1.45 1.4 1.35 1.3 1.25 Mag#4 at medium density 1.36 g/cm 0.1 vortex finder diameter 3.81 6.35 7.62 overflow . i . underflow a ^ o 1 10 0/U flowrate ratio (a) 58 100 • & m T3 E 3 E 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 Mag#2, at medium density 1.36 g/cm' vortex finder diameter 3.81 6.35 7.62 overflow underflow 0.01 0.1 1 0/U flowrate ratio (b) 10 E •(0 •a E E s^ 2.1 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 density 100 Mag#2at1.60g/cm3 Mag#2 at 1.36 g/cm density 0.01 0.1 1 10 100 0/U flowrate ratio (c) Figure 5.15 The overflow and underflow medium densities as a function of 0/U flowrate ratio 59 ^^  6 ft) •<3 1 x> ^ 1 n 0.11 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Mag#4, at medium density 1.36 g/cm^ Vortex diameter o 3.81 cm • 6.35 cm A 7.62 cm 0.8 1.2 1.4 1.6 Cone ratio 1.8 2.2 Figure 5.16 (a) The relationship between density differential and cone ratio 1 10 O/U flowrate ratio Figure 5.16 (b) The relationship between density differential and O/U flowrate ratio 60 0.6 0.5 I 1 f 0.4 0.3 0.2 0.1 IVIag#2, at medium ^ -Vortex diameter o 3.81 cm • 6.35 cm ^ 7.62 cm density 1.36 g/cm ^  • • o 0 °' ' A • • A ^ 1 1 1 • 1 0.5 1.5 2 Cone ratio 2.5 Figure 5.17 (a) The relationship between density differential and cone ratio 0.6 0.5 I 0.4 0.3 I-0.1 Mag#2, at medium ~ -Vortex diameter o 3.81 cm " 6.35 cm A 7.62 cm -~ 1 density 1.36 g/cm ^ > /o o '/' o / . y ^ / A • • / y^ A 1 1 0.01 0.1 1 0/U flowrate ratio 10 100 Figure 5.17 (b) The relationship between density differential and 0/U flowrate ratio 61 The medium composition has a significant influence on medium stability. At any given O/U flowrate ratio, a finer magnetite. Figure 5.18 (a), or a higher medium density resulted in a lower density differential. According to the results shown in Figures 5.16 to 5.18, the density differential for any given dense medium composition increases with O/U flowrate ratio. This is also confirmed in the full scale DMC separation test at BuUmoose Operating Corp. As indicated in Table 5.1, the value of the density differential doubles when the O/U flowrate ratio increases from 0.71 to 7.86. Strictly speaking, the density differential is also a function of vortex finder diameter. At any given O/U flowrate ratio, the density differential with a larger vortex finder diameter is always lower than that with a smaller vortex finder diameter; see Figures 5.16 (b) and 5.17 (b). 62 a> •ffl TO c a 0.6 0.5 0.4 0.3 0.2 0.1 0 Vortex finder: 3.81 & 6.35 cm Medium density: 1.36 g/cm^ Mag#2 0.01 0.1 1 0/U flowrate ratio 10 100 Figure 5.18 (a) Effect of magnetite particle size on the relationship between density differential and 0/U flowrate ratio o B a 1 a> I W c 0) Q 0.01 u.o 0.5 0.4 0.3 0.2 0.1 0 Vortex finder: --" 1 3.81 & 6.35 cm / Mag#2 at 1.36 g/cn? / ^ ^ " 7 ^ 5 ^ X Mag#2 at 1.60 g/cm^ o 1 1 0.1 1 10 0/U flowrate ratio 100 Figure 5.18 (b) Effect of medium density on the relationship between density differential and 0/U flowrate ratio 63 5.3 Discussion 5.3.1 Control range for O/U flowrate ratio To determine the optimum working range of OAJ flowrate ratio, it is necessary to explore the influence of O/U flowrate ratio on DMC performance over an extended range. It was anticipated that an excessively high or low O/U flowrate ratio could exert an adverse influence on DMC performance. Results shown in Figures 5.16 to 5.18 indicate that a low O/U flowrate ratio may help reduce the density differential. This is, however, achieved at the expense of an increased Ep value (see Figures 5.11 to 5.14). Short-circuiting to underflow is closely associated with low O/U flowrate ratio; part of the cyclone feed reports directly to the underflow orifice without going through the separation process. As shown in Figure 5.19, all the short-circuiting occurs at O/U flowrate ratios much lower than one. When the O/U flowrate ratio increases to above 1.0, the phenomenon of short-circuiting disappears. Short-circuiting is also sensitive to feed particle size. Figure 5.19 (a and c). It became increasingly significant when feed particle size decreased from 4x2 mm to 0.5x0.355 mm. A high O/U flowrate ratio may improve the separation efficiency. Figures 5.11 to 5.14. This is, however, normally accompanied by a prolonged residence time of near-density materials in the DMC. At near-zero feed-to-medium ratio, these particles would stay inside cyclone and are only discharged when the circuit is shut down. In normal production, the high feed-to-medium ratio (1:3 to 1:5 by volume) coupled with a high proportion of near-gravity material will result in a build-up of near-density materials inside the cyclone. As documented in the work of Davis (1989), the build-up of near-density materials causes the disappearance of the air core along the cyclone axis causing o I 100 80 u. S 60 a c o I 40 i. 20 1.1 Mag#2 0/U ratio 0.374 0.406 0.406 1.60 feed size .5X.355 .5X.355 1.X.71 .5X.355 64 1.2 1.5 1.6 Feed density (g/crr?) (a) 1.9 O /U=0 .48 \ 1 0/U=1.68\ medium density 1 ' l\/lag#4, feed size: 1.x.71mm iO/U=7.25 1 1 1.3 1.4 Feed density (g/cm ) (b) 1.5 1.6 '1.1 1.2 1.3 1.4 1.5 Feed density (g/cm^) (c) Figure 5.19 Bypassing of the low density feed particles at low 0/U ratio 65 congestion and eventual breakdown of the medium flow pattern. The cyclone content is discharged through the spigot in a roping flow pattern until the normal spraying flow pattern is re-established and the near-density material build-up process is repeated again. Such an intermittent roping discharge flow pattern is characteristic for the DMC treating coal with a high proportion of near-density materials at high density differential. Plugging of DMC may also occur as a consequence of the near-density material build-up. As observed in our full scale test at BuUmoose Operating Corp. with the use of the 680 mm DMC circuit, after the 200 mm spigot was replaced by a 180 mm spigot, the DMC spigot was frequently plugged when processing a particular coal seam which contained a large percentage of high density materials (>1.6 g/cm^); the entire medium and feed bypassed the cyclone through the vortex finder. According to the above analyses, the 0/U flowrate ratio should not be lower than 1.0 to avoid DMC short-circuiting. Although it is beneficial to use higher OAJ flowrate ratios to achieve a better separation efficiency (Figures 5.11 to 5.13), the improvement in the Ep value at 0/U ratio above 4.0 is minimal. In addition, the possibility of intermittent roping discharge flow pattern and plugging at high O/U ratio is substantially increased. It is recommended that the value of the 0/U flowrate ratio be close to the value of the concentrate to refuse output ratio, so that the product-to-medium ratios in the overflow and underflow streams are about the same. In the case of coal separation, refuse accounts for 20% to 50% of the feed volume. This translates into an O/U flowrate ratio range from 1.0 to 4.0. Based on the industrial practice and the conclusions obtained in this project, the optimum O/U flowrate ratio range can be further narrowed down to 2.0±0.5. 66 In accordance with this recommendation, the influence of medium properties on DMC performance, as will be discussed in later chapters, was investigated at a fixed O/U flowrate ratio of 1.8 which falls in the optimum O/U ratio range recommended above. 5.3.2 Applications of the O/U flowrate ratio control The findings regarding the properties of O/U flowrate ratio can be applied to DMC modelling, separation cutpoint control, and optimization. These results also provide a theoretical basis for the design of DMC with variable orifice diameters. The models commonly encountered in modelling the DMC separation cutpoint (Geer and Yancey, 1968; Clyburn, 1980; Scott and Napier-Munn, 1990) can be generalized by the following equation: where P and B are constants, 6„ is the feed medium density. Brien and Pommier (1965) and later Collins et al. (1983) took into account the effect of feed particle size on separation cutpoint and introduced feed particle size, d, into the model: 50 m „ where e varies between 1 and 2 with the two boundary values indicating Newtonian and Stokes' particle flow regime, respectively. The term B/d^ in the above equation is the cutpoint shift at a fixed O/U flowrate ratio: A65o=^ 5.3 (a) According to the results shown in Figures 5.3 to 5.6, the cutpoint shift (or B in the above 67 equation) is hnearly related to the O/U flowrate ratio, 9, in a semi-log plot: B=hlog(e) 5.3 (b) where k is a constant. By combining the above two equations, the following relationship is produced: ^ 5 HogCe) 5 3 The separation cutpoint model (Equation 5.2) can be written as: ^HogCe) 5 4 d^ This relationship can also be applied to control and monitoring of the separation cutpoint. In dense medium separation, two or more DMCs are normally connected in parallel to form a bank sharing a common feed pipe. Since the cyclones have the same design, the O/U flowrate ratios of these cyclones should be identical. Correspondingly, the density differentials and cutpoints (or cutpoint shifts) for these cyclones should also be identical. In the process of operation, the cyclones, especially the spigots, of the cyclones in the same bank may experience different degrees of wear. As a result, the O/U flowrate ratio, the cutpoint shift, and density differential all vary among these cyclones. As simulated in Figure 5.20, the deviation in separation cutpoint results in a lower overall separation efficiency. To ensure an identical separation cutpoint among different cyclones in the same bank, regular monitoring of the separation cutpoints of individual cyclones becomes essential. The conventional method of sampling the products of individual cyclones and performing the sink-float test on the samples is expensive and time-consuming. 68 overflow \ ^ Cyclone A N Feed \ ' 1 r underflow Cyclone B^ overflow ^ , *-Figure 5.20 (a) A typical parallel layout of two DMCs to form a banl< 100 Combined Ep=0.092 Cyclone B -Ep=G.066-1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 Feed density (g/cm^) Figure 5.20 (b) A reduced overall separation efficiency due to the variation in outpoint 69 According to the results of this investigation, the equal cutpoint shifts among the cyclones in a bank can only be achieved with equal OAJ flowrate ratios, which should also result in equal density differentials among the cyclones. The variations in O/U flowrate ratio should result in the variation in both cutpoint shift (Figures 5.3 to 5.6) and density differential (Figures 5.16 and 5.17). The simultaneous variations of the cutpoint shift and density differential in response to the change in O/U flowrate ratio provide a very practical indicator for monitoring the cutpoint deviation among different DMCs since monitoring the density differentials for individual cyclones is a very easy task. The density differentials for different DMCs in a bank should be the same, and any significant deviation in density differential indicates a major deviation in cutpoint shift; correction measures must be taken. The continuous spigot dilation due to wear during DMC operation causes the OAJ flowrate ratio and separation cutpoint to fall off. Figure 5.10. While frequent replacement of the spigot is costly, the results of this investigation lead to the following correction measures. One measure is to gradually increase the cyclone inlet pressure, and another to use a set of progressively larger vortex finders. These two measures can effectively maintain the O/U flowrate ratio constant, offsetting the influence of spigot dilation and increasing its service time. The fundamental properties of the O/U flowrate ratio also establishes the theoretical basis for the design of adjustable spigot diameter (Moorhead, 1991), or adjustable inlet pressure for separation cutpoint control. The adjustment in spigot and vortex finder diameters and in inlet pressure should be confined within a range so that the O/U flowrate ratio is maintained within the range from 1.0 to 4.0. 70 At present, it is a common practice in the optimization of cyclone performance to stipulate the range of cyclone orifice diameter ratios with respect to the cyclone diameter and to manipulate the cyclone orifice diameters individually in search of the optimum point. According to this study, the cyclone orifice diameters must be adjusted by taking the 0/U flowrate ratio into consideration. To optimize the DMC separation efficiency, the spigot and vortex finder diameters should be enlarged or reduced simultaneously to keep the 0/U flowrate ratio within the optimum range. At any fixed O/U flowrate ratio, according to the results in Figure 5.14, a better separation efficiency can be achieved with a combination of smaller spigot and vortex finder diameters at the expense of lower cyclone throughput. In general, an investigation into the influence of medium properties on DMC performance must be carried out in the context of optimized cyclone operating conditions; a satisfactory DMC performance can be achieved only with the combination of the optimum medium properties and cyclone operating conditions. 5.3.3 The mechanism of density separation in DMC The extensive results provided in this chapter present part of the experimental basis on which the mechanism of DMC separation concerning the separation cutpoint can be discussed. In summary, a postulated mechanism of DMC separation should explain the following: (1) the existence of cutpoint shift (either positive or negative); (2) higher cutpoint shift for finer feed particles; and (3) higher cutpoint shift at higher 0/U flowrate ratios achieved either by reducing the spigot diameter or by increasing the inlet pressure. Many hypotheses concerning the separation density in a DMC have been proposed. 71 Davis and Napier-Munn (1987) indicated that the separation density is inter-related with underflow medium density since at a constant feed medium density the cutpoint shift changes in the same direction as the underflow medium density does. This was also observed in this investigation (see Figure 5.21). This, however, does not explain the first two questions. Fahlstrom's hypothesis of crowding (Fahlstrom, 1960) suggested that the separation is not merely a question of hindered settling in a centrifugal field, but a question of hindered discharge through the spigot. According to Fahlstrom, the separation cutpoint is principally a function of the cyclone spigot capacity to handle the solid reporting to it; coarse particles receive preference and finer particles are thus directed to the overflow when the maximum capacity of the spigot is reached. This hypothesis cannot be applied to DMC since the cutpoint shifts in Figures 5.3 to 5.6 were observed even at a near-zero feed rate when crowding did not occur. It also fails to interpret the effect of medium viscosity on separation cutpoint. Increasing the medium viscosity by adding clay into the medium (Davis and Napier-Munn, 1987), or by increasing the medium density (see Chapter 6), supposedly increases the crowding and the cutpoint shift should increase, while the opposite was observed. Brien and Pommier (1964) have attributed the cutpoint shift to the increased composite medium density in the vicinity of the spigot, which forces particles heavier than the feed medium to the overflow. A decrease in the cyclone spigot diameter raises the composite medium density around the spigot, increasing the separation cutpoint. Driessen (1975) speculated that the medium solid particles have a longer residence time in the cyclone than the carrying liquid. The dense medium in the cyclone, therefore, has 72 1.8 1.7 i" 1.5 I. 1.3 1.2 IVIag#2, at medium density 1.36 g/cm' Feed size A 4x2mm o 1x.71mm A .5x.355mm 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Underflow density Figure 5.21 (a) The relationship between outpoint and underflow medium density 1.8 1.7 ^ 1 . 6 ^ 1 . 5 " 1.4 1.3 1.2 l\/lag#2, at medium -Feed size , 4x2mm o 1x.71mm A .5x.355mm i A C O • A O _ • density 1.36 g/cm A ^ A 3 - ^ 0 ° I A m 1 1 3 A • 1 A A OA • O O • 1 A A O 0 " • A • • A O 1 A 0 • 1 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35 1.36 Overflow density Figure 5.21 (b) The relationship between outpoint and overflow medium density 73 a density greater than that of the feed medium resulting in a higher separation cutpoint. Obviously, these hypotheses cannot explain the existence of negative cutpoint shift and the effect of feed particle size on cutpoint shift (see Figures 5.4 to 5.6). Collins et al. (1983) claim that since the ore particles are introduced at the periphery of the cyclone, positive inward radial movement of the low-density particles is required for their separation. Since the movement of finer feed particles is more sensitive to the influence of the medium movement to the product streams (i.e. viscous resistance), the inward radial flow of the medium tends to "sweep" the fine feed particles to the overflow by fluid drag. This results in a higher separation cutpoint and a lower separation efficiency. By taking the inward radial flow into consideration, King and Juckes (1988) have initiated a very important approach toward the theoretical modelling of the DMC separation. Scott et al. (1987) believe that the separation cutpoint shift reflects the variation in the density gradient of the medium in the cyclone, while the medium viscosity is influencing the cutpoint shift indirectly through changing the density gradient. They claimed that such an influence can be considered equivalent to that of changing the feed medium density. According to the model proposed by Tarjan (1958), the separation cutpoint, 650, is equal to the medium density, pp, prevailing at the locus of zero axial velocity. The locus forms the "envelope" at which the outer, downward vortex flow meets the inner, upward vortex flow. Apparently, this model is not entirely true since it cannot explain the variation of separation density with feed particle size (Figures 5.3 to 5.6). Even with the use of heavy liquid as a medium (po=Pni). the separation cutpoint higher than the heavy 74 liquid density was observed (Moder and Dahlstrom, 1952; Brien and Pommier, 1965). The equilibrium orbit hypothesis (Bradley, 1965), developed for a classifying cyclone, assumes that the particles that divide equally between the underflow and overflow products are the ones which occupy the equilibrium orbit on the locus of zero axial velocity. Following this hypothesis, Bradley (1965) derived the following equation to calculate the cutpoint size assuming laminar flow for the particles: » ^<?<6-p)' This equation was rearranged by Napier-Munn (1980) and applied directly to DMC to calculate separation cutpoint: According to this equation, at a constant feed medium density, p^, increasing the medium viscosity, T), or decreasing cyclone volumetric throughput, Q, will result in a higher separation cutpoint. This is in disagreement with the observation by Davis and Napier-Munn (1987) and with the full scale DMC test results given in Figure 5.10 (b). The above review of early publications has established the basis for proposing a more comprehensive model capable of interpreting the results presented in this chapter and in the following chapters. The postulation in this study is based on the theory proposed by Tarjan (1958) for DMC, and on the equilibrium orbit hypothesis for classifying cyclone (Bradley, 1965), while taking into account the two important phenomena in a DMC: the medium density gradient, and the medium inward radial flow. The cutpoint shift phenomena listed at the beginning of this section are the joint effects 75 of all these factors. Based on this postulation, a theoretical model for DMC will be derived as follows. The separation of a particle moving within a cyclone is mainly determined by a balance between two forces: the radial force due to centrifugal acceleration, F,.; and the drag force, Fj. The following equations have often been used to express these forces (Kelly and Spottiswood, 1982; Napier-Munn, 1990): nd\6-p)Vt 5 7 F_--c 6r where 6 and p are the densities of the feed particles and of the fluid surrounding the particle, respectively; A is surface area of the particle; r is the radial distance from the cyclone axis. The particle radial velocity relative to its surrounding medium is equal to the particle radial velocity relative to cyclone wall, v^ , plus the medium inward radial velocity, v^. Thus the drag force acting on particles moving toward the cyclone wall is: P,-\c^-p(yr^^j''A 5.9 According to the equilibrium orbit hypothesis, the particles which have equal chances to report to the underflow and overflow products should be the ones which establish equilibrium orbit on the envelope of zero axial velocity. Thus, the radial velocity of these particles relative to the cyclone wall is zero; Equation 5.9 reduces to: 76 F,-lc^P^lA 5.10 The centrifugal force and inward fluid drag on these particles are equal. By equating Equation 5.7 and Equation 5.10, the following relationship is produced: 7c</^(6-p)vf 1 2 . 5 11 At the locus of zero axial velocity, the radius r=ro, the medium density p=po, the particle density 5=850, ^^^ fo"" ^ spherical particle A=l/47i:d .^ By substituting these into Eq.5.11 and rearranging, one can get: ^so-Po-^c,p,r,(^f 5.12 Due to the medium classification, pg is not necessarily equal to feed medium density p„; the medium density is highest at the cyclone wall and decreases when moving toward the axis of the cyclone creating a radial density gradient in a DMC. For simplicity, a linear density gradient is assumed. This assumption is justifiable when the variation range in r is small. Thus, the po can be written as a function of feed medium density, p„, in a form: where TQ is the radius of the locus of zero axial velocity, r^ , is the radius of the constant medium density zone where the medium density is equal to the feed medium density, and a is the density gradient around the constant medium density zone. Substituting Eq.5.13 into Equation 5.12, one can get 77 where the term, Sjo-Pn,, is cutpoint shift. In the equation, the first term on the right side of the equation expresses the influence of medium stability in the form of density gradient (a) on cutpoint shift, while the second term reflects the effects of medium rheology in the form of drag coefficient (C^), which is related to the medium rheology by Equation 8.13 (see Chapters). The average inward radial velocity of the medium at the locus of zero axial velocity can be calculated from the following approximation: r — ? ^ 5.15 where Q^ /f is the cyclone overflow flowrate, and L the length of the imaginary cylindrical envelope formed by the locus. At any given O/U flowrate ratio, 9, the relationship between the DMC overflow flowrate and feed medium flowrate is given by: Q.M 5.16 Substituting Equation 5.16 into Equation 5.15 gives: V= Qg 5.17 "• 2jtroL(l+e) By substituting Equation 5.17 into Equation 5.14, one can get: " " ° ' 16 , . ' * / v,(i+e)' According to this equation, it can be concluded that: 78 (i) The cutpoint shift increases with decreasing feed particle size, d. (ii) The cutpoint shift increases with cyclone medium flowrate, Q, Figure 5.10 (b); since Q increases to the power of 0.86 to the inlet pressure, P (Olajide and Cho, 1989), the cutpoint shift should also increases with P. (iii) Increasing the radius of the locus of zero axial velocity, r^, which is achieved by increasing the O/U flowrate ratio, results in a higher cutpoint shift. This is the case with water-only cyclones where a very small spigot diameter is employed to create a strong inward radial flow and an elevated O/U flowrate ratio is used to achieve a high cutpoint shift. (iv) Decreasing the medium stability, which is associated with an increasing density gradient, a, will result in a higher cutpoint shift, Figure 5.6. In the special case where O/U flowrate ratio 0=1, the locus of zero axial velocity can be considered to be located within the constant medium density zone, TQ=r^; Equation 5.14 reduces to: 55o-P.=^^z,P. '-o(^)^ 5.19 The contribution of medium stability to cutpoint shift is zero, and the cutpoint shift is only determined by the inward radial fluid drag. With coarse feed particles (>2 mm), the particle Reynolds number is high in the intermediate and turbulent flow regime where drag coefficient (Cp) has the lowest value. The inward radial fluid drag and the induced cutpoint shift, as expressed by the term on the right side of Equation 5.19, are insignificant and negligible. Thus a zero cutpoint shift for 4x2 mm coarse feed particles is observed (see Figure 5.5); the separation density is equal to the feed medium density. 79 With decreasing feed particle size (d), the particle Reynolds number decreases and, correspondingly, the drag coefficient (CQ) increases. According to Equation 5.19, a positive cutpoint shift should be obtained. At the O/U flowrate ratio below 1.0, the underflow medium flowrate is higher than the overflow medium flowrate. The radius of the locus of zero axial velocity is smaller than the radius of constant medium density zone, ro<rj.. Also the medium density at the locus is lower than the feed medium density, Po<Pm- While the second term on the right side of Equation 5.18 is always positive, the first term becomes negative since ro<r^ . When the absolute value of the first term is higher than the second one, a negative cutpoint shift is obtained (see Figures 5.3 to 5.6). With less stable Mag#2 dense medium, its density gradient inside the DMC is higher than that of Mag#4 dense medium, 0CMag#2»«Mag#4- According to Equation 5.18, r^ is varied by means of changing the O/U flowrate ratio. The cutpoint shift with Mag#2 dense medium changes with O/U flowrate ratio at a higher rate than that with Mag#4 dense medium due to a higher aMag#2 value. This explains the results shown in Figure 5.6. This will also explain the finding in Figure 6.7 (b) in the next chapter. In another special case when a true liquid is used as medium, the medium density gradient in a cyclone is zero, a=0. The influence of density gradient as expressed by the first term on the right side of the Equation 5.18 becomes zero and this equation reduces to: According to this equation, the cutpoint shift exists even with a stable heavy liquid due 80 to the inward radial fluid drag. Evidence can be found from Moder and Dahlstrom's (1952) and Brien and Pommier's (1965) data on the separation of fine tin ore. With the use of true liquids as media, the cyclone separated the feed solid particles at a density higher than that of the liquid (55o>pn,). With coarse feed particles, however, the effect of inward radial fluid drag, as discussed earlier, is insignificant; the cutpoint shift is close to zero. This explains the findings by Davis and Napier-Munn (1987) in the separation of coarse coal in clay-stabilized magnetite dense medium and by Fontein and Dijksman (1953) in the separation of sylvite from halite in a stable medium of fine magnetite in saturated brine, where the cutpoint shifts were close to zero. 81 5.4 Summary The OAJ flowrate ratio is fundamentally related to DMC performance, while the cyclone geometric dimensions influence the DMC performance indirectly through, or partially through the O/U flowrate ratio. The overflow and underflow medium densities, as well as density differential, are all affected by the O/U flowrate ratio. At any given feed medium density, they all increase with the O/U flowrate ratio. At a O/U flowrate ratio below 1.0, very high Ep values are obtained. With increasing O/U flowrate ratio, the Ep value decreases continuously and levels off at a O/U flowrate ratio above 4.0. At any given O/U flowrate ratio, a combination of smaller vortex finder and spigot diameters affects a higher separation efficiency, at the expense of lower cyclone throughput. The cutpoint shift increases linearly with the O/U flowrate ratio on a semi-log plot. The slope of the linear relationship is higher with less stable dense medium. With decreasing feed particle size, the line only moves up to a higher position without significant change in slope. These relationships provide an experimental basis for DMC optimization, cutpoint control, and DMC modelling. The optimum O/U flowrate ratio is recommended in the range of 2±0.5 achieved with a combination of smallest possible vortex finder and spigot diameters. It is recommended that the density differential be used as a monitoring parameter to detect the deviation in cutpoint shift among DMCs in a bank. It is also recommended the use of higher inlet pressures or larger vortex finder diameters to offset the spigot dilation due to wear to increase the spigot life time. Based on the equilibrium 82 orbital hypothesis proposed for classifying cyclones and the hypothesis proposed by Tarjan (1958) for DMC, while taking into account the influence of the inward radial flow and medium density gradient in a DMC, the following equation is derived to interpret the cutpoint shift phenomena observed in this research: where the first term represents the influence of medium stability, and the second term reflects the effect of medium rheology. According to this equation, decreasing the feed particle size, raising the cyclone throughput (or inlet pressure), lowering the medium stability, or increasing the radii of the loci of zero-vertical velocity (which can be achieved by increasing the 0/U flowrate ratio) will result in an increase in cutpoint shift. This chapter establishes the experimental and theoretical basis for the DMC operating conditions which will be applied to study the effect of medium stability and rheological properties on DMC performance that follows. 83 6. THE EFFECT OF MEDIUM COMPOSITION ON DMC PERFORMANCE 6.1 Introduction In the previous chapter, the influence of operating conditions on DMC performance was examined. The DMC performance, as affected by the medium properties in terms of the medium composition, will be investigated in this chapter. While rheology and stability are the fundamental medium properties that are most directly related to the DMC performance, these properties are controlled and modified by the medium composition including medium solid content (or medium density), magnetite size distribution, particle shape, contamination, and demagnetization. The influences of these factors on DMC performance have been addressed by various researchers. However, conflicting conclusions have often been drawn. Stoessner (1987), in studying the effect of magnetite particle size on DMC performance, reported that the fine magnetite does not perform as well as coarse commercial magnetite. He attributed this to the deleterious effect of viscosity on DMC performance. A similar effect was also reported by Collins et al. (1974) when working at high medium densities in iron ore separation. However, a different conclusion was obtained by many other researchers (Sokaski and Geer, 1963; Fourie et al, 1980; Chedgy et al, 1986). They found that the separation efficiency improved when progressively finer magnetite was utilized due to increased medium stability. 84 In studying the effect of clay contamination on DMC performance, Davis and Napier-Munn (1987) found that with increasing clay contamination, the cutpoint shift decreased and approached zero when the level of clay contamination was very high. A different finding was, however, reported by Napier-Munn (1980), who used a heavy liquid as medium and modified the medium properties by adding fine quartz particles into the medium. He found that with increasing quartz contamination, the cutpoint shift increased. The effect of medium density on DMC performance was studied by Morrimoto (1952) and King and Juckes (1984). Morrimoto (1952) observed that the effect of medium density on separation efficiency was insignificant. King and Juckes (1988), on the other hand, found that when the partition curves obtained at different medium densities were normalized by plotting the partition number against the ratio x=relative density/cutpoint, the curves could be reduced to a single one. This implies that the Ep value is linearly proportional to the medium density. While reflecting the complexity of the DMC separation process, the conflicting findings quoted above, as will be discussed later, are attributed to the important roles played by the feed particle size and by the interaction between cyclone operating conditions and medium properties in the process. In the early investigations, the influencing parameters were more often studied over a narrow variable range, and the results present only part of the whole picture. In this study, the medium composition is modified by altering magnetite size distribution and medium density only; they were, however, varied over extended ranges. Fine density tracers, which are more sensitive to changes in medium properties, were used as cyclone feed. It is found that while the separation efficiency and cutpoint shift of coarse particles 85 (>2.0 mm) are more sensitive to the effect of medium stability, the separation of fine particles (<0.5 mm) is mainly determined by medium rheology. As a result, the separation of fine and coarse particles responds to the change in medium composition in a different fashion due to the opposite influences of medium stability and medium rheology on DMC performance. 6.2 Experimental Four different magnetite samples were used: Mag#l, Mag#2, Mag#3, and Mag#4. As shown in Table 4.1, they cover a wide particle size range from micronized-magnetite with d632=4.3 |am to a very coarse magnetite with d632=33.0 |am (for commercial magnetite, d^jj =30.5 |im). With each magnetite sample, the medium density was varied between 1.20 and 1.70 g/cm^ Three size fractions of density tracers: 4.0x2.0, 1.0x0.71, and 0.5x0.355 mm were used as cyclone feed. The cyclone inlet pressure was maintained at 154 cm medium column (lOxDc). The cyclone vortex finder and spigot diameters were 6.35 cm (2.5") and 5.08 cm (2.0"), respectively. 86 6.3 Results and Discussions 6.3.1 Effect of feed particle size on DMC performance The performance of a DMC, like all the gravity separation methods, is strongly affected by the feed particle size. In this study, the effect of feed particle size on DMC performance was tested under various conditions by changing the magnetite particle size and medium density, and by using different combinations of vortex finder and spigot diameters. As shown in Figure 6.1, all the data points can be confined within the range outlined by the two broken lines. This figure shows that: (1) The Ep value increases exponentially with decreasing feed particle size confirming the early findings by Driessen (1947) and Davies et al. (1963). (2) As feed particle size decreases, the range of variation in Ep values becomes broader due to an increasing sensitivity to the effects of medium properties and cyclone operating conditions. These characteristics make the optimization of the DMC separation of fine particles more imperative, and the consequent improvement can be more significant. The data in Figure 6.1 demonstrate that the effects of medium properties and cyclone operating conditions on the DMC performance can be effectively detected only with the use of fine feed particles; tests with coarse feed particles may give inconclusive information. 6.3.2 Control of cyclone operating conditions The DMC performance is a function of both medium properties and cyclone operating conditions. To study the effects of medium properties on DMC performance. 87 0.11 0.09 J 0.07 > a LU 0.05 0.03 0.01 0.1 lo T4 l^. -t o SG1.2;2.5-1.5;Mag#1 • SG1.5; 2.5-2.5; Mag#2 A SG1.3; 1.5-1.5; Mag#1 • SGI .4; 2.5-1.5; Mag#3 • SGI .3; 2.5-2.5; Mag#1 A SG1.5;2.5-1.5;Mag#2 t t I I I i f 1 Feed particle size (mm geom. mean) 10 Figure 6.1 The relationship between Ep value and feed particle size as affected by operating condition and medium properties 88 the cyclone operating conditions must first be optimized and then held constant during the entire investigation process. As indicated in the last chapter, the cyclone overflow to underflow flowrate ratio (0/U flowrate ratio) is a fundamental operating variable affecting DMC performance, while the DMC orifice diameters affect the DMC performance indirectly by changing the 0/U flowrate ratio. At any given DMC spigot and vortex finder diameters (see Section 6.2), the variation in medium properties caused by changing the medium composition should not significantly alter the OAJ flowrate ratio. Otherwise, the DMC vortex finder or spigot diameter has to be varied in the process of investigation in order to keep the OAJ flowrate ratio constant. The results in Figure 6.2 (a) indicate that, with the given orifice diameters and the constant inlet pressure head, the 0/U flowrate ratio is practically independent of magnetite particle size and medium density; it remained constant at around 1.8, which is within the optimum range of 2±0.5 recommended in the last chapter. Medium flowrate is another important operating variable. It determines the cyclone inlet velocity and consequently, the centrifugal acceleration. Thus, this parameter should also be maintained constant in this investigation. The results in Figure 6.2 (b) reveal that the medium flowrate at a constant inlet pressure of 154 cm liquid column is about 3.2 L/s and is practically independent of medium density and magnetite particle size distribution (with the only exception of coarse Mag#3 dense medium, which exhibited a higher flowrate). With a fixed cyclone configuration and, more importantly, with a constant 0/U flowrate ratio and a constant medium flowrate, any significant change in the DMC 89 Orifice:2.5"-2.0" i o Mag#1 o Mag#2 A Mag#3 * Mag#4 3 d ^-*-^%4^^^^^-.^^o^. 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Medium density (g/cm^) Figure 6.2 (a) DMC 0/U flowrate ratio as affected by the medium composition 3.5 \ ^ A^ ^ A ^ ^' 2.5 D D D D D ^ ,AO,o ^ , ^ , ^ ^ , ^ * % . ^ - " ^ oToOoOO ° Orifice:2.5"-2.0" ° Mag#1 o Mag#2 A Mag#3 A Mag#4 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Medium density (g/cm^) Figure 6.2 (b) DMC medium flowrate as affected by the medium composition 90 performance can be attributed to the change in the medium properties. 6.3.3 Dense medium stability Stability and rheology are the two principal medium properties affecting DMC performance. Like coal particles, the magnetite particles in a DMC are also subject to the effect of centrifugal acceleration and experience segregation which is reflected by the disparity between the cyclone overflow and underflow medium densities. The effects of the magnetite particle size and medium density on the overflow and underflow medium densities are shown in Figure 6.3; the diagonal line gives the feed medium density. The Mag#3 dense medium was highly unstable; it experienced a strong segregation with a highly concentrated underflow and a very diluted overflow. Such a strong segregation produces a high density gradient inside the cyclone and will result in congestion and intermittent flow pattern in the real production process. As will be shown later, the extremely low stability was responsible for the poor cyclone performance when Mag#3 was used. By comparison, the use of the micronized magnetite (Mag#4) produced a very low density gradient inside the cyclone. In this case, the overflow and underflow medium densities were almost identical. The density differential between cyclone underflow and overflow characterizes the medium stability. It is affected both by cyclone operating conditions (Figure 5.16) and by the medium composition (Figure 6.4). Therefore, it is considered to be a parameter describing the dynamic stability of the magnetite medium. For all the tested magnetite samples, the density differentials initially increased with medium density but then declined at higher medium densities. This was apparently due to the greater influence of medium 91 E CO 03 '*^ m c a> T3 E T3 0} E 3 2.2 2 1.8 1.6 1.4 1.2 1 • • • •« • • •• *:• • • v » » ^ - ^ • ^ ^^ -"''^° -" .-Xv^ - . - • ^ * ; ^ ° > • • y^„a V o ^A*o°v ^ 8 • _,.' Mag#3 underflow , ,'' y'' '' Mag#J'underflow M£rg#2 underflow 'K/lag#4 underflow Mag #4 overflow Mag #2 overflow Mag#1 overflow Mag#3 overflow 1 1 ^* • • A A D V o 1 1.2 1.4 1.6 1.8 Feed medium density (g/cm?) 2.2 Figure 6.3 The effect of magnetite particle size on overflow (0/F) and underflow (U/F) medium densities 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Feed medium density (g/cm^) Figure 6.4 Density differential as a function of magnetite particle size and medium density 1.9 92 rheology. Otherwise, the density differential should have followed the initial trend and continued to increase. Figure 6.4 also suggests that the 'transition point' where rheology becomes important in reducing the density differential occurs at increasing feed medium densities with increasing magnetite particle size. It can also be seen from Figure 6.4 that, at any given medium density, the density differential is higher with coarser magnetite samples. 6.3.4 Separation efficiency The magnetite dense medium properties affect DMC separation efficiency. As seen from Figure 6.5, the increasing medium densities, and the associated change in medium rheology, resulted in a general increase in Ep values. With finer feed particles, the Ep values increased more significantly especially over the high medium density range. Figure 6.5 also reveals that, for the coarse feed particles (4x2 mm), lower Ep values were obtained with the use of more stable Mag#2 dense medium, although the Mag#2 dense medium is more viscous. For the fine feed particles (0.5x0.355 mm), however, lower Ep values were obtained with the use of less viscous Mag#l dense medium, even though the stability of Mag#l dense medium is lower. These results suggest that the separation efficiency of coarse particles is not very sensitive to the effect of medium rheology but is more sensitive to the effect of medium stability. Lower Ep values were obtained for the coarse feed particles with the more stable Mag#2 dense medium. In comparison, however, the separation efficiency of fine particles is more sensitive to the effect of medium rheology while the effect of medium stability is less important. As a result, lower Ep values were obtained for the fine feed particles 93 0.08 0.07 0.06 0.05 <D 5 0.04 Q. Ill 0.03 0.02 0.01 Mag#1 . tracer .5x.355mm o tracer 1x.71mm . tracer 4x2mm • . ^* • -• O 0 ^ • 0 0 * * * A A ° A A A 1 1 1 1 • • • o 0 o A A A 1 • • iVlag#2 • • 9 m • • • o • • o . • . o • o o o ° o ** O A * * O A A A A A A A 1 1 1 1 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.3 1.4 1.5 1.6 1.7 1.8 Medium density (g/crc?) Figure 6.5 DMC separation efficiency as affected by medium density and magnetite particle size distribution 94 with the less viscous Mag#l dense medium. Above results also indicate that the significance of the effect of medium stability and medium rheology is determined not only by the medium composition itself, but also by the feed particle size. The DMC performance is significantly influenced by the magnetite particle size distribution. As shown in Figure 6.6, the Ep values with Mag#l, Mag#2 and Mag#4 dense media tend to increase with medium density. The most drastic increase in Ep value was observed with the micronized-magnetite Mag#4 at medium densities above 1.5 g/cm^ This obviously results from the change in medium rheology. The density differentials for the three magnetite dense media were all confined within 0.5 g/cm^ (Figure 6.4). According to Collins et al. (1974), the adverse effect of medium stability on separation efficiency was negligible under such conditions. Medium rheology becomes the dominant parameter in affecting the separation efficiency in these tests. The best separation was obtained with the Mag#l dense medium due to its low viscosity over the entire medium density range tested. At low medium densities (below 1.5 g/cm^), the effect of medium rheology is not very important for all magnetite dense media. As a result, the difference among the Ep values obtained with Mag#l and Mag#2 dense media were insignificant. Over the high medium density range, however, the difference expanded due to an increasing effect of medium rheology, and the advantage of using coarser Mag#l dense medium over this density range was evident. With the very coarse magnetite dense medium prepared from the Mag#3, however, the trend was reversed. The Ep value decreased with increasing medium density. With this magnetite, the medium rheology does not play a significant role and the DMC 95 0.08 0.07 0.06 5 Q. LU 0.05 0.04 0.03 -0.02 0.01 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Medium density (g/cmP) Figure 6.6 DIVIC separation efficiency as affected by magnetite particle size and medium density 96 performance is determined by the medium stability. The density differential for the Mag#3 dense medium ranged from 0.8 to 1.0 g/cm^ (Figure 6.4), well above the values recom-mended by Collins et al. (1983) and Scott et al (1985). The extremely low stability exerted a deleterious effect on the DMC separation efficiency; very high Ep values were observed over the low medium density range. With increasing medium density, the medium stability improved and a better separation efficiency was achieved. The existence of the two opposite trends in Figure 6.6 suggests that there should exist a magnetite sample with particle size distribution somewhere in between Mag#l and Mag#3, for which the separation efficiency will remain unchanged over a wide medium density range. This may offer an explanation for the observations made by some researchers (Morrimoto, 1952) that the medium density did not affect the cyclone separation efficiency. The results in Figure 6.6 also indicate that the top particle size of a magnetite sample is not as important as its particle size distribution. The top particle sizes of Mag#l and Mag#3 were almost identical (Mag#3 was obtained by removing fines from Mag#l). With Mag#3, the effect of medium rheology on separation efficiency diminished, while the effect of medium stability became dominant. According to the results in Figure 6.6, the best separation efficiency over the low medium density range (<1.5 g/cm^) is achieved by using the Mag#l or Mag#2 dense media. The extremely low stability of the Mag#3 dense medium, and the high medium viscosity of the Mag#4 dense medium contribute to the low separation efficiencies with these two magnetite samples. In the DMC separation of fine coal, a higher centrifugal acceleration and finer magnetite dense medium are advocated (Klima et al, 1990). 97 According to Figure 6.4, the density differential of Mag#l dense medium is close to the upper limit recommended by Collins et al. (1974). Any attempt to use higher centrifugal acceleration for such a magnetite would cause an excessive medium segregation. This might offset any beneficial gain from an increased centrifugal acceleration and the separation efficiency might deteriorate. On the other hand, the Mag#2 dense medium characterized by an intermediate particle size distribution is a compromise that maintains a higher medium stability without imparting a significant effect of medium rheology on DMC separation. Obviously, the Mag#2 dense medium allows the use of a higher centrifugal acceleration, which may result in a much better separation efficiency. Over the high medium density range (>1.5 g/cm^), medium rheology emerged as a dominant factor in controlling the cyclone performance. As a result, it became desirable to use coarser magnetite (Mag#l or Mag#3) to achieve a better separation efficiency over this density range (see Figure 6.6). The competing dominance between medium stability and rheology and their opposite influences on DMC performance offers part of the explanation for the conflicting findings concerning the effect of magnetite particle size obtained by different researchers (see Introduction to this chapter). In the first case (Stoessner, 1987; Collins et al, 1974), the effect of medium rheology dominated, while the effect of medium stability is minimal especially in the iron ore separation at high medium densities. Thus, increasing medium particle size reduced medium viscosity and improved the separation efficiency. In the second case (Sokaski and Geer, 1963; Fourie et al, 1980; Chedge et al, 1986), however, the effect of medium stability dominated, while the effect of medium rheology was insignificant. Decreasing the magnetite particle size increases the medium stability and 98 improves the separation efficiency. The competing influences of medium stability and medium rheology can also be illustrated by the finding of Collins et al. (1983) on the separation of tin ore. They reported that there was a gradual increase in the separation efficiency as the density differential decreased from 0.85 to 0.41 g/cm^. Furthermore, when the density differential decreased further from 0.41 to 0.1 g/cm\ the separation efficiency deteriorated. In the first portion of the test, the influence of medium stability dominates; decreasing the density differential, although achieved by increasing the medium viscosity, results in a higher separation efficiency. In the second portion of the test, however, the effect of medium viscosity dominates. The beneficial effect of the improved medium stability is minimal, while the increased viscosity reduces the separation efficiency. This theory can be further applied to explain another pair of conflicting findings by early researchers. Chedgy et al. (1986) found that, when using commercial magnetite (similar to Mag#l) at low medium densities, the separation efficiency deteriorated when the cyclone inlet pressure was increased. On the other hand, an opposite trend was observed by Klima et al. (1990) when using micronized-magnetite (similar to Mag#4) in the separation of fine coal; a sharper separation was obtained at a higher cyclone inlet pressure. Obviously, the medium stability with coarse commercial magnetite in the first case was the dominant factor. An increased inlet pressure only further worsened the medium stability. As a result, it more than offset the beneficial gain from an increased centrifugal acceleration resulting in a decrease in separation efficiency. With the extremely stable micronized-magnetite dense medium in the second case, the medium rheology became the 99 dominant peirameter. Increasing the inlet pressure would improve the separation efficiency without inducing undue medium classification. The results of Figure 6.6 may suggest that the use of micronized-magnetite (Mag#4) over the high medium density range be prohibitive. According to the above two entirely different trends reported by Chedgy et al. (1986) and Klima et al. (1990), however, the separation efficiency using the micronized-magnetite (Mag#4) at low medium densities may eventually become superior over that using Mag#2 or Mag#3 under elevated cyclone inlet pressures. 6.3.5 Cutpoint and cutpoint shift The cutpoint shift is a function of both cyclone operating conditions and medium properties. The effect of cyclone operating conditions on cutpoint shift has been discussed in Chapter 5. The effects of medium stability and medium rheology on cutpoint shift can also be interpreted with the use of the model derived in Chapter 5: 55o-P .=«( ' -o -0-^^z>[p . -« ( ' ' o -0>o(^) ' 6.1 where the influence of the medium stability on cutpoint shift is represented by the first term on the right side of the equation, while the effect of medium rheology is represented by the second term. The effects of magnetite particle size on the cutpoint and cutpoint shift are compared in Figure 6.7. With the highly stable Mag#4 dense medium, the cutpoint, 850, for the 1.0x0.71 mm feed particles in Figure 6.7 (a) is almost identical to the medium density; the corresponding cutpoint shift in Figure 6.7 (b) is close to zero. As the medium 100 1.9 1.8 1.7 ;ri.6 E o ^ 1 . 5 o in Q 1.4 1.3 1.2 --' • • ' " 0 x' A° 0 • •• • 1 • , ' ' Mag#3 . Mag#1 '^ Mag#2' '^  oo x • 0 o , ' ' ^ o A O , ' 8 y-^ A 0 ^ * • • A ° ,-« Mag #4 • . ° A' ^ .L ^ o A ' ^ A , . > ' 0 A , ' ' • 1 1 1 1 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Medium Density (g/cm^) Figure 6.7 (a) Separation cutpoint as a function of magnetite particle size and medium density 0.4 0.3 i 0.2 S 0.1 CO ^ • ' o % 0 o -0.1 -0.2. Tracer 1.X.71 mm, orifices 2.5"-2.0" 1.1 Mag#3 Mag#1 Mag#2 Mag#4 1.2 1.3 1.4 1.5 1.6 1.7 Medium Density (g/cm^) Figure 6.7 (b) Cutpoint shift as a function of magnetite particle size and medium density 1.8 1.9 101 stability decreases with the Mag#l and Mag#2 dense media, the 850 starts to deviate from the medium density, and a larger cutpoint shift is observed. With the extremely unstable Mag#3 dense medium, it became very difficult to accurately control 850 since any slight variation in feed medium density resulted in a dramatic 650 fluctuation. In the above tests, medium stability was altered by changing the magnetite size distribution. Davis and Napier-Munn (1987), who stabiHzed the medium by increasing the amount of fine clay contaminant, observed a similar phenomenon. The cutpoint shift decreased as the amount of fine clay contaminant increased; with a highly stable magnetite dense medium, the cutpoint shift approached zero. These results are also in agreement with those obtained by other researchers (Davies et al., 1963; Collins et al, 1983). This has led to the general belief that the cutpoint shift is affected by the medium stability, while the medium rheology only influences the cutpoint shift indirectly through changing the medium stability. However, the cutpoint shift is also directly affected by the medium rheology through the inward radial fluid drag as expressed by the second term on the right side of Equation 6.1. The inward radial fluid drag tends to "sweep" the flne feed particles toward the centre of the cyclone creating a higher cutpoint shift. As the feed particle size decreases, such an effect becomes increasingly important. According to this analysis, the cutpoint shift of the fine feed particles (<0.5 mm) should increase with medium density. Thus, two opposite trends in cutpoint shift for fine and coarse feed particles should be observed. This is confirmed by the results in Figure 6.8. For the coarse feed particles (4.0x2.0 mm), the influence of fluid drag is negligible; the cutpoint shift is only a 102 0.15 Mag#2 4x2nnm 1x0.71 mm 0.5x0.355mm 1.2 1.3 1.4 1.5 1.6 1.7 IVIedium density (g/cm^) 1.3 1.4 1.5 1.6 1.7 Medium density (g/cm?) 0.2 0.15 0.1 0.05 1.8 Figure 6.8 Cutpoint shift as a function of feed particle size and medium density 103 function of medium stability. An increase in medium density, which is accompanied by an increase in medium stability, resulted in a cutpoint shift decrease. The cutpoint shift approached zero at medium densities above 1.6 s.g when the dense medium became very stable. The shape of the cutpoint shift versus medium density curve for the 4.0x2.0 mm feed particles in Figure 6.8 is similar to that of density differential versus medium density curve in Figure 6.4. As the feed particle size decreases, the medium rheology starts to play a direct role in affecting the separation. The cutpoint shift versus medium density curve for the intermediate size fraction (1.0x0.71 mm), shows a joint effect of medium stability and medium rheology. For fine feed particles (0.5x0.335 mm), the effect of medium rheology and the "sweeping" effect become dominant. The fluid drag increases with medium density resulting in a continuous increase in cutpoint shift. This result may provide an explanation for the different findings obtained by Davis and Napier-Munn (1987) and by Napier-Munn (1980). The size of the feed particles used by Davis and Napier-Munn (1987) was 5.0 mm. They were more sensitive to the effect of medium stability. Increasing the level of medium contamination improved the medium stability; the cutpoint shift decreased. The size range of the feed particles tested by Napier-Munn (1980) was only -0.3+0.076 mm. The separation of these fine particles was more strongly affected by medium rheology. Increasing the level of medium contamination increased the medium viscosity and inward radial fluid drag; the cutpoint shift increased. Since the O/U flowrate ratio was fixed at 1.8, the medium density prevailing at the locus of zero axial velocity, po, (see Chapter 5) is normally equal to or higher than the feed medium density. So does the SJQ. AS the medium stability deteriorates, the Po, 104 and consequently the 850 and the cutpoint shift in Figure 6.7 increase. It is obviously possible that under certain circumstances, the value of Po may become lower than the feed medium density. This would result in a 650 lower than the feed medium density and a negative cutpoint shift. This is the case for the highly unstable Mag#3 dense medium at medium densities below 1.35 g/cm^. Under such conditions, the magnetite particles were highly concentrated in a thin layer near the cyclone wall due to an excessive classifica-tion. The medium density at the locus of zero axial velocity po, and consequently the 850, were lower than the feed medium density. As a result, a negative cutpoint shift was observed. In general, it can be seen from the results in Figures 6.5 and 6.8 that, while the separation efficiency and cutpoint shift of coarse particles (>2.0 mm) are more affected by medium stability, the separation of fine particles (<0.5 mm) is mainly determined by medium rheology. 105 6.4 Summary Medium rheology and medium stability exert opposite influences on DMC performance. As a result, opposite trends can be observed depending on which of the two medium properties is the dominant affecting factor. With fine magnetite dense medium, which is very stable, the effect of medium rheology plays a major role. Thus, the separation efficiency improves when the medium density is decreased or when the centrifugal acceleration is increased. With coarse magnetite dense medium, which is not very viscous, the effect of medium stability becomes predominant. Consequently, an increase in medium density and a decrease in centrifugal acceleration results in a better separation efficiency. The influences of the medium stability and rheological properties on DMC performance are also dependent on feed particle size. The separation of coarse feed particles (>2.0 mm) is more sensitive to the influence of medium stability, while the effect of medium rheology is insignificant. Thus, the separation efficiency of coarse feed particles improves when finer magnetite dense medium is used, and the cutpoint shift increases with medium density over the lower medium density range and decreases over the higher medium density range. On the other hand, the separation of fine feed particles (<0.5 mm) is more strongly affected by the medium rheology. Consequently, the separation efficiency of the fine feed particles improves when coarser magnetite dense medium is used, and the cutpoint shift exhibits a continuous increase with increasing medium density. At low medium densities (<1.5 g/cm^), the best separation efficiency is achieved by using magnetite with intermediate particle size distributions (d63.2= 15-20 jim). This 106 compromise allows a low medium viscosity to be achieved without affecting the medium stability. At high medium densities (>1.5 g/cm^), the effect of medium rheology becomes dominant. In this density range, it is better to use coarser magnetite to improve separation efficiency. In the separation of fine particles under high centrifugal acceleration, fine magnetite (Mag#4) should be used to produce a stable dense medium. The medium stability and rheology are determined by the magnetite particle size distribution and solids content. Therefore, an appropriate control of the magnetite particle size distribution is more important than controlling its top particle size. The optimum magnetite particle size distribution in one type of cyclone systems could be an inferior one in another, depending on the cyclone operating conditions, medium density and feed particle size being processed. In the present coal preparation practice, the size distribution of the magnetite is fixed (or standardized). In other words, there is practically only one commercial grade of magnetite available to coal producers, irrespective of the cyclone system and operating conditions employed. Apparently, this situation should be changed. The magnetite grade should be tailored to each particular DMC system. 107 7. RHEOLOGY OF MAGNETITE SUSPENSIONS 7.1 Introduction Medium rheology plays a very important role in dense medium separation of fine particles. It not only exerts viscous resistance to the movement of feed particles through the medium but also influences the separation performance through affecting the medium stability. The non-Newtonian nature of the dense medium, however, has complicated the issue. The use of a single rheological parameter, viscosity (or apparent viscosity), is inadequate to describe such a complex rheological behaviour. Instead, two or more rheological parameters are required. The particle movement and the separation process in the non-Newtonian dense medium are affected by all these rheological parameters. This chapter and the two chapters that follow will address the third part of this whole investigation: the effect of medium rheology on DMC performance. The purpose of this chapter is to characterize the non-Newtonian properties of magnetite suspensions, to derive rheological parameters through flow curve modelling, and to evaluate their responses to the change in medium composition and temperature. Extensive rheological tests reveal that magnetite suspensions exhibit non-Newtonian yield-thinning properties, and their flow curves are best described by the Casson equation. Yield stress is the controlling parameter in characterizing the medium rheology, while viscosity is a subordinate parameter less sensitive to the change in medium composition. While the influence of temperature on medium rheology is inconsequential, the strong effect of 108 magnetite particle size distribution can be described by a single parameter termed relative hydrodynamic volume factor. The hydrodynamics of particle movement in non-Newtonian fluids and the effects of non-Newtonian properties on DMC performance will be discussed separately in Chapters 8 and 9. 7.1.1 Theory of rheology For Newtonian liquids such as water, a linear relationship exist between shear stress, T, and shear rate, du/dy: X=T1^ 7.1 dy The coefficient or slope of the shear stress versus shear rate plot, T|, is the fluid dynamic viscosity and its unit is Pascal-second (Pa-s). Viscosity can be interpreted as the resistance of the fluid to shear. Fluids which do not obey Equation 7.1 are collectively termed non-Newtonian fluids. The various types of non-Newtonian fluids are identified in Figure 7.1: Bingham plastic, pseudo-plastic, pseudo-plastic with yield stress, and dilatant. The Bingham plastic fluid (Bingham, 1922) is characterized by a yield stress which is usually defined as the minimum value of the shear stress which must be exceeded before the fluid can be made to flow. It can be expressed by the equation: where T|p, is the plastic viscosity and Xp, is the plastic yield stress. The existence of yield stress in a solid suspension is the result of particle-particle interactions leading to 109 CO CO 0) ro 0) x: Shear rate D 1. Bingham plastic 2. Dilatant 3. Pseudoplastic with yield stress 4. Newtonian 5. Pseudoplastic Figure 7.1 Types of rheological flow curves no formation of a structural network. Fluids which are thinning with increasing shear rates are called pseudo-plastic. Based on the attractive-disruptive forces assumptions, Casson (1955) derived a model to describe the flow of shear thinning fluids exhibiting or possessing a yield stress: T^/2=tf+(Ti^-D)i/2 7.3 where x^ is the Casson yield stress, and r\^ the Casson viscosity. The viscosity of dilatant fluids increases when shear rate is raised. This is caused by insufficient lubrication by water to prevent particles from 'jamming' at high shear rate, while sufficient lubricant exists at low shear rates. The flow curves of pseudo-plastic and dilatant fluids can be described by a power law model (Hanks, 1981): T:=kD" '^•^ For n less than one, the model describes pseudo-plastic flow; for n greater than one, it describes the dilatant flow. In the special case where n is equal to one, it becomes the Newtonian equation. The Herschel-Bulkley model is a combination of the power law model and the Bingham model (Herschel and Bulkley, 1926); it describes the flow of pseudo-plastic fluids with yield stress, t=x,,.fe-D'' 7.5 where, T^b is the Herschel-Bulkley yield stress, and k and n are two constants with no direct rheological meaning. I l l 7.1.2 Rheological properties of magnetite suspensions The rheological properties of magnetite suspensions are mainly controlled by solid content (medium density), particle size distribution, particle shape, clay contamination and demagnetization. Whitmore (1957) in his early studies reported that if the solid concentration is less than about 30% by volume, the suspension behaves as Newtonian fluid. Berghofer (1959), who first measured the complete rheological flow curves of magnetite suspensions, found that magnetite suspensions display non-Newtonian behaviour. Meerman (1957), Whitmore (1958) and Yancey et al. (1958) indicated that magnetite suspensions sampled from operating coal preparation plants behaved like Bingham plastic fluids. These findings were later confirmed by Valentik and co-workers (1964, 1976) and employed by others (Graham and Lamb, 1983, Klein et al, 1988). Nevertheless, the rheological behaviour of a dense-medium suspension is more complicated. It may exhibit Bingham, shear-thinning, or dilatant properties depending on the medium composition and shear-rate region. Govier et al. (1957) demonstrated that the rheological behaviour of a magnetite suspension is a function of shear rate by exhibiting pseudo-plastic characteristics at low shear rates (up to about 300 s"^ ) and dilatancy at high shear rates. Collins et al. (1983), when working on ferrosilicon dense media, found that the rheological properties of ferrosilicon suspensions range from Newtonian at low densities (<2.8 g/cm') and low shear rate, to pseudo-plastic at higher densities and low shear rates. At shear rates greater than 200-400 s"', dilatancy was observed. Increasing the medium density (solid content) has a drastic influence on the medium rheology due to increased particle-particle interactions (friction and collision). 112 It was shown by Geer et al. (1957) that the apparent viscosity of magnetite suspensions increases linearly with magnetite content up to approximately 25% by volume, and then rises sharply in a exponential manner. On the other hand, Collins et al. (1983) indicated that on a semi-log plot the relationship between apparent viscosity and magnetite content is linear. The medium rheology is also strongly affected by the solid particle size. As observed by Valentik and Patton (1976), both plastic viscosity and yield stress increased significantly with decreasing ferrosilicon particle size. Similar results were later obtained by Klein et al. (1988) with magnetite suspensions. Various chemical additives, both organic and inorganic, have been used to reduce viscosity and to increase stability of the solid suspensions. The general effect of these modifiers (polyethyleneoxides, polyvinylalcohol, carboxymethyl cellulose, guar gum, dextrin, sodium alginate, lignin, hydrolysed polyacrylamide and sulphonated polystyrene), as claimed by Schantz (1954) and Meerman (1957), is to reduce the yield stress rather than the plastic viscosity. However, the results of Valentik and Patton (1976) seemed to indicate that the addition of polymer modifiers resulted in an increase in both yield stress and plastic viscosity. Valentik (1972) attributed the increased stability of the ferrosilicon dense media to the increased yield stress, which presented an infinite viscosity to small particles (medium particles) and relative low viscosity to large pieces of rock allowing them to move freely in the fluid. An opposite conclusion was obtained by Klassen et al. (1968), who conducted a series of experiments to investigate the effect of polymer modifiers and found that both viscosity and yield stress decreased initially with increasing polymer dosage, until a plateau was reached. Then they started to increase with dosage 113 of reagent. Apian and Spedden (1964), who used apparent viscosity to characterize the medium rheology, showed that the addition of dispersant (sodium hexametaphosphate) reduces the apparent viscosity and increases the suspension stability. Clay contamination strongly influences the rheology of magnetite suspensions. Geer et al. (1957) and Apian and Spedden (1964) showed that clay contamination could dramatically increase the apparent viscosity. The clays, especially montmorillonite, swell and become highly solvated in aqueous suspensions adsorbing up to thirteen times their own weight of water. The significant increase in the hydrodynamic solid concentration and the formation of a structural network of clay particles in water lead to a dramatic increase in yield stress and viscosity. The degree of magnetization of the magnetite particles, induced in magnetic separators, has been found to influence significantly the viscosity of the medium due to the aggregation of magnetite particles caused by remnant magnetic forces. Napier-Munn and Scott (1990), who used an on-line demagnetising coil on the cyclone circuit, noticed that the apparent viscosity decreased substantially as the duration of demagnetization increased. Erten (1964) and Klein (1992) observed that magnetizing a magnetite suspension increased the yield stress, while the plastic viscosity did not change significantly. 114 7.2 Flow Curve Type and Modelling In dense medium separation of coal, the magnetite solid content is normally confined within the range of 7.5% to 15% by volume, which corresponds to a medium density range from 1.3 to 1.6 g/cml Shear rates ranging from 50 s ' (CoUins et al., 1957) to 200 sec"' (Graham and Lamb, 1985) have been assumed in the principal separating zone in the DSM and Vorsyl DMCs. In this investigation, a solid content range from 5% to 30% by volume was covered; the flow curves were measured in the shear rate range from 0 to 300 s ' . 7.2.1 Flow curve type The flow curves for magnetite suspensions shown in Figure 7.2 generally exhibit shear-thinning properties with yield stress. While the yield stress for coarse magnetite suspensions (Mag#l) at low solid content (below 10%) is very low, the existence of yield stress is more clearly manifested in fine magnetite suspensions (Mag#4 and Mag#5). The shear thinning properties, as explained by Casson (1959), result from the formation of particle aggregates due to inter-particle attractive forces. In a suspension at rest, the solid particles are randomly distributed throughout its volume. While some particles will appear as individual entities, others will form aggregates. In the absence of strong inter-particle attraction forces, the aggregates easily disperse and the particles act as individual units. The non-aggregating suspensions exhibit properties of a Newtonian fluid provided that the particles are not markedly asymmetric. Otherwise, the particles in the aggregates are held together by the attractive forces and move as separate units. To make the medium flow, a disruptive force (equal to yield stress) is required to break down 115a o 5 4 , ^ (0 a^ CO 0 3 ^ H—» CO 1 > . CO 0 ^ 2 1 n Mag#1 .,••** . Solid content 30% ,•**' ....••* 28% • * » • * • * »* t * * * * ^ , , * 25% • * * • * » * * * * * * * * + * * * * • . • ' * • '57». . • * ^ * * * * * * * * * * * * * * * * * * * * * * SO/ 4 * * * * * o /o . ' ' • * * 1 1 1 1 1 Mag#2 ...••*** Solid content 28%^^..*•* t * . . * * " .•*'* «» • ..*** ** *** *** 25% .,.••*• * ** *, ****** m + * * * ^*** 22% ^^^,******* ^ *********** 20% ^^********* ,,*** * ******** J , * * * i * * * l O / o * * • * ** ****** ******* 4, * * * * * * * * * * ..*** . . , . . . ' • * 12% . . . K * * + * * * * * * * « * * * ********* ••** * * * * * * * ^ • * * * * * * * ' , * * * * * * * * * * ' . " • * * * * * * * • ' • • • * 5 % 8 7 6 5 4 3 2 1 50 100 150 200 250 300 50 100 150 200 250 300 Shear rate (S) (a) (b) Figure 7.2 The flow curves of magnetite suspensions 115b 60 501 ^ 40 Q. OT V) 2 30^ CO cu x : CO Solid content 25% 20 10 Mag#4 22% 18% 15% 10% 5% 0 50 100 150 200 250 Solid content 22% Mag#5 20% 18% 15% 12% 2% •I I" 40 30 20 -10 (C) 300 50 100 150 200 250 300 Shear rate (S'^ ) (d) Figure 7.2 The flow curves of magnetite suspensions 116 the network of aggregates into smaller ones. The sizes of the aggregates, which control the suspension viscosity, decrease as the shear rate increases. Consequently, the non-Newtonian properties can be interpreted as a result of the viscosity dependence on aggregate size. The same view is also held by others (Patel and Russel, 1988; Potanin and Uriev, 1991). They consider that the formation and destruction of the aggregates are reversible processes. Although the non-Newtonian properties require more than one parameter to define the shear stress-shear rate relationship, investigators in studying the rheology of blood (Rand et al., 1964; Pruzanski and Watt, 1972), coal-water slurry (Nakabayashi et al, 1987), food (Cooley et al, 1954), paint (Ehrlich et al, 1972), polymer suspension, (Gu, 1988), and mineral suspensions (Lilge et al, 1958; Collins et al, 1983) have all commonly presented their rheological results by plotting the apparent viscosity against the shear rate. Such an approach is much simpler because of the similarity of meaning and the identity of units and dimensions of apparent viscosity and Newtonian viscosity. The apparent viscosity data obtained from Figure 7.2 are plotted against the corresponding shear rate (see Figure 7.3). In a log-log plot, certain linearity between apparent viscosity and shear rate can be observed, especially with fine magnetite suspensions at high solid contents. Dilatancy is observed with coarse magnetite suspensions (Mag#l and Mag#2) at low solid content (below 10% vol.) over the high shear rate region (above 200 s'). This observation seems to contradict the early interpretation that dilatancy is due to the insufficiency in lubricating liquid among particles and the consequent jamming. According to this interpretation, dilatancy should be more significant with finer magnetite suspen-117a 10 I 0.1 30% (0 Q. E 8 0.1 o (0 > c 0) CO Q. a. ^ < 0.01 •> 28 25 o o 20 „ 15 o 10 = 5 % Mag#1 30% o 28 25 20,. 1 5 . 10„ 5% l\/lag#2 o o o o : : < ^ i O -1.0 0.1 0.01 1 10 100 Shear rate (S^) (a) 0.1 1 10 100 Shear rate (S^) (b) 1000 Figure 7.3 The apparent viscosity as a function of shear rate 117b 10 1.0 Q. CO o .« 0.1 > c (D CO Q. Q. < 0.01 25% o 22 18 0 15 o 10% — o o 5% 1 l\/lag#4 o o o o o % ° % V \ \ "• V •••. \ o 1 1 3° l\/lag#5 22% 20 18 o o 15 ° " 0 Ofj<^(v 10% %^  " ^ ^ v ° °°°°°^^ 5% °% \ ^ "o ^ — 1 1 1 0.1 10 100 1000 1 Shear rate (S )^ 10 100 100 10 1.0 0.1 0.01 1000 (c) (d) Figure 7.3 The apparent viscosity as a function of shear rate 118 sions at higher solid contents. Obviously, the dilatancy with coarse magnetite suspensions at such low solid contents cannot be explained by the theory of "jamming". It is believed that the dilatancy revealed in Figure 7.3 reflects the flow regime transition in the process of increasing the shear rate from laminar flow at low shear rate (<100 s') to turbulent flow at high shear rate (>100 s'^ ). At any given shear rate, the Reynolds Number, pud/T], for coarse magnetite suspensions with lower solid contents will be much higher due to their lower viscosities than that of fine magnetite suspensions with higher solid contents. Thus for coarse magnetite suspensions with low solid contents, turbulent flow develops at much lower shear rates. In the laminar flow regime, the fluid layers in the viscometer sensor slide over one another with minimum energy exchange due to viscous friction only. When turbulent flow develops, the intermixing among different shearing layers greatly increases the energy consumption. Also, the apparent viscosity increases. 7.2.2 Modelling of rheological flow curves The above method of plotting apparent viscosity against shear rate transforms the rheological flow curves into apparent viscosity versus shear rate curves. These curves still cannot be employed in the hydrodynamic analysis of particle movement in non-Newtonian fluids in which the Reynolds number requires the use of constant rheological parameters to characterize the fluid rheology. Such characteristic rheological parameters can only be derived from the flow curves through modelling. In this work, five models (Table 7.1) were examined. They were first screened by using the correlation coefficient, r^ . Three models: the Bingham, the Herschel-Bulkley, and the Casson models were found to have r^  values generally above 0.9 over the entire 119 variable ranges. The yield-thinning properties of the magnetite suspensions also suggest that the model have a yield stress term. The three models satisfy this requirement and are isolated for further analysis. Table 7.1 The rheological models tested Name Newton Bingham Ostwald Herschel-Bulkley Casson Model X = riD x = Tp,+ rip,-D T = KD" T = To + K-D" X = [<" + (Tlc-D)"']' The effectiveness of each of the models varies as a function of suspension solid content and magnetite particle size distribution. For simplicity, the solid content, c, and the magnetite particle size modulus, d632, are combined to form a single parameter S=c/d632. Apparently, S reflects the total solid-liquid interfacial area in unit volume suspension. By plotting r^  against S in Figure 7.4, it can be found that the Bingham model possesses the highest r^  value at low S values (below 0.42 )im''). It then starts to fall off with the increasing S values, while the r^  values of both the Casson model and the Herschel-Bulkley model continuously increase. In the intermediate range of S values, both the Casson and the Herschel-Bulkley models fit the flow curves satisfactorily. At high S values (above 4.2 |im"*), the r^  value for the Casson and Bingham models decline rapidly, and the Herschel-Bulkley model becomes the only effective model in this range. 120 Apparently, none of the three models showed an unequivocal superiority over others over the whole S value range, if judged by correlation coefficient. Examination of the curve fitting of the models to the actual flow curves in Figure 7.5 reveals that the Bingham model does not describe properly the flow curve data in the low shear rate region (<100 s"'), where a marked non-linearity exists. It tends to overestimate by a large margin the yield stress for all the flow curves. The Herschel-Bulkley model, on the other hand, tends to underestimate the shear stress in the high shear rate region (>250 s"'). A major drawback for the Herschel-Bulkley model, T=Xo+KD", is that the two parameters in the model, K and n, do not have direct rheologi-cal meanings. This makes the interpretation of the medium rheology using these parameters difficult. The Casson model was derived by considering the inter-particle attractive forces and disruptive stresses. It proved to be very effective in describing the flow curve data in a broad magnetite particle size range (from d63 2=30 |im resembling the commercial magnetite used in industrial operation down to micronized-magnetite with d j^ 2=2.7 [mi), and over the solid content range from 5% to 25% vol. (which covers the entire solid content range for dense medium separation). The Casson (1957) model was thus preferred over the Herschel-Bulkley and Bingham models in describing the rheological flow curves of magnetite suspensions. From this model, two rheological parameters, the Casson viscosity and the Casson yield stress can be derived and employed to characterize the medium rheology. It must be home in mind that the Casson model is applicable within the above specified solid content range. Beyond these limits the effectiveness of the Casson model 121 0.95 C 0.9 c O 1 o o c: o a <a \— \  o O 0.85 o.a 0.75 0.7 0.65 0.1 a A o D • D D °- O O A O oy A ^ D °oO • Bingham A Casson o H.-Bulkley A n D A A D • 10 S value Figure 7.4 The correlation coefficient of the three rheological models 122a J I I L-0 50 100 150 200 250 0 50 100 150 200 250 300 Shear rate (S"') Casson model (a) (b) Figure 7.5 Curve fitting of the three rheological models to the flow curves of the magnetite suspensions 122b 50 100 150 200 250 Shear rate (s'^ ) (c) 50 100 150 200 250 30?) Shear rate (s ) (d) Figure 7.5 Curve fitting of the three rheological models to the flow curves of the magnetite suspensions 123a 50 100 150 200 250 300 50 100 150 200 250 300 Shear rate (S ) (a) Shear rate (S ) (b) Figure 7.6 Curve fitting of the Bingham model over the higher shear rate region 123b 60 50 ^ 40 CO « 2 30 V) CD CO 20 10 25%^.,.,-**'"'*''*'""^ , - • • • • " l\/lag#4 ^^"'i-.*——^-^^ '''  18% 15% l\/lag#5 _ — - - - ^ ^ ^—T^^^^^^^^ 20% — T T : ^ ^ ^ ^ ^ ^ " " ' " ' T 8 % 15%^^^____^^_^_„ 12%____ „__ 1 1 1 1 1 40 30 20 10 50 100 150 200 250 300 50 100 150 200 250 300 Siiear rate (S"^ ) Siiear rate (S"^ ) (c) (d) Figure 7.6 Curve fitting of tiie Bingiiam modei over tlie iiigii siiear rate region 124 deteriorates quickly with increasing solid content, and the three-parameter Herschel-Bulkley equation has to be used. Examination of the flow curves in Figure 7.2 reveals that the non-linearity can be confined within the low shear rate range up to 100 s"', and linearity can be observed at higher shear rate range. This may imply the need for using different models to describe the flow curve over different shear rate ranges. As shown in Figure 7.6, a near perfect fit can be obtained by using the Bingham model to fit the flow curve data over the shear rate range from 100 to 300 s'\ The approach to model the flow curves over different shear rate ranges may create difficulty in its application, since it requires the knowledge of characteristic shear rate range for each particular system in question. When a DMC operates at low inlet pressure, for example, the vortex flow shear rates (i.e. the characteristic shear rates determined by Equation 3.4) are assumed to be around 50 s'\ Since the characteristic shear rates are within the nonlinear portion of the flow curve (Figure 7.6), the Casson viscosity and Casson yield stress have to be used to define the medium rheology. The rheological behaviour at shear rates much higher than 50 s"' is irrelevant for this particular application. When a much higher inlet pressure is employed for the same DMC-dense medium system, the characteristic shear rates increase to around 150 s"' in the linear portion of the flow curve. The Bingham viscosity and Bingham yield stress can be used to define the medium rheology. The drawback for this procedure is obvious since many applications cover wide shear rate ranges, or their characteristic shear rates are difficult to estimate. 125 7.2.3 Casson yield stress and Casson viscosity The yield stress can be determined either by extrapolating flow curve data or by fitting the data to an appropriate model to find the zero shear rate intercept on the shear stress axis (Mewis and SpauU, 1976). The latter method is superior to the extrapolation method (Nguyen and Boger, 1983). The yield stresses of the magnetite suspensions, as estimated by the Bingham, Casson, and Herschel-Bulkley models, are compared in Figure 7.7. The Bingham yield stress tends to over-estimate the yield stress by a big margin since it is obtained from a linear extrapolation from the high shear rate region. Furthermore, it fails to describe the non-linearity at low shear rate region. The Herschel-Bulkley model, on the other hand, gives the lowest estimate of the yield stress. However, the differences between the Casson yield stress and the Herschel-Bulkley yield stress are almost indistinguishable. The Casson yield stress values for the four magnetite suspensions shown in Figure 7.7 are combined in Figure 7.8. With increasing solid content and decreasing magnetite particle size, the Casson yield stress exhibits a considerable increase in a well defined pattern. Yield stress is usually defined as the minimum value of shear stress which must be exceeded before the fluid can be made to flow. The existence of yield stress in suspensions is due to the inter-particle attractive forces. These forces lead to the formation of structural aggregates in the suspension, restrict positional change of volume elements, and give the suspension a solid character. External forces, if smaller than those inter-particle attractive forces, will not be able to make the suspension flow. Only when the externally applied forces become so large that they can overcome the network forces (or 126 1.0 (0 Oj, a> 9 >-Mag#1 ^Casson ^H.-Bull<ley ^Bingham Mag#2 10 0.1 0.01 0 0 1 L — I — ' • — < • — < • — t — ! — I — f — I 1 — ' — I — ' — I — I — I — I — I 0 . 0 0 1 1.1 1.3 1.5 1.7 1.9 1.3 1.5 1.7 1.9 Medium density (g/cnf) (a) (b) 100 10 to ^ > 0.1 Mag#4 ^Casson ^H.-Bulkley -^Bingham Mag#5 100 10 0 0 1 ' — ' — I — I — I — I — I — I — ' — I — I — I — I — I — I — I — 1 — I — I 0 . 1 1.1 1.3 1.5 1.7 1.9 1.3 1.5 1.7 1.9 Medium density (g/crrf ) (c) (d) Figure 7.7 Comparison of the yield stress as estimated from the three rheological models 127 100 10 i" 1 ; g g> • > . g 0.1 O 0.01 0.001 Temp.=19C 1 1 1 1 1 1 1 1 A Mag#1 • Mag#2 o Mag#4 A Mag#5 1 1 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Medium density (g/cm?) 2.1 2.2 2.3 10 15 20 Solid content (%vol.) 25 30 Figure 7.8 The effect of magnetite particle size and medium solid content on Casson yield stress 128 the yield point), does the network collapse, and the suspension starts flowing. The existence of the yield stress is a controversial issue. Wildemuth and Williams (1985) argued that under normal conditions, the rheological measurement only gives an apparent yield stress instead of the real one due to an instrumental artifact. Given sufficient time, applying a small stress will cause a fluid with an apparent yield stress to deform. Thus the measured yield stress value may vary depending on the measurement time or the increasing speed of the external forces applied on the fluid. Cheng (1985) suggested using a measurement time that best suits the characteristic time of a particular process. Obviously, the data given in Figure 7.7 are the apparent yield stresses since, as revealed in Figure 7.3, the minimum shear rate for the HAAKE viscometer employed is around 0.7 s"' which is very high in terms of the yield stress measurement. The yield stress which is the shear stress at zero shear rate is only obtained by the mathematical extrapolation using the Casson (or other) equation. As will be shown in the next chapter, the evaluation of the real yield stress is meaningful only in determining the minimum diameter of a particle which is capable to overcome the fluid yield stress and move relative to its surrounding fluid. The hydrodynamic process of particle movement in non-Newtonian fluids is only fundamental-ly related to the shear stress-shear rate relationship around the characteristic shear rate region. Compared to the yield stress, the viscosity does not show a well defined relationship with medium composition (see Figure 7.9, which is plotted using a variation of the "connect the dots" approach in which, the average of the measurements are connected). The Casson viscosity does not respond in a predictable way to changes in 129 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Medium density (g/crrP) 2.1 2.2 2.3 10 15 20 Solid content (%vol.) 25 30 Figure 7.9 The effect of magnetite particle size and medium solid content on Casson viscosity 130 magnetite particle size or in medium density. The Casson viscosity of Mag#2 suspension is virtually independent of the medium density and remains approximately at 1.5 mPas over the entire medium density range tested. With coarser magnetite (Mag#l), the Casson viscosity increases slightly from 1.6 to 3.0 mPas over the same medium density range. With the micronized-magnetite suspensions (Mag#4 and Mag#5), the Casson viscosity initially decreases with medium density and then starts to increase drastically at medium densities exceeding 1.6 g/cm^. Comparison of Figures 7.8 and 7.9 reveals that while the Casson yield stress varied by an order of two over the density range from 1.2 to 1.8 g/cm^ the variation in Casson viscosity over the same range can be mainly confined within the range from 0.5 to 2.5 mPa-s. Such properties are clearly demonstrated in Figure 7.2. With increasing medium density, the flow curves only move up vertically without changing markedly the slopes. This results in a group of near parallel flow curves. In addition, the Casson yield stress also responds to the change in magnetite particle size in a clearly defined manner (see Figure 7.8). With decreasing magnetite particle size, the yield stress vs. medium density curve moves up to a higher parallel position. By comparison, the Casson viscosity is not sensitive to the influence of magnetite particle size (see Figure 7.9). These results demonstrate that the Casson yield stress is the principal rheological parameter which is sensitive to the change in the dense medium properties, while the Casson viscosity is only an subordinate parameter. If the Casson viscosity for a magnetite suspension is treated as a constant over a medium density range from 1.2 to 1.7 g/cm^, the introduced error is insignificant, especially with the Mag#2 dense medium. In studying the effect of medium rheology on DMC performance, the use of the Casson yield stress 131 to correlate with DMC performance, while treating the Casson viscosity as a constant, may then be justified. The use of the Casson viscosity to represent the medium rheology, and to correlate it with DMC performance, may lead to entirely wrong conclusions. Valentik and co-workers (1964, 1976) claimed that for dense medium suspensions, the yield stress is a function of the plastic viscosity; it increases with plastic viscosity. In order to determine the relationship between Casson yield stress and Casson viscosity, the Casson yield stress data from Figure 7.8 are correlated with the corresponding Casson viscosity data from Figure 7.9. As shown in Figure 7.10, no relationship can be observed. Apparently, the Casson yield stress and Casson viscosity are two independent parameters that jointly determine the rheological behaviour of magnetite suspensions. The similar results obtained by Klein et al. (1988) also reveal that with increasing solid content the yield stress increases considerably, while the plastic viscosity only changes marginally. This again implies the independence of the two rheological parameters. The independence of the non-Newtonian rheological parameters illustrates one of the difficulties in attempting to represent the rheological properties of non-Newtonian suspensions by a single rheological parameter. Both parameters must be used to fully describe the rheological properties of such suspensions. The apparent viscosity has been widely used for non-Newtonian fluids in studies on the effect of medium rheology on the DMC performance (Geer et al, 1957; Napier-Munn, 1980; Davis and Napier-Munn, 1987). With yield-thinning or Bingham plastic fluids, the apparent viscosity, ri^  can be respectively expressed as: 132 100 10 (0 (A (0 £ • > . c o (0 CO O 0.1 0.01 0.001 ^ A A A A £00 ^ * ^ A A ••k A A A O O OO ^ OO O O D cp o O O O p O * n D D A A J^ Temperature=19°C o Mag#1 o Mag#2 A iVIag#4 . Mag#5 2 3 4 Casson viscosity (mPa.s) Figure 7.10 The relationship between Casson viscosity and Casson yield stress ^^^'^' 133 7.6 or D D ^° n n V According to the above equations, the apparent viscosity for a given non-Newtonian fluid is a function of shear rate, D; and it decreases with increasing shear rate. The relationships between apparent viscosity and shear rate for the suspensions of the four magnetite samples have been given in Figure 7.3. In most applications including DMC separation, the characteristic shear rate does not assume a single value, instead it covers a wide shear rate range. As a result, the corresponding apparent viscosity also varies within the characteristic shear rate. The common practice to determine and use a single apparent viscosity value at an arbitrarily selected shear rate becomes fundamentally questionable. Since the absolute value of Casson viscosity, Ti^ . is much lower than that of Casson yield stress (Figures 7.8 and 7.9), the apparent viscosity, according to Equation 7.6, is mainly determined by the Casson yield stress, and a linear relationship between apparent viscosity and yield stress should be observed especially at low shear rates: ^y_L or Ti = ^ 7.8 The slope of the linear relationship is equal to the reciprocal of the shear rate, D, selected to measure the apparent viscosity, and the intercept is determined by the Casson viscosity. As shown in Figure 7.11, where the apparent viscosities obtained at three different shear 134 0 0.5 1 1.5 2 2.5 3 3.5 1 2 3 4 5 Casson yield stress (Pa) Casson yield stress (Pa) (a) (b) 10 20 30 40 Casson yield stress (Pa) (c) 50 5 10 15 20 25 Casson yield stress (Pa) (d) 30 Figure 7.11 The relationship between apparent viscosity and Casson yield stress 135 rates: 50, 100, and 250 s ' are plotted against the Casson yield stress, the best linear relationships between apparent viscosity and yield stress are obtained with the Mag#4 and Mag#5 dense media which have much higher Casson yield stress value than the Casson viscosity value. This result confirms that the apparent viscosity is primarily given by the yield stress, while the Casson viscosity in Equation 7.6 is negligible. With the coarser Mag#l and Mag#2 dense media, the linearity is still observed at low shear rate (50 s"'). At high shear rates (100 and 250 s"^ ), however, the influence of the Casson viscosity can not be ignored; and the relationship between apparent viscosity and Casson yield stress loses linearity. From the above results, it can be summarized that the Casson yield stress and Casson viscosity are two independent rheological parameters that jointly describe the non-Newtonian behaviour of magnetite suspensions. The change in rheological behaviour due to the variation in medium composition is more sensitively reflected by the Casson yield stress, while the Casson viscosity can be treated as a constant for the coarse magnetite suspensions (Mag#l and Mag#2) or can be ignored for the fine magnetite suspensions (Mag#4 and Mag#5). The apparent viscosity is mainly a function of Casson yield stress and shear rate. While the Casson yield stress for a given medium composition is constant, the apparent viscosity still varies at a function of shear rate. Thus, the Casson yield stress is the most fundamental rheological parameter in characterizing the rheological properties of magnetite suspensions; the Casson viscosity and the apparent viscosity are secondary rheological parameters. This is further confirmed in the DMC separation test in which close correlations between the DMC performance and the Casson yield stress of the dense medium are observed (see Chapter 9). 136 7.3 Effect of Magnetite Particle Size Distribution It has been claimed (Chong et al, 1971) that if suspended particles are smooth and spherical, the monodispersed suspension viscosity is independent of particle size; it is only a function of concentration. The rheology of irregular-shaped solid particle suspensions is, however, affected by both solid concentration and particle size. As observed by Valentik and Patton (1976), at a constant solid content, both plastic viscosity and yield stress increased with decreasing solid particle size for a mono-dispersed system. The magnetite suspensions of practical interest are seldom mono-disperse. The joint effect of particle size distribution and particle shape on the suspension rheology is not well understood, although an extensive work has been carried out by researchers (Ward and Whitmore, 1950; Maude, 1960; Chong et al, 1971; Wildemuth and Williams, 1985) to model the viscosity of solid suspensions as affected by the solid content by introducing a parameter termed the maximum solids concentration, C„, at which the viscosity approaches infinity. The study on the effects of solid particle size distribution and particle shape on medium yield stress is virtually non-existent. It is intended in this section to generalize the effects of particle shape and size distribution on dense medium yield stress and to characterize such effects with a single parameter termed relative hydrodynamic volume factor. 7.3.1 Theory Steinour (1944) in studying particle settling rate, and Ward and Whitmore (1950) in studying suspension viscosity, considered that the effect of particle size and shape on the settling rate or on suspension viscosity is due to the immobile liquid layer which 137 accompanies angular particles in amounts determined by their shape and surface area (Whitmore, 1958). When irregular-shaped particles are dispersed in liquid, a certain amount of liquid forms a film attached to the particle surfaces and smooths off the irregular outline of each particle. The resulting shapes would not differ greatly from spheres. Each solid particle plus the attached immobile liquid layer behaves as a single spherical particle. The suspension of irregular particles could then be considered to behave as a suspension of spheres at a higher concentration. The concentration of the dry solid plus the immobile liquid is called the hydro-dynamic volume concentration. When the dry volume concentrations are replaced by the hydrodynamic volume concentrations, the trend showing the increase in apparent viscosity with decreasing particle size disappears. This theory might be employed to explain the phenomenon encountered in dense medium separation: the apparent viscosities of atomized ferrosilicon suspensions are significantly lower than those of the ground ferrosilicon suspensions. Apparently, the specific surface area of the irregular ground ferrosilicon particles is greater than that of the spherical atomized ferrosilicon particles. To smooth off the irregular outline, the amount of immobile liquid attached to the irregular ferrosilicon particles is greater than that attached to the spherical ferrosilicon particles. Thus, at any given dry solid content, the hydrodynamic volume concentration and apparent viscosity of the ground ferrosilicon suspension are higher than those of the atomized ferrosilicon suspension. The interpreta-tion given by Colhns et al. {191 A) that the higher viscosity is due to a greater friction when the irregularly shaped particles collide seems to be less persuasive. The ratio of the hydrodynamic volume concentration, Q , to the corresponding dry 138 solid volume content, C ,^ is called hydrodynamic volume factor, O, or ^=€^0^. Apparently, the value of O increases with decreasing solid particle size and with increasing irregularity of particle shape, and the suspension of spherical particles possesses the lowest hydrodynamic volume factor close to one. This theory may also be applied to interpret the effects of particle shape and particle size distribution on the Casson yield stress and Casson viscosity of magnetite suspensions. Based on this theory, all the magnetite suspensions, irrespective of the particle shape and size distribution, should possess the same Casson yield stress and Casson viscosity values at identical hydrodynamic volume concentrations. In order to determine the hydrodynamic volume concentration, a set of standard suspensions of spherical particles is required to generate a standard yield stress (or viscosity) vs. solid content curve. Strictly speaking, these spherical particles should not possess any immobile Uquid attached to them. That is, their hydrodynamic volume factor is equal to one. By matching the rheological parameters of an irregular-shaped particle suspension with the standard curves, the hydrodynamic volume concentration of the suspension, which is equal to the solid concentration of the standard spherical suspension, can be determined. As a matter of fact, any spherical particles in a suspension carry a certain amount of immobile liquid resulting in a hydrodynamic volume factor greater than one. Thus, the concept of determining the hydrodynamic volume factor by using standard suspensions only has a theoretical meaning. In view of this, a concept of relative hydrodynamic volume factor is proposed in the following section. 139 7.3.2 Relative hydrodynamic volume factor A relative hydrodynamic volume factor, ()), is defined here as the ratio of the hydrodynamic volume factor of a magnetite suspension in question, O, to the hydrodynamic volume factor of a reference magnetite suspension, O", at the same hydrodynamic volume concentration; that is, {t)=<I)/0°. Since <I>=Q/Cd and ^"=Ci,°/C°, the relative hydrodynamic volume factor becomes: ^0 ^0 ,^0 Since C[,=Ch°, the above equation becomes: (|)=A=fk 7.10 Thus, the relative hydrodynamic volume factor for a magnetite suspension is equal to the ratio of the dry volume content of the reference magnetite suspension to the dry volume content of the magnetite suspension in question. Since the two magnetite suspensions in Equation 7.9 have an equal hydrodynamic volume concentration, their Casson yield stress or Casson viscosity should be identical. Thus, the relative hydrodynamic volume factor can be interpreted as the ratio of the dry solid content of the sample to the dry solid content of the reference sample when their suspensions have the same Casson yield stress or Casson viscosity. According to Equation 7.9, the relative hydrodynamic volume factor of the reference solid suspension is equal to one. The relative hydrodynamic volume concentration of the magnetite suspension is equal to its dry solid content divided by its 140 relative hydrodynamic volume factor. Obviously, the selection of the reference magnetite sample is arbitrary. In this study, Mag#l is selected and its Casson yield stress (or Casson viscosity) vs. solid content curve serves as a standard curve. By matching the Casson yield stresses of the Mag#2, Mag#4, and Mag#5 suspensions with those of the Mag#l suspension (Figure 7.8), the relative hydrodynamic volume factors for these suspensions can be determined. They are 1.18, 2.53, and 2.82 for Mag#2, Mag#4, and Mag#5 respectively. These numbers give the dilution factors for the corresponding magnetite suspensions with respect to the reference Mag#l suspension in order to have an equal yield stress value. For example, the Mag#4 suspension, if 2.53 times as diluted as that of the reference Mag#l suspension, shall have the same Casson yield stress value as the reference Mag#l suspension. The Casson yield stress data from Figure 7.8 are re-plotted against the relative hydrodynamic volume concentration. As shown in Figure 7.12, all the data points fall reasonably well onto one curve. This result suggests that the hydrodynamic volume concentration of a magnetite suspension determines its Casson yield stress. The effect of the magnetite particle size distribution and particle shape on the suspension rheology could then be characterized by a single parameter: the relative hydrodynamic volume factor. When the dry solid contents are divided by the corresponding relative hydrodynamic volume factors, the effects of the magnetite particle size distribution and particle shape on the Casson yield stress disappear. The above relative hydrodynamic volume factor is an average value obtained by assuming that such a factor is independent of the suspension solid content. This is confirmed by the reasonably good overlap of the curves in Figure 7.12. Strictly speaking. 141 CO (A (0 to a> • > . c o (A (A CO O 100 10 0.1 0.01 Temp. = 19°C o 0 4o° ^ • Mag#1 o Mag#2 A Mag#4 A Mag#5 0.001 10 20 30 40 50 60 70 Relative hydrodynamic volume cone. (% vol.) Figure 7.12 The relationship between Casson yield stress and relative hydrodynamic volume concentration (%vol.) 142 however, the relative hydrodynamic volume factor is not entirely independent of solid content. As the solid content increases, more particles aggregate, resulting in a reduced amount of attached water on the particle surfaces. Thus the relative hydrodynamic volume factor should slightly decrease. The same approach is also applied to the Casson viscosity data from Figure 7.9. No clear information can be retrieved from the resulting graph (see Figure 7.13). Since the relative hydrodynamic volume factor reflects the amount of the binding immobile liquid attached to the solid particles, it should be proportional to the specific surface area of the solid particles if the thickness of the immobile liquid is relatively constant. This is confirmed in Figure 7.14 where the relative hydrodynamic volume factor increases with the reciprocal of dg3 2, which is proportional to the specific surface area of the magnetite samples. The introduction of the relative hydrodynamic volume factor and the results in Figure 7.12 have estabhshed part of the theoretical and experimental basis for modelling the Casson yield stress, and for studying the effects of magnetite particle shape and size distribution on dense medium rheology. The relative hydrodynamic volume factor may also be used in the magnetite production and in optimizing the medium composition. 143 ^ 5 CO Q . E w o u CO > 3 c Q O 2 Temp.=19C • Mag#1 o Mag#2 A Mag#4 A Mag#5 D D D ? o OS ^ o A A A A A A. A A A A 10 20 30 40 50 Relative hydrodynamic volume cone. (%vol.) 60 70 Figure 7.13 The relationship between Casson viscosity and relative hydrodynamic volume concentration (%vol.) 144 O ^ 2.5 o E 3 O E CO c >. T3 O 2 -S 1.5 cc 0.5 -X ^ a g # 2 Mag#1 1 1 Mag#4 ^ ^ ' ^ 1 1 1 Mag#5 1 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1/d 63.2 Figure 7.14 Relative hydrodynamic volume factor as a function of specific surface area 145 7.4 Effect of Temperature 7.4.1 Introduction Although temperature has a significant effect on the viscosity of water, its influences on the relative viscosity of solid suspensions (Rutgers, 1962) or on the yield stress of blood samples (Merrill et al, 1963) were found to be limited. With non-Newtonian magnetite suspensions, which require two parameters, the viscosity and the yield stress to fully define their rheological properties, the effect of temperature on these two parameters may differ. In order to study the influence of temperature on the rheological properties of magnetite suspensions, two magnetite samples: Mag#2 and Mag#5 were tested over a temperature range from 10 to 40°C. Prior to each rheological measurement, the magnetite suspension was first enclosed in the rheometer sensor cup (see Chapter 4, Experimental Program) and pre-heated in a thermal bath to a pre-set temperature. After the suspension reached the pre-set temperature, the rheometer cup was uncapped and inserted into the thermal jacket attached to the rheometer. The suspension temperature was also checked with a thermometer both before and after the rheological measurements. 7.4.2 Results and discussions Three selected sets of rheological flow curves for Mag#2 and Mag#5 are presented in Figure 7.15. The increasing temperature results in changes in the medium rheology which are manifested by the downward shift of the flow curves. The shift with the coarser Mag#2 suspension is relatively more significant than that with the finer Mag#5 suspension. With the Mag#2 suspensions at different solid contents, the shift is more 146 1.2 s- 1 I 0.8 I 0-6 w 0.4 0.2 Mag#2at12%vol. 19<C lot: • ^ " o C O o o o o o o o o oO o o o o o . , 0 0*- (a) o O ^ .SftS ^ o o ° < >o ° " o " > 0 " ° ° o O O o < > O O o .sot \42.5'C 50 CO 0} w 4.5 4 3.5 3 2.5 2 1.5 1 0.5 100 150 200 Shear rate 250 300 i\/lag#2, at 22% vol. 19<C Jf o o " o o o o ? ° o o " " " *^ ° - o o o g o ^ o o o " " - o o o o c o o o o o g g o - o j o o o o o o o k W „ o O > o o = " \ \ 42 .5 t ! ^ 0""° „ 0 0 g o o 5 o o O ° ° ' ° ° o o o 8 e 8 8 8 8 » ° . „ „ . o o T o ° ° ° ° ° ' 1 0 0 ° ^ ° (b) 50 CO is a> w 50 40 30 20 10 100 150 200 Sliear rate 250 300 10t! ig'b - o o o o o o o o o o o o c x - - -o c o o o o 0 0 \42.5'C 30=0 iVlag#5, at 22% vol. (c) 50 100 150 200 Shear rate (S"') 250 300 Figure 7.15 Effect of temperature on medium rheology at different medium density and magnetite size distribution 147 significant at lower solid content. DeVaney and Shelton (1940) suggested that the value of viscosity obtained at very high suspension densities cannot be reduced by temperature increase since the temperature effects are negligible compared with the particle interactions in the suspension. According to this interpretation, the particle interaction becomes increasingly significant for suspensions with higher solid content or with finer particle sizes, and comparatively, the influence of temperature in such cases becomes less significant. This is clearly in agreement with the results in Figure 7.15. Since yield stress and viscosity are two independent parameters, their responses to temperature change may also differ. Results in Figure 7.16 reveal that the temperature has only a very minor influence on Casson yield stress and such an influence is also determined by the solid content of the suspension. At high medium densities (above 1.8 g/cm^), the Casson yield stress is practically independent of temperature; at medium density between 1.4 to 1.8 g/cm^, the Casson yield stress decreases with increasing temperature; and at low medium densities (below 1.4 g/cm^), the Casson yield stress is so low that the influence of temperature is overshadowed by the random error. In general, the effect of temperature on yield stress is negligible. In comparison, temperature has a much stronger effect on Casson viscosity. As shown in Figure 7.17, increasing the temperature causes the Casson viscosity vs. medium density curve to move to a lower position. At low temperature (10°C), the Casson viscosity shows a continuous increase with medium density. At higher temperatures (30°C and 40°C), however, the Casson viscosity decreases with solid content in the intermediate density range and then increases sharply at high medium densities. Over the same 148 10 1 -I •I J 0.1 0.01 0.001 - ft 1 6 1 ^ o 1 o D 1 A O D 1 i 1 § 1 s 1 g A Mag#2 * 19 t A l o t o 30tl a 40^1 1 1 4 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Medium density (g/cm^) 2.1 2.2 2.3 Figure 7.16 Effect of temperature on Casson yield stress 149 3.5 CO I 2.5 w o 2 o CO • > c 1.5 O 0.5 l\/lag#2 _J I L_ 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 IVIedium density (g/cnrf) Figure 7.17 Effect of temperature on Casson viscosity CO CO Q . E, CO o o CO > 20 40 60 Temperature ( C) 80 100 Figure 7.18 Effect of temperature on water viscosity (after P.W. Atl<ins, 1981) 150 temperature range, the viscosity of water decreases by about 50 percent (see Figure 7.18). A comparison of the data in Figures 7.17 and 7.18 also reveals that for magnetite suspensions, the values of their Casson viscosity and their range of variation are in a similar scale of magnitude (0.7 to 1.4 mPas for water, and 1.0 to 3.5 mPas for magnetite suspensions). These results may suggest that temperature affects the dense medium rheology mainly through affecting the viscosity of water, rather than the interactions of the suspended particles. The apparent viscosities obtained from the flow curves in Figure 7.15 (b and c) are plotted against shear rate (see Figure 7.19). Comparison of the two figures (Figures 7.15 and 7.19) indicates that the apparent viscosity versus shear rate curve is less capable to differentiate the variation in medium rheology than the flow curves. The clear shift of the flow curves in Figure 7.15 is not reflected by the apparent viscosity in Figure 7.19. The reason can be explained through Equation 7.6. Although temperature has a significant effect on Casson viscosity, the change when translated to apparent viscosity via Equation 7.6 becomes insignificant due to a much greater Casson yield stress value, which is not very sensitive to the effect of temperature. 151 l U "w" 1 CO Q L E. 5" •§ 0.1 o » • > •g S-0.01 Q. < n nnn * * \ -0 1093 o 19S3 A 3093 * 42.5^: 1 i\/lag#2,22% v/v 1 1 0.1 1 10 Shear rate (S )^ 100 1000 Figure 7.19 (a) Effect of temperature on apparent viscosity (Mag#2 suspensions) 100 i (0 o c (0 Q. Q. < 10 0.1. \ ^ D Q \ A \ 0 lO^C o 19=0 A 30=0 * 42 .5 t 1 l\/lag#5, 22% v/v 1 1 0.1 10 Shear rate (S )^ 100 1000 Figure 7.19 (b) Effect of temperature on apparent viscosity (i\/lag#5 suspensions) 152 7.5 Summary Extensive rheological measurements reveal that magnetite suspensions exhibit non-Newtonian yield-thinning properties. The slight dilatancy for the diluted coarse magnetite suspensions at high shear rate is believed to result from the conversion of the medium flowing state from laminar to turbulent flow. In general, the flow curves are best described by the Casson equation: The Casson yield stress and Casson viscosity are two independent parameters that jointly determine the rheology of magnetite suspensions. While the Casson viscosity is not very sensitive to the changes in medium composition, the Casson yield stress responds to the changing medium properties in a well defined pattern. With coarse (commercial) and intermediate magnetite suspensions, the Casson viscosity can be treated as constant. With very fine magnetite suspensions, the Casson yield stress is so high that the impact of the Casson viscosity is negligible. The strong influence of magnetite particle size distribution and particle shape on yield stress can be described by a single parameter termed relative hydrodynamic volume factor. For a given magnetite sample, its relative hydrodynamic volume factor is basically independent of the suspension solid content. The relative hydrodynamic volume factor reflects the relative amount of immobile liquid attached to the magnetite particle surfaces and is, therefore, a function of the specific surface area of the magnetite sample. These properties may have profound implication in modelling and prediction of medium rheology as well as in magnetite production. The Casson yield stress is not sensitive to the effect of temperature. The relative 153 variation in Casson yield stress in the temperature range from 10 to 40°C is negligible. The effect of temperature on Casson viscosity is relatively stronger; the value of the Casson viscosity and its magnitude of variation are similar to those of water. These results may suggest that temperature affects the dense medium rheology mainly through affecting the viscosity of water rather than through affecting the interactions among the suspended magnetite particles. 154 8. PARTICLE MOVEMENT IN NON-NEWTONIAN FLUIDS 8.1 Introduction Separation in dense medium results from the relative movement of treated particles: the floating of light particles and the sinking of dense ones. The movement of mineral particles relative to the medium is not only determined by the size and density of the treated particles, but also by the rheological properties of the medium. While the rheological properties can be easily identified as viscosity for Newtonian fluids, for non-Newtonian fluids two or more rheological parameters such as Casson viscosity and Casson yield stress have to be employed to define such properties. Apparently these non-Newtonian rheological parameters are collectively influencing the particle movement. To identify and interpret the role played by individual rheological parameters in affecting the particle movement and in influencing dense medium separation, we must first deal with the hydrodynamics of particle movement in non-Newtonian fluids, to which the standard definition of Reynolds number, Re=udp/ri, does not apply. The formulation of a general form of Reynolds number, Re^, capable of reflecting the rheological type of the fluid behaviour becomes a critical step. This is because from the relationship CD=f(Ren,), the influences of non-Newtonian rheological parameters on particle movement, and on dense medium separation can be analyzed. The hydrodynamics of particle movement in Newtonian fluids is well established. The theory is widely applied in mineral processing. With non-Newtonian dense medium, 155 however, the drag coefficient-Reynolds number relationship (Cp-Re) for spherical particles does not follow the same Cp-Re relation as obtained for Newtonian liquids. In addition, the very definition of the Reynolds number, Re=udp/T|, is not applicable to non-Newtonian fluids. Although the non-Newtonian behaviour of magnetite suspensions has long been recognized (Govier et al, 1957; Berghofer, 1959), the hydrodynamic theory of particle movement in Newtonian fluids is still, as reviewed in Chapter 3, being incorrectly used to interpret and to model the DMC separation process. As a result, the vahdity of the theoretical models is questionable and, more importantly, the influence of the non-Newtonian properties of the dense medium (or more specifically, yield stress) on DMC performance remains a subject of controversy (Whitmore, 1958, Napier-Munn, 1980). Whitmore and co-workers (Whitmore, 1958; Valentik and Whitmore, 1964; Valentik, 1972) interpreted the yield stress as a measure of the rigidity of the dense medium before movement is achieved. They claimed that when a particle is locked in a suspension, the yield stress is responsible for it, but when it is moving in any direction, its velocity is a function of plastic viscosity. They further concluded that due to the movement of feed particles through the separator, the circulation of the medium, and the current set up to prevent settling of media, the turbulence is strong enough to provide the feed particles with inertial forces, enabling them to overcome the yield stress of the medium. Thus, the influence of medium yield stress could be ignored. This interpretation has apparently over-simplified a much more complicated issue. A different view on the possible influence of yield stress on dense medium separation has been suggested by many other researchers (Geer etal, 1957; Napier-Munn, 1980). As pointed out by Napier-Munn (1980), the studies which concentrate on the 156 correlation between separation efficiency and viscosity of the suspension by leaving out yield stress may wind up obtaining unclear information on their relationship. In this chapter, the hydrodynamic theory of particle movement in non-Newtonian fluids will be tackled from a rheological perspective. The shear rate due to particle-to-fluid relative movement, the particle Reynolds number in non-Newtonian fluids, and the general form of Stokes' equation for non-Newtonian fluids, are derived. It is concluded that the fluid drag on a sphere moving in a yield-thinning or Bingham plastic fluid is jointly determined by the yield stress and viscosity. For fine particles, the influence of the yield stress becomes dominant. From this conclusion, it is further predicted that the dense medium separation of fine particles is more closely related to the medium yield stress. The supporting experimental evidence from DMC separation will be presented and discussed in the next chapter. 157 8.2 Particle Reynolds Number in Non-Newtonian Fluids The fluid drag on a moving particle is the sum of two components: the viscous drag due to viscous friction and the form drag due to boundary layer separation in the wake of the particle movement (Blevins, 1984). The fluid drag is expressed by the drag coefficient defined as CD=4(ps-p)gd/3pu^. From its relationship with the Reynolds number, CD=f(udp/r|), one can determine the influence of fluid rheology on fluid drag and derive the terminal velocity of the particle as a function fluid viscosity, rj, from this relationship. In dealing with particle movement in non-Newtonian fluids, the main point is to re-formulate the Reynolds number so that it reflects the non-Newtonian nature of the fluids. Particle settling problems in non-Newtonian fluids can be solved in a similar way to that for Newtonian systems. Ansley and Smith (1967) in the conventional dimensional analysis derived the following general relation between the variables in the plastic fluid system: C,=^(^,^) 8.1 Obviously, the first dimensionless term, dup/r|p„ is analogous to Reynolds number; the second term, dXt/uTip,, represents the influence of yield stress, XQ. However, this dimensional analysis does not provide any clue as how to combine the two dimensionless parameters in the above equation to form a single parameter analogous to the Reynolds number. As a result, different forms of modified particle Reynolds numbers, Re ,^, have been formulated by various researchers from hydrodynamic considerations. They are summarized as follows: 158 Re = P!^ 8.2 m r]ji/d+7nz J24 Ansley and Smith (1967) Re = ' ^ 8.3 " -^p/-^Tl^/M/£0 dup Dedegil (1987) j^ ^^^ 8.4 - Saha, Purohit, and Mitra (1992) where u is particle-to-fluid relative velocity, and d particle diameter. Thomas (1960), in studying the flow of Bingham plastic fluids in pipelines, showed that the Reynolds number for such system can be written as: fe,= '''"" 8.5 where dj is the inner diameter of the pipe. These modified Reynolds numbers are all formulated for Bingham fluids. Although presented in various forms, they can be generalized as follows: Re dup 8.6 v^^ hild where k, as will be discussed in detail later, is a shear rate constant reflecting the thickness of the boundary layer. As discussed in the last chapter, the apparent viscosity of a Bingham plastic fluid is expressed as: 159 Tla = V^"V - ^ , V 8.7 Thus, from a rheological perspective, the denominator of Equation 8.6 is fundamentally the apparent viscosity, and the term ku/d is the shear rate, D. As will be discussed in the next section, ku/d is the shear rate induced by the particle-to-fluid relative movement. By substituting Equation 8.7 into Equation 8.6, one can get: Re=^ 8.8 This is the general form of particle Reynolds number. Its form is similar to that for Newtonian fluids except for the viscosity term being replaced by the apparent viscosity. Apparently, the Reynolds number for Newtonian fluids is a special form of Equation 8.8. From this general form of Reynolds number, the particle Reynolds number in fluids of any rheological types can be formulated, provided that an appropriate mathematic model can be obtained to describe the flow curves of the non-Newtonian fluid in question. The flow curves for magnetite dense medium, as discussed in Chapter 7, can be described by the Casson equation: T=[tf+(Tl,-P)^/¥ :fu^ .n^l/2l2 8.9 The corresponding apparent viscosity is Thus, the Reynolds number for particles moving in magnetite suspensions can be obtained by substituting Equation 8.10 into Equation 8.8: 160 Re^. ^ 8.11 Since D=ku/d, the above equation becomes: Re^. d^ 8.12 The same approach can be applied to any other fluid. The implication of developing the modified Reynolds number can be illustrated using the findings by Ansley and Smith (1967) and Dedegil (1987). They found that the data points for spheres settling in Bingham fluids are severely scattered in the C^-Re (Re=dup/r|p,) graph as shown in Figure 8.1 (a). When the Re is replaced by the Re ,^ defined by Equations 8.2 and 8.3, the data points fall on a single curve similar to the CQ-Re relationship for Newtonian fluids in Figure 8.1 (b). The severe data point scattering in Figure 8.1 (a) also suggests the strong influence of yield stress on particle movement in non-Newtonian fluids. More importantly, from the CD-Re^ , relationship for particles moving in magnetite dense medium: Co-A—jr^ 1 8.13 the influence of the rheological parameters, x^ and rj^, on particle movement and on DMC separation can be analyzed (see next Chapter). 100 10 -Q o 1 -%^ o -° o o o o o o o o 1 Re calculated with plastic viscosity o o o o oocP ° „ ° o cP ° o ^ ° a ® n ® OO * o °°o oo § o CP O /> ° ON, lO'^S 10'"4 10'"5 Re 161 Figure 8.1 (a) The correlation between drag coefficient and Reynolds number calculated without taking yield stress into account (Data adapted by Dedegil, 1987 from the experimental results of Valentyik and Whitmore, 1965) 100 10 -Q O 0.1. 0 Rem calculated with both plastic viscosity and and yield stress o \ \ . . 1 1 1 1 0.1 10 10'"2 Rem lO'^S 10'"4 Figure 8.1 (b) The correlation between drag coefficient and Reynolds number calculated by taking yield stress into account (Data adapted by Dedegil, 1987 from the experimental results of Valentyik and Whitmore, 1965) 162 8.3 Shear Rate and Shear Rate Constant One question that remains is the definition of shear rate, D=ku/d, and subsequently, the meaning of the shear rate constant, k. According to the dimensional analysis given in Equation 8.1, the first dimensionless term, dup/T|p„ is analogous to the Reynolds number; the second term, dT(/ur|p„ represent the ratio of yield stress, Tp„ to viscous stress, T|piU/d. Rheologically, the shear stress at any shear rate, D, is equal to the sum of the yield stress and the viscous stress. For the Bingham fluids, the viscous stress is equal to TlpfD. By comparing the two viscous stresses: rip,u/d and TipfD, it can be inferred that the term, u/d, is equivalent to shear rate induced by particle-to-fluid relative movement, or it can be equated to shear rate by introducing a shear rate constant: £>=^ 8.14 d From the modified Reynolds numbers proposed by Ansley and Smith (1967) (Equation 8.2) and Saha et al, (1992) (Equation 8.4), the k values are 24/771 and 6, respectively; while according to Dedegil (1987) who arbitrarily defined D=u/d, k is equal to one (Equation 8.3). In essence, the shear rate induced by the particle-to-fluid relative movement can be directly derived. Figure 8.2 shows a sphere of diameter d moving relative to the fluid at velocity, u. The relative moving velocity of the fluid along the axis of the sphere is zero, and at the surface of the boundary layer the velocity is u. Thus, the average shear rate across the particle is 163 U H = U (d+a)/2^ Figure 8.2 A schematic diagram for shear rate derivation Jii 1.5 CO m c o " 1 W 0.5 k=2/{1+9.06/Re'^0.5) Ansley and Smith Dedegil 1.01 0.1 1 10 10'^2 lO'^a 10''4 10'^5 Reynolds number Figure 8.3 Shear rate constant as a function of Reynolds number 164 D- ("-0) - 2" 8.15 (d+2o)ll d+2o where a is the thickness of the attached boundary layer defined as the distance from the solid surface to the region where the velocity reaches 99% of the external flow (Concha and Almendra, 1979). The thickness of the boundary layer is a function of Reynolds number and can be expressed as follows (McDonald, 1954; Abraham, 1970; and Concha and Almendra, 1979): •Z^ °o 8.16 McDonald (1954) gave a value of ao=9.06. The same value was used by Abraham (1970) and Concha and Almendra (1979). Combining the above two equations gives: D= — 8.17 (l+9.06//?ci/V This is the general form of the shear rate equation induced by the particle-to-fluid relative movement. According to this equation, the shear rate is not only a function of particle-to-fluid relative moving velocity and particle diameter but also a function of Reynolds number. The importance of Equation 8.17 is in that it links the rheological variable (D) with the hydrodynamic variables (u, r, and Re). Thus, it bridges two theories, rheology and hydrodynamics. As will be discussed later. Equation 8.17 will enable us to treat a hydrodynamic issue of particle movement in non-Newtonian fluids from a rheological perspective. Comparing the Equation 8.17 with Equation 8.14, one can derive the definition for 165 k-= = 8.18 Thus k is not a constant. Instead, it varies as a function of the Reynolds number. As shown in Figure 8.3, where the k value is plotted against Reynolds number, the asymptotic minimum and maximum k values are zero and 2, respectively. Apparently, the k values adopted by Dedegil (1987) and Ansley and Smith (1967) are special cases over the Re range from 80 to 100. The k value (k=6) used by Saha et al. (1992) in Equation 8.4, which stems from the plastic fluid Reynolds number for pipeline flow (Thomas, 1960), is unrealistic and far beyond the maximum value of 2. According to Equation 8.18 and Figure 8.3, k represents the thickness of the boundary layer around a spherical particle; it varies as a function of Reynolds number from 0 when the boundary layer thickness is infinity, to 2 when the boundary layer thickness is zero. The meaning of the k can also be explained in a different way. Equations 8.6 and 8.12 can be rearranged respectively as: kpu^ Re^=^^ 8.6a m Re = ^Pff 8.12a where the terms pu^, r|u/d, and TQ are the characteristic inertial stress, viscous stress, and yield stress, respectively. The variation in k value in the denominator of the above equations can be explained as the ratio of the yield stress to the viscous stress terms in 166 their contribution to the resisting force on the sphere (Ansley and Smith, 1967; Saha et al, 1992). It should be borne in mind that the boundary thickness equation (Equation 8.16) is derived for Newtonian fluids. For non-Newtonian fluid, the Re in the equation should be replaced by Re ,^. In such a case, the value of OQ might not be equal to 9.06. However, the curve shape in Figure 8.3 will not change; the asymptotic minimum and maximum k values remain zero and 2, respectively. Apparently, the calculation of real shear rate through Equation 8.17 is very complicated. For practical purposes, the k value may be treated as constant. According to the results in Figure 8.1, where the k value is fixed at one over the Re ,^ value range of 0.3 to 2000, or Re value range of 200 to 4x10'*, the induced error is insignificant since all the data points fall reasonably well on a single curve. This is also confirmed by the results of Ansley and Smith (1967) who set the k value at 24/77U (1.09). As will be shown in the following section, the treatment of the k value as a constant greatly facilitates its application. 167 8.4 Stokes' Equation for Non-Newtonian Fluids In a Newtonian fluid, the viscous drag exerted on a sphere by the fluid in the laminar flow regime is given by: FJ^=3^zd^u 8.19 The corresponding Stokes' equation is: ^_g(5-p)rf^ 8.20 18TI The viscous drag equation in laminar flow regime can be directly obtained from the linear portion of the Cp-Re plot. From the rheological point of view, Equation 8.20 is a special form of Stokes' equation applicable only to Newtonian fluids. In order to obtain a more general form of terminal velocity equation in non-Newtonian fluid, a rheological approach is employed here to correlate the viscous drag directly with the shear stress. This is because the viscous drag exerted on a particle by the ambient fluid is more fundamentally related to the shear stress, which is defined as the viscous drag on unit surface area. Thus, the viscous drag on a particle of surface area A can be written as: F=CV4T 8.21 where x is the shear stress, and c a constant. With the Newtonian fluid as a special case, a linear relationship exists between the shear stress and shear rate: x=TiD. The surface area of a sphere is A=47td ,^ and the shear rate due to the particle moving relative to its ambient fluid is D=ku/d where k is taken as one here. Substituting the above equations into Equation 8.21, one can get: 168 Fjj=c-4n(f'-r\-— = 4cndr\u 8.22 This is the viscous drag equation derived from the rheological approach. By comparing the above equation with Equation 8.19, one can get c=3/4. With Bingham plastic fluids, the relationship between shear stress and shear rate is described by the Bingham equation: x=Xp,+r|piD, and D=u/d. By substituting these equations into Equation 8.21, one can get the viscous drag equation in Bingham plastic fluids: Fj^=3-ndr\pfi+'iTZ(fT:pi 8.23 With magnetite suspensions, the relationship between shear stress and shear rate, as shown in Chapter 6, can be described by the Casson equation. Thus, the viscous drag on a spherical particle in a magnetite suspension is: F^=37rj2[(^)i/2,,i/2j2 8.24 d Under the gravitational force, the terminal velocity of a spherical particle in a non-Newtonian fluid can be derived by equating the particle movement driving force F=l/67id^(8-p)g to the viscous drag equation (Equation 8.23). In Bingham fluids, the particle terminal velocity is: ^_g(5-p)J^ -^p^ 8.25 ISrip/ %i In the fluids obeying Casson equation( Equation 8.24), the terminal velocity is: 169 g(5-p)J 'x, 8.26 \ 9TI: In the field of centrifugal acceleration such as in dense medium cyclones, the gravitational acceleration, g, in Equations 8.25 and 8.26 should be replaced by the centrifugal acceleration, UjVr. From the terminal velocity, the shear rate induced by the particle-to-fluid relative movement can be derived by substituting Equation 8.25 into D=u/d for Bingham fluids: l^Tlp/ Tip; or by substituting Equation 8.26 into D=u/d for magnetite suspensions: 8.27 j _ g ( 5 - p ¥ , ^ c g(5-p)JT^ 9Tif 8.28 170 8.5 The Effect of Yield Stress on Particle Movement Equation 8.25 can be taken as a general form of Stokes' equation. Obviously, when the Bingham yield stress approaches zero, the Bingham fluid becomes a Newtonian fluid, and Equation 8.25 reduces to Stokes' equation (Equation 8.20). When there is no relative movement between particle and fluid (u=0), Equations 8.23 and 8.24 are reduced to Ff^=3Tz<fxpi and FQ=3Tid^x^ 8.29 This is the threshold drag for a particle to overcome before it can start moving relative to the medium. Apparently, the threshold drag is only determined by the yield stress and is independent of fluid viscosity. At any given density difference between particle and medium (6o-p), the minimum particle size, dg, required to overcome the threshold drag in a Bingham plastic or yield thinning fluid is: \i:4(6,-p)g=3n4z, 8.30 D ° (6„-p)« where TQ is the real yield stress. In using Equation 8.31, it is critical to correctly determine the medium yield stress, XQ. Since the yield stress is the maximum shear stress at zero shear rate, it cannot be directly measured using the conventional rotational viscometer. As discussed in the previous chapter, the yield stress can only be estimated based on the shear stress data at near-zero shear rates either through extrapolation or through mathematical modelling. Thus, the accuracy of the estimation depends on the closeness of these data points to the 171 shear stress axis in the flow curve diagram. Since the rheological measurement program adopted in this study (see Chapter 4) is not designed for such a purpose, the yield stress data in Chapter 7 should be considered as apparent yield stresses; they should not be used in Equation 8.31. According to Equations 8.23 to 8.26, the viscous drag on a spherical particle and its terminal velocity in non-Newtonian fluids are functions of both yield stress and viscosity. The viscous drag in Bingham plastic or in yield-thinning fluids consists of two components: the first term due to viscosity, and the second term due to yield stress. Whitmore (1958) and Valentyik (1972) claimed that the yield stress ceases to influence the particle movement in the process of particle-to-fluid relative movement. It can be seen from Equation 8.31 that, contrary to these conclusions, the yield stress determines the threshold drag on particles before particle-to-fluid relative movement is achieved. Also, more importantly, the yield stress determines the viscous drag in the process of particle movement (Equations 8.23 and 8.24) as one of the two contributing components. The total viscous drag during the particle movement increases above the threshold drag, and it is higher than the viscous drag calculated without yield stress. Due to the effect of yield stress, the terminal velocity in a Bingham plastic fluid or in a yield-thinning fluid according to Equations 8.25 and 8.26 will be lower than that in a Newtonian fluid at the same viscosity as determined by Equation 8.20. Thus, when only the Bingham or Casson viscosity is correlated with the particle movement and with dense medium separation ignoring the yield stress, the estimation of viscous drag and particle terminal velocity would be in error. Subsequent interpretation of the rheological influence on dense medium separation (Whitmore, 1958; Valentik and Whitmore, 1964; 172 Valentik, 1972) will be incomplete. The effect of yield stress may dominate over viscosity in determining the viscous drag under certain conditions. This can be evaluated using the ratio of yield stress term to viscosity term as given in Equation 8.23 or 8.24, R=Xp,d/(T|p,u) or R=x^dJ{r\^u). At p^=1.45 g/cm^, a typical medium density for dense medium separation of coal, the values of Casson viscosity and Casson yield stress obtained from Figures 7.8 and 7.9 are tabulated in Table 8.1. The shear rates, D, induced by a near-density fine particle (1.55 g/cm' in density, and 0.5 mm in diameter) are calculated using Equation 8.28 by replacing the gravity acceleration, g, with centrifugal acceleration of 40 m/s^. The R values are given in the last column. The negative shear rates in Table 8.1 only have a mathematical meaning. Physically it means that the particle is unable to overcome the yield stress and is "locked" in the dense medium with a real shear rate of zero. Table 8.1. Particle shear rate (D) and R value (x^d/(i]^u)) in the magnetite suspensions at medium density of 1.45 g/cm^ Mag#l Mag#2 Mag#4 Mag#5 mPa 62 118 2110 2660 mPas 1.85 1.50 0.70 6.69 D S-' 17.4 8.7 -255 (0) -178 (0) R value 1.18 4.84 (oo) (oo) 173 The results in Table 8.1 indicate that with the Mag#l dense medium, the yield stress and viscosity contributions to the total viscous drag are comparable. With the finer Mag#2 dense medium, the contribution of the yield stress to total viscous drag is 4.84 times as high as that of viscosity. As the magnetite particle size further decreases, the influence of the yield stress dominates. Thus the yield stress in the separation of fine particles using fine magnetite dense medium (Klima et al, 1990) becomes the dominant factor in determining the viscous drag and terminal velocity of the particles, while the effect of the Casson or Bingham viscosity is insignificant. From the above discussions, it can be predicted that the dense medium separation of fine particles, which requires the use of fine magnetite dense medium, is more closely related to the medium yield stress than to the medium viscosity. This has been confirmed in our dense medium cyclone separation tests, and it will be discussed in the next chapter. The effect of viscosity becomes dominant only when the yield stress is very low and the shear rate is high. This is the case when separating large particles using coarse magnetite dense medium at low medium densities. The above discussion has been based on the particle movement in the laminar flow regime, where no boundary layer separation occurs, the fluid drag is equal to viscous drag, and C^ shows a linear relationship with Re^. Such a linear relationship can be greatly extended from Re<l for Newtonian fluid up to Ren,<20 to 80 (Dedegil, 1987; Ansley and Smith, 1967) for Bingham fluids. Beyond this range, the influence of the non-Newtonian rheological parameters on particle movement can be interpreted through the general relationship Cp-Re^: 174 Co=Ji—^^) 8.32 for Bingham plastic fluids as shown in Figure 8.1 (b), or C o - A - ^ 3 8-33 for Casson yield-thinning fluids. 175 8.6 Application of Apparent Viscosity The apparent viscosity has been widely used by researchers in dealing with non-Newtonian fluids and in interpreting the effect of medium rheology on dense medium separation performance (Geer et al, 1957; Napier-Munn, 1980; Davis and Napier-Munn, 1987). Since the apparent viscosity for Bingham plastic or yield-thinning fluid can be expressed by Equation 8.7 or 8.10, Equations 8.23 and 8.24 can both be reduced to: F^=37i:JMri„ 8.34 and the particle terminal velocity in non-Newtonian fluids becomes: ^^^g(^zML 8.35 That is, for non-Newtonian fluids the viscous drag and the terminal velocity can be calculated using the same equations as for Newtonian fluids; only the apparent viscosity should be used in place of the Newtonian viscosity in these equations (Equations 8.34 and 8.35). It should be pointed out that the apparent viscosity, ri^, in Equation 8.35 must be measured at the characteristic shear rate that actually occurs in the system. Unlike Equation 8.25 in which all the parameters can be directly obtained. Equation 8.35 contains a variable, Tj^ , which varies as a function of shear rate, D=u/d. Determination of the characteristic shear rate, at which the r\^ is measured, requires the knowledge of the particle velocity which in turn is the unknown, being determined in Equation 8.35. The common practice to measure the apparent viscosity at an arbitrarily chosen shear rate instead of the characteristic shear rate calculated by D=u/d can only serve the comparison purpose to determine the relative viscosities of fluids. The apparent viscosity 176 thus obtained can not be used in Equations 8.34 and 8.35 to calculate the real viscous drag and terminal velocity. With the yield-thinning and Bingham plastic fluids, the apparent viscosity decreases with increasing shear rate. However, this does not mean that the viscous drag on particles in such fluids decreases with increasing shear rate. As shown by Equations 8.23 and 8.24, with increasing shear rates (or particle velocity, u) in shear-thinning fluids, the fluid drag increases, too. Throughout this chapter, both the Bingham and the Casson equations have been used to develop the particle Reynolds number in non-Newtonian fluids and to derive the viscous drag and terminal velocity equations in such fluids. The same approach can be applied to any other fluid provided that a proper model can be found to describe the shear rate-shear stress relationship for the fluid. 177 8.7 Summary The general form of Reynolds number applicable to any types of fluids is: For the Bingham plastic or the Casson yield-thinning fluids, the Reynolds number becomes: ^i+'^pflku or Re=^ ^ " ^ respectively The shear rate induced by particle-to-fluid relative movement is expressed as: d This equation is crucial in bridging two separate theories, rheology and hydrodynamics. The shear rate constant, k, varies as a function of Reynolds number in the range from 0 when the boundary layer thickness is infinity, to 2 when the boundary layer thickness is zero. For practical purposes, the k value can be set at one. The fluid drag on a particle and its velocity in a yield-thinning or a plastic fluid are functions of both yield stress and viscosity. Yield stress not only determines the threshold drag on particles before particle-to-fluid relative movement is achieved, more importantly, it also determines the viscous drag during the particle-to-fluid relative movement. The general relationship between the fluid drag and the non-Newtonian 178 rheological parameters can be expressed as: for Bingham plastic fluids, or dup Cj) =/[—— ] for Casson yield-thinning fluids. The particle terminal velocity in the Bingham plastic fluid and the Casson yield-thinning fluid in the laminar flow regime can be expressed respectively as: ^_8(b-p)d' -^p^ and 1811. Ti, ^ 8i6-p)d'-z 3 , 'c 9TI' The Stokes' equation is a special form of above equation when yield stress, tpi, is zero. At any given density difference between particle and medium (6o-p), the minimum particle size, d^ capable to overcome the yield stress and to move relative to the fluid is: . 18xo (6o-p)^ where XQ is the real yield stress of the fluid. For non-Newtonian fluids, the viscous drag and the terminal velocity can be calculated using the same equations for Newtonian fluids; only the apparent viscosity should be used in place of the Newtonian viscosity in these equations. 179 9. THE EFFECT OF DENSE MEDIUM RHEOLOGY ON DMC PERFORMANCE 9.1 Introduction It is still unsolved how individual rheological parameters affect dense medium separation in a non-Newtonian magnetite dense medium. The influence of the yield stress which is the focal point of the issue remains controversial. Whitmore and co-workers (Whitmore, 1958; Valentyik and Whitmore, 1964; Valentyik, 1972) interpreted the yield stress only as a measure of the rigidity of the dense medium before movement is achieved. They put forward the turbulence theory which maintains that in dense medium separation process, the movement of mineral particles through the separator, the medium circulation, and the current set up to prevent medium particle from settling, produce turbulence which is strong enough to provide the mineral particles with inertial forces, enabling them to overcome the yield stress of the medium. Accordingly, they claimed that the yield stress does not affect dense medium separation, and that the separation efficiency is only a function of the medium plastic viscosity. A different view on the possible influence of yield stress on dense medium separation has been suggested by many other researchers (Geer et al, 1957; Yancey, 1958; Napier-Munn, 1980). As pointed out by Napier-Munn (1980), the studies which concentrate on the correlation between separation efficiency and viscosity of the suspen-sion by leaving out yield stress, may wind up obtaining unclear information on their 180 relationship. He further speculated that since the near-density materials are more likely to be locked in the medium due to the existence of the yield stress, a horizontal plateau region should exist on the partition curve centred around feed medium density. According to the hydrodynamic analysis in the previous chapter, the yield stress not only determines the threshold drag on particles before their relative movement to the fluid is achieved but also contributes to the total fluid drag during their movement. The influence of the non-Newtonian Theological parameters (Casson viscosity and Casson yield stress) on dense medium separation can be interpreted via the relationship: Cn-A-Z^ J 9.1 or, in the Bingham plastic fluid: ^ ^ = ^ — ^ ^ ' • ' r]pi+T:pid/ku Based on these relationships, it can be postulated that the DMC separation is a function of both viscosity and yield stress, and the influence of the yield stress dominates over that of viscosity in the DMC separation of fines. This is confirmed by the extensive experimental data provided in this chapter. Results show that the medium stability, the separation efficiency and cutpoint shift of fine particles, are closely interrelated with the medium yield stress. On the other hand, no clear correlation between DMC performance and Casson viscosity can be observed. 181 9.2 Results 9.2.1 The effect of medium rheology on medium stability The medium rheology has a major effect on the stability of magnetite suspensions. Due to a very low magnetite particle velocity relative to its ambient fluid, u, and a much greater absolute value of Casson yield stress than that of the Casson viscosity (Figures 7.8 and 7.9), the fluid drag on magnetite particles according to Equation 9.1 or 9.2 is determined predominantly by the yield stress as represented by the second term in the denominator in these equations. This is the case for stagnant magnetite suspensions, for which a good correlation between the yield stress and the medium stability as measured in a volumetric cylinder has been observed (Valentik, 1972). This is also evident in the dynamic DMC process in which high shearing conditions prevail. As shown in Figure 9.1, the density differentials for the three magnetite suspensions all experienced exponential decrease with increasing Casson yield stress. Over the very low yield stress range (<Xp), however, the density differential showed a rapid increase with yield stress until it reached a maximum value at T=Xp. Apparently, the yield stress below Xp was not large enough to effectively prevent the medium from classification. Increasing the medium density, although accompanied by an increased yield stress, resulted in a higher density differential. For comparison, the density differential data are also related to the Casson viscosity. As shown in Figure 9.2, no clear relationship between the density differential and the Casson viscosity can be found. It should be mentioned that selecting an appropriate parameter to characterize medium stability under dynamic conditions in a DMC is also very important. Settling rate. 0.45 u.<: 0.15 ' 0.1 0.05 1 i i \ i 1 • \ • \ 1 Mag#2 • \ • 1 1 1 1 0.04 0.03 0.02 0.01 0 0.1 0.2 0.3 0, Casson yield stress (Pa) 4 0 0.2 0.4 0.6 Casson yield stress (Pa) 0 2 4 6 8 Casson yield stress (Pa) Figure 9.1 The effect of Casson yield stress on medium stability 00 U . 3 0.45 „ „ - ^ ^ 0.4 o ^ .« 0.35 4 ^ C (D k -(D :t= =6 0.3 >. +-• 'to c a> 0 0.25 0.2 Mag#1 • • • • . 9 • • • • _• • 0 • • _ •• • 1 1 0.25 0.15 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Casson viscosity (mPa.s) 0.05 u.ut 0.035 0.03 0.025 0.02 0.015 0.01 0.005 A Mag#4 • • • • • • • - • • • • 1 1 1 1 • • • • • • • 1 1 1 1 1 1 1.3 1.4 1.5 1.6 1.7 1.8 0.5 0.7 0.9 1.1 1.3 1.5 Casson viscosity (mPa.s) Casson viscosity (mPa.s) Figure 9.2 The relationship between density differential and Casson viscosity 00 CO 184 which is obtained in a graduated volumetric cylinder by measuring the mud-hne falling rate under static conditions, is often used to characterize the dense medium stabihty. With hindered settling, which is characterized by the formation of distinct zones in suspension, the mud-line falling rate provides only information about the supernatant-suspension interface, and ignores the other three zones. Thus, settling rate is not necessarily interrelated with the bulk medium properties. In addition, medium stability in a DMC is also subjected to the effect of dynamic operating conditions. Under higher centrifugal acceleration (higher inlet pressure), or higher cyclone overflow to underflow flowrate ratio, the same magnetite suspension may experience stronger classification. It is obvious that the settling rate determined in a volumetric cylinder cannot reflect these characteristics. As a result, a loosely defined correlation between the settling rate and the yield stress has been reported (Klein et al, 1990) in Figure 9.3. 9.2.2 The effect of medium rheology on DMC performance As revealed in Figures 6.4 and 6.5 (Chapter 6), the Ep values deteriorate with increasing medium density and with decreasing magnetite particle size. This becomes more significant for finer feed particles especially over the high medium density range. The increasing Ep value (Figure 6.4) is apparently caused by the change of the medium rheological properties. The DMC separation efficiency is mainly determined by the behaviour of the near-density material in the feed. According to Equation 9.3 Z) g ^ i-m^ ^ the movement driving force on these particles is very low due to the low density 185 0.8 1.6 2.4 Settling rate x 10 '^ 4 (m/s) Figure 9.3 The relationship between settling rate and yield stress (after B. Klein et al, 1990) 186 difference (6-pn,); they are more easily misplaced. Therefore, this discussion on the effect of medium rheology on DMC performance focuses on the behaviour of the near-density fractions. According to Equation 9.1, the significance of the Casson yield stress or Casson viscosity in influencing the particle movement and DMC separation is determined not only by the relative values of the two parameters, but also by the near-density feed particle size, d, and its moving velocity relative to the surrounding dense medium, u. Taking Mag#2 dense medium as an example, the value of the Casson yield stress is 78 times as high as that of the Casson viscosity at medium density of 1.45 g/cm^ (Figures 7.8 and 7.9), while the shear rate, ku/d, for the 0.5 mm near-density particles is below 8.7 (see Table 8.1). The second term in the denominator of Equation 9.1 is 9 times as large as the first term. Thus, the fluid drag on these near-density fine particles is mainly determined by the Casson yield stress as represented by the second term of the denominator, while the effect of the Casson viscosity as represented by the first term is insignificant. The dense medium separation of fines is therefore strongly affected by the medium yield stress. To verify this, the Ep values in Figure 6.5 (Chapter 6) are correlated separately with the corresponding Casson viscosity and Casson yield stress data. While the correlation between Ep value and Casson viscosity is poor (Figure 9.4), the close correlation between Ep value and Casson yield stress is evident (Figure 9.5). Due to the existence of yield stress, part of the fine near-density material may be "locked" in the medium and short-circuited to the products. Napier-Munn (1980) specu-lated that this effect will lead to the establishment of a horizontal plateau region on the 0.08 0.07 0.06 a> a 0.05 Q. HI 0.04 0.03 0.02 0.01 1 Mag#1 -A A A • o* o A • o 1 A A A A A • . • « o 1 ) 7 1.8 1.9 2 2.1 2.2 2.; Casson viscosity (mPas) 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Mag#2 -A , A A A % • -• 0 ooo 1 1 A A A A • • . A ^ o ° 0 " • o • 0 o 1 1 1 A ^ A • A A ^ • • • •o^° 1 1 1 0.07 0.06 0.05 0.04 0.03 0.02 • • • • • • • 1 1 IVIag#4 Feed size 0 4x2 mm • 1x0.71 mm ^ 0.5x0.355mm • • • • • • • • • 1 1 1 1 1 1 1 1 1.35 1.45 1.55 1.65 1.75 Casson viscosity (mPas) 0.5 0.7 0.9 1.1 1.3 1.5 Casson viscosity (mPas) Figure 9.4 The relationship between Ep value and Casson viscosity 00 188 • ^ * 0 3 CO 1 \ . o 1 o \ ' E ^ E ?: >< o o o \ o 1 \Q --~ 00 vw m "a-n CM T— to o in d ^ o CO d o T— o u> C\J o CM O in o ^ o m o o a. F ^ to T3 0) s? 0] a. F !^  >--a a. F !8 0) IS • a 0} >->, o c CD O i t 0 c o 13 I _ CO Q . <D V) c o m CO 0} CO T3 0) c o CO CO CO O H— o ts a> * : CD o x: 1-in c» 3 C7) LL CO 1 ^ o o d d 8 in 5 CO o o o d d d CM o d o d an|BA dg 189 partition curves, centred around the medium density. Such a by-passing phenomenon was indeed observed in our tests. As shown in Figure 5.19, the by-passing is affected by the feed particle size and the cyclone overflow-to-underflow flowrate ratio (0/U flowrate ratio). It is intensified when the 0/U ratio was decreased below 0.5 and when finer tracers were used (0.5x0.355 mm). To test the reproducibility of the by-passing phenomenon, the experiments in the by-passing region were repeated several times and, as Figure 5.19 reveals, the data in this region were very reproducible. Some detailed information shown in the figure is in disagreement with Napier-Munn's initial speculation. Instead of a plateau, the partition curves show a sharp dip at the lower near-density range. In addition, the by-passing occurred at lower near-density range instead of centring around the medium density as claimed by Napier-Munn (1980). The cutpoint shift is also affected by the medium rheological properties. As discussed in Chapter 6, while the medium rheology influences the cutpoint shift of coarse feed particles (>2 mm) indirectly through changing medium stability, it affects the cutpoint shift of fine feed particles (below 0.5 mm) directly through exerting inward radial fluid drag on these particles. As a result, two opposite trends are expected in response to changes in medium rheology. Since both the medium stability (Figure 9.1) and fluid drag on fine particles are mainly determined by the Casson yield stress, the cutpoint shift should be more closely related to the yield stress, As shown in Figure 9.6, the coarse feed particles (4x2 mm) are not sensitive to the effect of fluid drag; their cutpoint shift is more directly related to medium stability. Thus, increasing the Casson yield stress decreased the cutpoint shift due to the improved 0.25 r 0.2 0.15 o CO ^-* c g 0.1 O 0.05 feed size 0.15 0.05 ^0.05 feed size .5x.355mm Mag#2 J I I I I I v.uo 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 --' r\ ..£ ^V V) feed size \ 1x.71mm Mag#4 0.05 0.1 0.15 0.2 0.25 Yield stress (mPa) 0 0.1 0.2 0.3 0.4 0.5 0.6 Yield stress (mPa) 0 1 2 3 4 5 6 7 8 Yield stress (mPa) Figure 9.6 Effect of Casson yield stress on outpoint shift (D o 191 medium stability. This result is similar to that between cutpoint shift and apparent viscosity earlier reported by Davies and Napier-Munn (1987). The initial increase in the cutpoint shift for intermediate and coarse feed particles in Figure 9.6 is due to the fact that low Casson yield stress values in this range (up to Xp in Figure 9.1) are not sufficient to prevent the classification of the magnetite suspensions. Increasing medium density resulted in a higher density differential (Figure 9.1), and consequently a higher cutpoint shift. The fine feed particles (0.5x0.355 mm), on the other hand, are more sensitive to the influence of medium rheology. Raising the Casson yield stress, which increases the fluid drag, caused a continuous increase in cutpoint shift. In comparison, the cutpoint shift did not show any clear correlation with the Casson viscosity (see Figure 9.7). The results discussed above prove that the dense medium separation of fine particles is closely interrelated with the medium yield stress even in a dynamic DMC separation process. In interpreting and modelling the dense medium separation, the influence of the yield stress must be taken into account. 9.2.3 DMC separation using bimodal magnetite dense medium It is well known that at any given solid content, the bimodal suspensions with compositions of 25% to 40% fines of the total solid content yield a minimum apparent viscosity (Parkinson etai, 1970; Chong etal, 1971; Ferrini etal, 1984), Figure 9.8. Due to the instrumental difficulty in rheological measurement of fast-settling bimodal magnetite suspensions at low concentrations, only demonstration tests were conducted on quartz-heavy liquid suspensions. The results are given in Figure 9.9. 0.25 0.2 0.15 £ "o t 0.1 0.05 • 4.0x2.0mm o 1.0x.71mm A .5x.355mm Mag#1 1 o o •o o o o ° o 0.15 0.1 0.05 1.7 1.8 1.9 2 2.1 2.2 Casson viscosity (mPa.s) 0.05 Mag#2 ^ A A 4 ^ ' ' ' AA 0 8 -^  ° ^ o "" o o o o o o o O oO _l I I I I I 0.03 0.02 0.01 0.01 1.4 1.5 1.6 1.7 Casson viscosity (mPa.s) -0.02 0.5 0.7 0.9 1.1 1.3 1.5 Casson viscosity (mPa.s) Figure 9.7 The relationship between cutpoint shift and Casson viscosity ^3 193 diO 24 ^.m^ CO d 9-20 2> a> o M 16 > •i^ c <D 2 12 Q. Q. < 8 — — — — Coal-water slurry 72% wt. \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /O \ /^ \ / \ / I I I 1 20 40 60 Percent of fine (%) 80 100 Figure 9.8 (a) Apparent viscosity of bimodal coal-water slurry (after F. Ferrini et ai, 1984) 2.6 2.2 CO o o •^1.8 1 0) 1.4 1.0 25 50 Percent of fines (%) polymethylmethacrylate bimodal suspension in Nujol / ^ ^ \ \ ^ X y ^ / A -^ / pf - « / / "* 1 6 10 40 f •1 1 I B I 75 100 Figure 9.8 (b) Relative viscosity of b imodal poly spheres suspens ion in Nujol (after C. Parkinson et al , 1970) 20 40 60 Percent of fine (%) 80 194 4.7 o X « 4.3 CO a^ J 59 8 3.9 OT • > 4 - ; C cd a 3.5 < Bimodai quartz suspension Geometric mean size - coarse size: 53.2 micron - fine size: 6.9 micron -3 \ • z ' 1 1 y ° 1 1 100 Figure 9.9 Tlie rheoiogical properties of bimodai suspensions 0.08 0.07 0.06 0.05 Mag#4 and Mag#6 bimodai magnetite dense medium at 1,55 g/cm ^  20 40 60 Percent of Fine {%) 80 100 Figure 9.10 Separation efficiency as affected by the proportion of fines in the bimodai dense medium 195 The unique rheological properties of bimodal suspensions may have a great potential for application in dense medium separation. The bimodal magnetite dense medium composed of a coarse and a fine narrow size fractions may reduce the adverse effect of medium rheology and improve separation efficiency. A preliminary investigation was conducted on our DMC loop to examine the DMC separation behaviour using the bimodal magnetite dense medium. The results are presented in this section. For a bimodal suspension to substantially manifest its unique rheological properties, at least a fivefold to sevenfold difference between the large and small size components is required (McGeary, 1961; Barnes et al, 1989). In this test, Mag#4 and Mag#6 were used as the fine and coarse size fractions, respectively. Their size ratio was about 8.1 (Table 4.1). According to the results in Chapter 6 (Figures 6.4 and 6.5), the effect of medium rheology on DMC performance becomes significant only at high medium densities. The beneficial effect of using a bimodal dense medium can thus be best demonstrated over the high medium density range. Accordingly, the bimodal medium densities in the present tests were fixed at approximately 1.55 g/cm^. At the constant medium density of 1.55 g/cm^ as seen from Figure 9.10, the Ep values, in response to the change in the percentage of fine in the medium, followed the same trend as that in Figures 9.8 and 9.9. A significant improvement in separation efficiency was achieved by using the bimodal dense medium, especially for the fine feed particles (0.5x0.355 mm). The minimum Ep value for the 0.5x0.355 mm feed particles with bimodal dense medium was about 0.035, while the Ep values at the same medium density with monomodal Mag#6 and Mag#4 dense media (0% and 100% of fine, respectively) were 0.065 and 0.075, respectively. The optimum separation efficiency was 196 achieved at around 25% of fine magnetite, which corresponds to the optimum bimodal composition (Figures 9.8 and 9.9). The stability of the bimodal dense medium, on the other hand, was not directly related to the medium rheology. As revealed in Figure 9.11 (a), with increasing percentage of the fines, the density differential decreased continuously and the medium become more stabilized, even though the medium apparent viscosity (or yield stress; for the relationship between apparent viscosity and yield stress, see Equations 7.6 and 7.7) decreased. It is speculated that the density differential is mainly controlled by the classification of the coarse magnetite fraction in the medium, while the fine magnetite suspension serves as the medium for the coarse magnetite fraction. Increasing the percentage of fines in the medium inhibited the classification of the coarse particles, and the intensity of classification was further weakened by the simultaneous decrease in coarse magnetite content. These were reflected by the decreasing underflow medium density curve in Figure 9.11 (b). The close resemblance of the V-shaped curves in Figures 9.8 to 9.10 indicates a close relationship between the separation efficiency and the bimodal medium rheology. It is concluded that at medium densities above 1.5.g/cm ,^ the separation efficiency is mainly determined by the rheology of the dense medium. The variation in stability of bimodal suspensions at this high medium density does not exert a significant effect on DMC separation efficiency. The cutpoint shift, on the other hand, is more closely related to the medium stability. Both cutpoint shift and density differential exhibited similar trends in response to the increasing fine magnetite content (Figures 9.11 (a) and 9.12). As discussed in 197 20 40 60 Percent of Fine (%) 100 Figure 9.11 (a) Effect of fine magnetite content on bimodal dense medium stability 1.2> Bimodal dense medium at 1.55 g/cm"" overflow 20 40 60 Percent of Fine (%) 80 100 Figure 9.11 (b) Effect of fine magnetite content on overflow and underflow medium densities 198 Chapter 5, the cutpoint shift is a function of both medium stability (through density gradient) and medium rheology (through fluid drag), as seen from Equation 5.18. At 100% fine magnetite content, the density differential (or gradient) is close to zero (Figure 9.11); the influence of the medium stability can be ignored. In this case, the cutpoint shift can entirely be attributed to the inward radial fluid drag. As shown in Figure 9.12, the fluid drag is significant only with fine feed particles (0.5x0.355 mm); it resulted in a cutpoint shift of 0.06 g/cm^. However, the effect of fluid drag on the coarse feed particles (4x2 mm) was not significant, and their cutpoint shift was virtually zero. As the fine magnetite content decreases, the increasing density differential comes into play causing an additional cutpoint shift, which adds up to the one induced by the fluid drag. According to Equation 5.18, the cutpoint shift induced by the density gradient is independent of feed particle size. So, the additional cutpoint is equally added up to the cutpoint shift of all feed size fractions, and a group of parallel cutpoint shift curves can be observed. It was expected that, as the content of fine magnetite changes, the fluid drag and its induced cutpoint shift should also change. Apparently, the variation in cutpoint shift induced by the change in inward radial fluid drag is not significant enough to be detected in Figure 9.12. 199 0.5 0.4 -0.3 0.2 c o a O 0.1 -0.1 Bimodal dense medium at 1.55 g/cm ~ ^ ^ ^ ^ ^ ^ ^ ^ ^ 5 _ ^ ^ _ _ ^ ^ — • Feed size • .5x.355mm o 1x.71mm A 4x2mm 3 1 1 1 1 20 40 60 Percent of Fine (%) 80 100 Figure 9.12 Effect of fine magnetite content in the bimodal suspension on outpoint shift 200 9.3 Discussion 9.3.1 The influence of medium theology on DMC performance The fact that medium stability, as measured by the density differential, and DMC performance, as determined by the Ep value and cutpoint shift, are both closely interrelated with the medium yield stress, indicates that the yield stress has a significant effect on DMC separation. Although the two rheological parameters, yield stress and viscosity, reinforce each other in Equations 9.1 and 9.2 in influencing the particle movement, their contributions may differ significantly. The underlying rheological parameter that dominates is determined by the relative values of the two terms in the denominators of Equations 9.1 and 9.2. The above result seems to suggest that the effective velocities of these particles relative to the medium, u, are very low. When this is coupled with a much higher x^  value than r|c (Figures 7.8 and 7.9), the first term in the denominator of Equation 9.1 becomes much smaller than the second one. The Re^,, and consequently the Cp, for these particles are mainly determined by the medium yield stress. Thus, a close relationship between the separation of fine particles and medium yield stress should be observed. The results in Figures 9.4 to 9.7 may be taken as an experimental proof for this assumption. This is especially true in the dense medium separation of fines (<0.5 mm) using micronized-magnetite (Mag#4). In this case, the value of the Casson yield stress is 350 to 2400 times higher than that of the Casson viscosity in the medium density range of 1.3 to 1.6 g/cm^ (Figures 7.8 and 7.9). Obviously, the yield stress not only characterizes the rigidity of the stagnant magnetite suspension before fluid movement is achieved (Whitmore, 1958), it also 201 determines the fluid drag on the particles in the process of relative movement and consequently influences the dense medium separation. With even finer feed particles (<0.3 mm), the separation efficiency will be determined to an even larger extent by the yield stress. In the empirical relationship proposed by Napier-Munn (1990) to describe the influence of medium rheology on DMC separation, the Ep value was related to the medium apparent viscosity by: where (]) is a function of apparent viscosity, ^=f{^^, cyclone geometry). Since the apparent viscosity for magnetite dense medium is expressed by Equation 7.6, correlating the separ-ation efficiency with apparent viscosity is equivalent to correlating it with both Casson yield stress and Casson viscosity. When the first term in Equation 7.6 is much greater than the second one. Equation 7.6 can be reduced to T l « - - 9.7 '" D Thus, the apparent viscosity in Equation 9.4 may be replaced by the yield stress under the conditions specified above and the separation efficiency is a function of the Casson yield stress. The close correlation between cyclone performance and yield stress shown in this study, as well as the close correlation between the performance of classifying cyclone and yield stress as observed by Horsley and Allen (1987), seem to confirm the above rheological analyses. With stable dense medium, the zero cutpoint shift with coarse feed particles (4x2 mm) in Figure 9.12 suggests that the fluid drag on the coarse feed particles is negligible. 202 the particle Reynolds number is close to the turbulent flow regime where the drag coefficient is nearly independent of Reynolds number. This is also confirmed in Figure 9.4 by the insignificant increase in Ep value for the 4x2 mm feed particles. In dense medium separation of large feed particles using coarse magnetite dense medium, the high velocities, u, of the large feed particles, coupled with the low yield stress value, XQ, of the coarse magnetite medium may substantially reduce the value of the term, T^d/ku, in Equation 9.1. As a result, the influence of the yield stress could be ignored. This might be the case in the early investigation by Whitmore (Whitmore, 1958) on dense medium bath separation of coarse coal (19 to 114 mm). He reported that the yield stress did not have a significant effect on the separation efficiency, which was found to be a function of medium plastic viscosity. Based on this result, Whitmore (1958) proposed an empirical model for dense medium bath separation: Ep= ^"^pi 9.8 d where Ep is a function of medium plastic viscosity, r|p,. Apparently, this model may not be employed in dense medium separation of fine particles, which entails the use of finer magnetite (Klima et al, 1990; Kempnich et al, 1993). In addition, the Reynolds number of coarse feed particles may be located in the turbulent flow regime. The fluid drag coefficient becomes constant, and the dense medium separation is completely independent of medium rheology. The use of the C^-Re^ relationship to interpret the effect of medium rheology on DMC separation presents a simplified version of a very complicated process. The falling ball experiments in non-Newtonian fluids were conducted in stagnant fluids (Valentik and 203 Whitmore, 1965). The hydrodynamic conditions in a dynamic process such as in a DMC are very different. The medium itself, not just the treated particles, is in motion. Some experiments indicate that a particle settles faster in fluids under dynamic conditions than under stagnant ones as a consequence of the rheological response of the fluid changing under dynamic conditions (Briscoe et al, 1993). The beneficial effect of vibrating the medium on the separation efficiency of a dense medium bath has been reported by Krasnov et al. (1977). In addition, the feed particles in actual dense medium separation process may interact with each other analogously to hindered settlings. 9.3.2 The characteristic shear rate in a DMC With a non-Newtonian system, the rheological properties vary with shear rate. The knowledge of the shear rate prevailing in the system (or the characteristic shear rate) becomes essential in relating the apparent viscosity to cyclone performance. The characteristic shear rate is also needed to estimate the particle Reynolds number in non-Newtonian fluids (Equations 9.1 and 9.2). Furthermore, as discussed in Chapter 7, the rheology of magnetite suspensions is best described by the Casson yield stress and Casson viscosity due to the marked non-linearity of the flow curves at low shear rate region (<100 s'). Over the high shear rate region (>100 s"'), however, the flow curves clearly show linearity and are best described by the Bingham equation. Thus selecting the Bingham viscosity and Bingham yield stress to describe the rheology of the magnetite suspension is also justifiable provided that the characteristic shear rate in the DMC is in the high shear rate region (>1(X) s"'). In order to measure the shear rate in a DMC, Lilge et al. (1957) followed Kelsall 204 (1953) and measured the tangential velocity distribution of the magnetite dense medium along the radial direction of the cyclone. From the tangential velocity distribution, they derived the tangential velocity gradients (or vortex flow shear rate) and concluded that the tangential velocity distribution profile of dense medium in a cyclone was similar to that of water (Kelsall, 1953) at a lower magnitude. The data of shear rate profile were then correlated with the shear stress/shear rate measurements obtained by Govier et al. (1957) to calculate the apparent viscosities of a variety of media at different points in the cyclone. This information was then used to interpret the results of the separation test work. According to the measurements of Kelsall (1953) and Lilge et al. (1957), the shear rates of vortex flow vary from minimum values at the cyclone wall, to a maximum at a point near the centre of the cyclone. The principal separating zone of the cyclone is normally in the annular area between the cyclone wall and vortex finder within which the shear rate, as measured by Collins et al. (1957) on two 10" DSM and Vorsyl dense medium cyclones, is around 50 s''. Thus, they employed the shear rate value of 50 s"' for apparent viscosity determination. Since the vortex flow shear rate is a function of cyclone diameter, inlet pressure, and medium composition, it may vary from one system to another. As a result, a different shear rate of 200 s"' has been arrived at by Graham and Lamb (1983). In a dense medium cyclone, however, there exist two types of shears: 1) the vortex flow shear rate due to the relative movement among different fluid layers and, 2) the shear rate due to the particle-to-fluid relative movement. From the empirical equation: v,r"=K (Bradley, 1965), and the vortex flow shear rate is expressed by Equation 3.4 205 (Chapter 3): D =±1 = -J^ 9.9 " dr r^^n while the shear rate due to the particle-to-fluid relative movement is defined as: D = ^ 9.10 " d Thus, the question posed here is: which shear rate is more fundamentally linked to density separation and should be used as the characteristic shear rate? The density separation process takes place in the radial direction of the cyclone with light feed particles moving inward to the axis of the cyclone, and heavy particle moving outward to the cyclone wall. Since the vortex flow shear rate occurs in the tangential direction of the cyclone, the vector of the corresponding shear stress acting on the particles is also in the tangential direction, which is perpendicular to the particle separation movement. As indicated by Napier-Munn (1990): "the shear of the medium in a direction perpendicular to the (radial) motion of the coal particle does not necessarily represent the sole component of the viscosity term in the equation of motion of the particle". This is apparently true. As a matter of fact, the density separation process is more closely related to the shear rate due to the particle-to-fluid relative movement. It generates shear stress acting on particles in the radial direction against the particle movements, both toward the cyclone wall, and toward the cyclone axis. The implication of such an argument is that in the rheological measurement of a non-Newtonian dense medium, where selection of the characteristic shear rate range is 206 important, the characteristic shear rate, as estimated using the equation D=ku/d, may differ significantly from that estimated from the vortex flow (Kelsall, 1952; Lilge et al, 1957; Bradley, 1965; Collins et al, 1983). The particles of various sizes and densities in the same cyclone, according to equation D=ku/d, should generate different shear rates. The characteristic shear rate varies depending on the size and density of the particles being processed. The shear rate range, as estimated by the vortex flow, reflects the shearing state of the medium itself, and is independent of the size and density of the feed particles. The fluid Reynolds number for the flow of the dense medium can be in the turbulent flow regime, while the particle Reynolds number may remain in laminar flow regime, or vice versa. 207 9.4 Summary The influence of the non-Newtonian rheological parameters on DMC performance can be interpreted via the general relationship: According to this relationship, the dense medium separation is affected by both the Casson viscosity and the Casson yield stress. The DMC performance in the separation of fine particles and the medium stability are mainly determined by the Casson yield stress. As confirmed by the results of this investigation, the medium stabihty, as characterized by the density differential in a DMC, is closely interrelated with the Casson yield stress; it decreases exponentially with increasing Casson yield stress. The results also show that the Ep value increases continuously with the Casson yield stress, and the increase is especially significant for finer feed particles (<0.5 mm). A close correlation between Ep value and Casson yield stress is observed. On the other hand, the relationship between Ep value and Casson viscosity can not be clearly defined. The cutpoint shift for fine feed particles (<0.5 mm) is directly affected by the inward radial fluid drag. Increasing the Casson yield stress of the medium, which is associated with a higher fluid drag on feed particles, results in a greater cutpoint shift. The cutpoint shift for coarse feed particles (<2.0 mm), on the other hand, is more sensitive to the influence of medium stability. In this case, increasing the Casson yield stress improves the medium stability and reduces the cutpoint shift. In the DMC separation of fine particles using bimodal magnetite dense medium, the separation efficiency is more closely related to the medium rheology. The minimum 208 Ep value is obtained when the proportion of the fine magnetite is around 25%, corresponding to the optimum rheological composition for bimodal suspensions. On the other hand, the cutpoint shift is more closely related to the medium stability. Increasing the proportion of the fine magnetite in the medium improves the medium stability, resulting in a continuous decrease in cutpoint shift. 209 10 CONCLUSIONS The DMC performance is jointly determined by the cyclone operating conditions, the medium properties, and the feed particle size. (1) The O/U flowrate ratio is the fundamental operating parameter directly related to the DMC performance, while the cyclone geometric dimensions influence the DMC performance indirectly through, or partially through the O/U flowrate ratio. At any given feed medium density, density differential increases with the O/U flowrate ratio, while the Ep value decreases with increasing O/U flowrate ratio and levels off at O/U flowrate ratio above 4.0. The cutpoint shift increases linearly with the O/U flowrate ratio on a semi-log plot; the slope value of the linear relationship is higher with less stable dense medium. It is recommended that the O/U flowrate ratio be controlled in the range of 2±0.5 achieved with a combination of smallest possible vortex finder and spigot diameters. Based on the equilibrium orbital hypothesis by taking into account the medium density gradient and inward medium radial flow, the following equation is derived to interpret the phenomena of cutpoint shift: where the first term represents the influence of medium stability and the second term 210 reflects the influence of medium rheology. According to this equation, decreasing the feed particle size, raising the cyclone throughput (or inlet pressure), lowering the medium stability, or increasing the radii of the loci of zero-vertical velocity (which can be achieved by increasing the 0/U flowrate ratio) will result in an increased cutpoint shift. (2) Extensive rheological measurements reveal that magnetite suspensions exhibit non-Newtonian yield-thinning properties. The slight dilatancy for the diluted coarse magnetite suspensions at high shear rate is believed to be attributed to the conversion of the medium flowing state from laminar flow to turbulent flow. In general, the flow curves are best described by the Casson equation: T^/2=tf+(Ti^-D)»/2 10.2 The Casson yield stress and Casson viscosity are two independent parameters jointly determining the rheology of magnetite suspensions. The Casson yield stress is the principal rheological parameter and responds to the changing medium properties in a well defined pattern, while the Casson viscosity can be treated as constant for coarse (commercial) and intermediate magnetite suspensions, or can be ignored with very fine magnetite suspensions. The strong influence of magnetite particle size distribution and particle shape on yield stress can be described by a single parameter termed relative hydrodynamic volume factor. For a given magnetite sample, its relative hydrodynamic volume factor is basically independent of the suspension solid content. The relative hydrodynamic volume factor reflects the relative amount of immobile liquid attached to the magnetite particle surfaces and, therefore, is a function of the specific surface area of the magnetite sample. The 211 relative hydrodynamic volume factor has implications in rheological modelling and characterization and in medium composition optimization. The Casson yield stress is not sensitive to the effect of temperature. The effect of temperature on Casson viscosity is relatively stronger; the value of the Casson viscosity and its magnitude of variation are similar to the viscosity of water. (3) The general form of Reynolds number applicable to any fluid types is: Re^=udph^ 10.3 The particle Reynolds numbers in the Bingham plastic fluids and in the magnetite suspensions are Re = ^"P 10.4 and Re^^ d}^ 10.5 respectively. The shear rate induced by particle-to-fluid relative movement is expressed as: D=— 10.6 d This is a fundamental equation in bridging two separate theories, rheology and hydrodynamics. It has a far-reaching implication in the hydrodynamic theory of particle movement in non-Newtonian fluids. The shear rate constant, k, varies as a function of the particle Reynolds number with the asymptotic minimum and maximum of zero and two, 212 respectively. For practical purposes, the k value can be set at one. The general relationship between the fluid drag and the non-Newtonian rheological parameters can be expressed as: C ^ = A — ^ ^ ) 10.7 for Bingham plastic fluids, or for Casson yield-thinning fluids. The yield stress not only determines the threshold drag on particles before particle-to-fluid relative movement is achieved. More importantly, it also determines the viscous drag during the particle-to-fluid relative movement. The particle terminal velocities in the Casson yield-thinning and the Bingham plastic fluids in the laminar flow regime can be expressed respectively as: 2 \ 9TI: and ^_8{b-p)d' V 10.10 Thus, the Stokes' equation is a special form of above equation when the plastic yield stress is equal to zero. At any given density difference between particle and medium (SQ-p), the minimum particle size, dg, capable of overcoming the threshold drag in a Bingham plastic or yield thinning fluid is: 213 d„=- i? !L_ 10.11 where XQ is the real yield stress. (4) The influence of the non-Newtonian rheological parameters on DMC separation efficiency can be interpreted via the general relationship expressed by Equation 10.8. According to this relationship, the dense medium separation is affected by both Casson viscosity and Casson yield stress. Due to a much greater value of the Casson yield stress than that of the Casson viscosity, the DMC separation of fine particles is mainly determined by the Casson yield stress. Very close correlation between the DMC performance and the Casson yield stress is obtained. It is found that with increasing yield stress, the density differential decreases exponentially, while the Ep value increases. This increase is especially significant for finer feed particles (<0.5 mm). On the other hand, the relationships between the separation efficiency and the Casson viscosity, and between the medium stability and the Casson viscosity cannot be clearly defined. (5) The medium rheology and medium stability exert opposite influences on DMC performance. As a result, opposite trends can be observed depending on which of the two medium properties is the dominant affecting factor. With fine magnetite, the effect of medium rheology plays a major role, while the influence of medium stability is insignificant. Thus, the separation efficiency improves when the medium density is decreased or when the centrifugal acceleration is increased. 214 With coarse magnetite, however, the effect of medium stability becomes more important, while the influence of medium rheology is minimal. Consequently, an increase in medium density and a decrease in centrifugal acceleration results in a better separation efficiency. The influence of the medium properties on DMC performance is also a function of feed particle size. The separation of coarse feed particles (>2.0 mm) is more sensitive to the influence of medium stability than to the influence of medium rheology. As a result, decreasing the magnetite particle size in a proper range improve the separation efficiency on the coarse feed particles due to the improved medium stability. On the other hand, the separation of fine feed particles (<0.5 mm) is more strongly affected by the medium rheology than by medium stability. A decrease in the magnetite particle may deteriorate the separation efficiency of the fine feed particles due to an elevated medium viscosity. At low medium densities (<1.5 g/cm^), the best separation efficiency is achieved by using magnetite with intermediate particle size distributions (d63 2=15-20 fim). This allows a low medium viscosity to be achieved without substantially decreasing the medium stability. At high medium densities (>1.5 g/cm^), the effect of medium rheology becomes dominant, while the effect of medium stability is less significant. In this case, it is better to use coarser magnetite to improve medium rheological properties. In the separation of fine particles, high inlet pressures may need to be employed to improve the separation efficiency. In this case, medium stability becomes important. Fine magnetite (Mag#4) has to be used to produce a stable dense medium. The medium stability and rheology are determined by the magnetite particle size distribution, solids content and inlet pressure; an appropriate control of these variables is 215 very important in achieving a balanced stability and rheological properties of the dense medium. The optimum magnetite particle size distribution in one type of DMC systems could be an inferior one in another depending on the cyclone operating conditions, medium density and feed particle size being processed. The magnetite particle size distribution should be tailored to each particular DMC system. (6) The influences of medium rheology and medium stability on the cutpoint shift can be interpreted through Equation 10.1. The cutpoint shift for fine feed particles (<0.5 mm) is directly affected by the medium rheology in the form of inward radial fluid drag. Increasing the medium Casson yield stress, which is associated with a greater fluid drag, results in a higher cutpoint shift. The cutpoint shift for coarse feed particles (<2.0 mm), on the other hand, is more sensitive to the influence of medium stability. Increasing the Casson yield stress improves the medium stability, reduces the density gradient in Equation 10.1, and decreases the cutpoint shift. (7) In the DMC separation of fine particles using bimodal magnetite dense medium, the separation efficiency is closely related to the medium rheology. Thus, the minimum Ep value is obtained when the proportion of the fine magnetite is around 25%, corresponding to the optimum rheological composition for bimodal suspensions. On the other hand, the cutpoint shift is more closely related to the medium stability; increasing the proportion of the fine magnetite in the medium improves the medium stability, resulting in a continuous decrease in cutpoint shift. 216 11 RECOMMENDATION FOR FUTURE WORK This thesis serves as a summary of the investigation carried out in the last few years. A large amount of work remains to be continued. It can be categorized into the following areas: DMC separation tests, DMC modelling, dense medium rheology, and particle movement in non-Newtonian fluids. 1. DMC separation tests The influences of the following important factors on DMC performance remain to be tested: inlet pressure, cyclone diameter, and clay contamination. Having been examined separately by various researchers, the effects of these factors on DMC performance have not been studied in the context of their inter-relations with other factors. Based on the investigation results in Chapters 5 and 6, the general pattern of the effect of the above factors can be predicted. Obviously, with any specific dense medium, increasing the inlet pressure or reducing the cyclone diameter will result in an initial improvement in DMC performance. Further increasing the inlet pressure or reducing the cyclone diameter will cause an excessive medium classification; the DMC performance will drop. However, such a statement is not enough in the actual application where concrete data may be required in the mill design to select the optimum cyclone diameter and inlet pressure for a specific type of dense medium. Similarly, for clay contamination, DMC separation tests are needed to determine. 217 under different cyclone operating conditions, the maximum level of clay contamination allowable in the medium. Such data will be used in the plant operation to control the medium cleaning circuit. Very fine magnetite, e.g. micro-mag, were shown to work very well at low medium densities. Since these suspensions are very stable, a better separation efficiency should be achieved at higher inlet pressures. This needs to be clarified in additional tests in which the joint effects of magnetite particle size distribution and inlet pressure on separation efficiency should be tested. This investigation has led to the conclusion that the DMC performance is predominantly determined by the medium yield stress. Further DMC separation tests at high medium densities such as those used in the diamond and iron ore separation are recommended. With high medium densities, the influence of yield stress will be more clearly manifested. 2, DMC modelling The two most basic performance models for DMC are separation efficiency model and cutpoint shift model. A literature review indicates that the DMC models developed by various researchers are mostly empirical. In this investigation, a theoretical model for cutpoint shift has been derived in Chapter 5, while the separation efficiency model remains to be developed. Since the DMC separation efficiency of fine particles is mainly determined by medium rheology, it is recommended that the separation efficiency model be developed through the general relationship between the fluid drag coefficient and non-Newtonian Reynolds number given by Equations 8.6 and 8.12. 218 3. Dense medium rheology The dense medium rheology is mainly determined by the medium composition. The major composition variables include solid particle size distribution, solid content, clay contamination and chemical additives. The influences of the last two variables on medium rheology remain to be studied. Another important rheological issue for solid suspensions is concerned with the existence of real yield stress. As indicated in this thesis, the conventional instrumentation and flow curve modelling can only give an apparent yield stress. A special procedure or instrument may have to be developed to measure the real yield stress of unstable solid suspensions. 4. Particle movement in non-Newtonian fluids A theoretical framework for particle movement in non-Newtonian fluids has been developed in Chapter 8. The theory needs to be experimentally verified. The recommended future testwork will be composed of two parts: the settling of spherical particles in non-Newtonian fluids and the rheological characterization of the non-Newtonian fluids. The data acquired from the testwork will be employed to verify the equations derived in Chapter 8. 219 12 REFERENCES Agar, G.E., and Herbst, J.A., 1966, "The Effect of Fluid Viscosity on Cyclone Classification", Trans. AIME, July, 1966, pp. 145-149. Ansley, R.W. and Smith, T.N. 1965, "Motion of Spherical Particles in A Bingham Plastic", AIChE. J., Vol.13, No.6, pp.1193-1196. Apian, F.F., and Spedden, H.R., 1964, "Viscosity Control in Heavy-Media Suspensions", in Proc. 7th Int. Mineral Processing Congr., New York, pp. 103-113. 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