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Synthetic fibre fractionation in hydrocyclones Ho, Sheau Ling 2001

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S Y N T H E T I C F IBRE F R A C T I O N A T I O N I N H Y D R O C Y C L O N E S By Sheau Ling H o B.Sc. (Applied Mathematics) Feng Chia University MA.Sc. (Operations Research) New York Polytechnic University A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F C H E M I C A L A N D B I O L O G I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A June 2001 © Sheau Ling Ho, 2001 In presenting this thesis in partial fulfillment 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. Sheau Ling Ho Department of Chemical and Biological Engineering The University of British Columbia 2216 Main Mall Vancouver, Canada V6T 1Z4 Date: ii ABSTRACT Literature on fibre fractionation was reviewed. Some equations of motion for spheres and cylinders moving through a fluid in a centrifugal field were solved. These solutions indicated that long, coarse fibres with low specific surface tended to move faster in a radial direction than did short, fine fibres with high specific surface. A model for a swollen particle was developed based on the inclusion of measurable values for specific surface and volume. For swollen particles it was noted that long, coarse fibres having low values of specific surface and high values of specific volume/specific surface ratio tended to move faster than short, fine fibres with high specific surface and low specific volume. In a given time particles in a hydrocyclone will move a certain distance towards the hydrocyclone wall. In the wall region there is a flow directed towards the rejects tip opening. Thus long, coarse fibres of low specific surface and high specific volume/specific surface ratio are more likely to be entrained in this reject bound flow and be rejected than their opposite counterparts. Calculation of anticipated fibre diameter based Reynolds numbers in a hydrocyclone indicated that they could be high enough that available drag coefficient formulations could be invalid. Equations for calculating separation efficiency for fibres in a hydrocyclone were derived. These allow estimates of how effective a hydrocyclone could be in concentrating coarse (short) fibres in the rejects stream and fine (long) fibres in the accepts. Experimental work, done in fractionating nylon fibre mixtures of known coarseness and fibre length, showed that the nylon fibres were similar in behaviour to wood pulp fibres in that there was a tendency for short, coarse fibres to be rejected. The hydrocyclone used tended to reject short fibres. Other types of hydrocyclones tend to reject long fibres. Fibre fractionation in terms of coarseness and fibre length was affected by the feed flowrate to the hydrocyclone and by consistency. As flowrate increased, maxima (minima) were observed in the differences between rejects and accepts coarseness (fibre length). The lower the consistency the greater the difference between rejects and accepts coarseness and fibre length. Separation efficiencies, in addition to being affected by flowrate and consistency, were also affected by fibre coarseness and by fibre length. Mass reject ratios were measured. These were dependent on feed flowrate, consistency, reject tip opening diameter, coarseness and fibre length. Ill Computational Fluid Dynamics (CFD) models of the flow inside the hydrocyclones used in the experimental work, were utilized in predicting profiles of axial, radial and tangential velocities and pressure. While the predicted profiles seemed to be reasonable, they did not suggest any obvious reasons for the maxima observed when the difference between rejects and accepts coarseness was plotted against feed flowrate. iv T A B L E OF C O N T E N T S Abstract ii List of Tables vi List of Figures vii Nomenclature xv Acknowledgements xviii 1. Introduction 1 1.1 Fibre Fractionation 7 1.1.1 Why Fractionate? 7 1.2 Objectives 9 2. Literature Review on Fibre Fractionation in Hydrocyclones 11 3. Theoretical Analysis 52 3.1 Principles of Hydrocyclone Operation 53 3.2 Equations of Motion in a Centrifugal Field 55 3.2.1 Spherical Particles 58 3.2.1.1 For an Ursudlen, Spherical Particle 58 3.2.1.2 A Water Swollen, Spherical Particle 67 3.2.2 For an Ideal, Cylindrical Fibre Model 71 3.2.2.1 Urswollen Ideal Cylindrical Fibre Model 71 3.2.2.2 Swollen Ideal Cylindrical Fibre Model 80 3.3 Reynolds Number of a Fibre Moving inside a Hydrocyclone 91 3.4 Separation Efficiency on Mass Basis (SEm) 94 4. Experimental Materials and Methods 109 4.1 Hydrocyclone Test Equipment 109 4.2 Hydrocyclone Used U l 4.3 Hydrocyclone Measurements 112 4.4 Synthetic (Nylon) Fibres 114 4.5 Fibre Mixtures, Consistencies and Reject Tip Openings Used 119 4.6 Fibre Property Measurements 120 4.7 Experimental Reproducibility 123 V 5. Experimental Results and Discussion 124 5.1 Synthetic Fibres (Nylon) Fractionation 124 5.1.1 Coarseness 125 5.1.2 Fibre Length 150 5.1.3 Mass Reject Ratio 163 6. Computational Fluid Dynamics 176 6.1 Introduction 176 6.1.1 The Mathematical Model 177 6.1.1.1 Turbulence Model '. 177 6.1.1.2 Boundary Conditions (B.G) and Assumptions 179 6.1.1.3 Air Core '.. 180 6.1.2 Computational Code 181 6.1.2.1 The Particle Separation Efficiency 183 6.1.2.1.1 Particle Trajectory 183 6.2 Computational Results 184 6.2.1 The Velocity and Pressure Profiles 184 7. Conclusions 197 7.1 Theory. 197 7.2 Nylon Fibre Fractionation 198 7.3 Computational Fluid rj)ynarnics 201 8. Recommendations for Future Work 202 Bibliography. 204 Appendix A 215 Summary of Literature Review on Fibre Fraaionation in Hydrocyclones Appendix B 223 Density Measurements Appendix C • 224 Microphotographs of Nylon Fibres Appendix D 227 Consistency Measurement Appendix E 228 Hydrocyclone Operations vi LIST O F T A B L E S Table 2-1 .- 31 Paavilainen's hydrocyclone fibre fractionations data. Table 2-2 40 Demuner's hydrocyclone fibre fractionations data Table 2-3 43 Kure et al.'s hydrocyclone fibre fractionation data for a newsprint pulp. Table 2-4 44 Kure et aL's hydrocyclone fibre fractionation data for a super calendar magazine pulp. Table 3-2-1 82 Comparison of the calculated total surface area of a fibre cylinder with (A*) and without (A) the ends. Table 4-4-1 117 Properties of nylon fibres and fibre suspensions used in the experiments. Table 4-5-1 119 Characteristics of nylon fibres used in the experimental work, mixtures are characterized as percentages on a mass basis. Table 4-5-2 120 Consistencies of the feeds and the reject tip openings used in the experimental work. Table 4-6-1 122 Average densities of the nylon fibres observed from the experimental measurements. Table 4-6-2 - 122 Fibre thickness values of calculated from the coarseness definition and measured from the microphotographs. Table 4-7-1 123 Overall percentage errors of fibre fractionation experimental measurements. Table 6-2-1 184 Dimensions, feed flowrates (kg/s), and overflow/underflow ratio used in CFD, see Figure 4-2-1, page 111.. vii LIST OF FIGURES Figure 1-1 2 Illustration of the geometry and dimensional symbols used for the hydrocyclones used in this thesis. Figure 1-2 3 Diagram illustrating the main flow structures in a hydrocyclone. Figure 1-3 4 Arithmetic average fibre length of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. Redrawn from [85]. Figure 1-4 4 Coarseness values of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. Redrawn from [85]. Figure 1-5 5 Burst index values of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. Redrawn from [85]. Figure 1-6 5 Tear index values of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. Redrawn from [85]. Figure 2-1 24 Bauer McNett fractions for deinked ledger stock for feed, accepts and rejects. Figure 2-2 25 Bauer McNett fractions for recycled corrugated boxes for feed and rejects. Figure 2-3 45 Data of Kure et al. (1999) news print pulp. Figure 2-4 45 Data of Kure et al. (1999) SG A magazine pulp. Figure 3-1-1 54 (a) Axial velocity profile (b) Radial velocity profile (c) Tangential velocity profile of a hydrocyclone. Kelsall[59] Figure 3-2-1 59 Fraction factor (drag coefficients) vs. Reynolds numbers for particles of different sphericities. Brown at aL [21]. Figure 3-2-2 64 Relation between angular velocity (?) and radial position (r). Data from Hsieh [51], page 137, for a hydrocyclone. Figure 3-2-3 65 Radial velocity (V r ) vs. radial position (r) of spherical particles having the same volumes as nylon fibres having various fibre lengths and coarseness values. Figure 3-2-4 66 Radial position of a spherical particle as a function of time. Figure 3-2-5 67 Reynolds numbers (N )^ for the various particles described in Figure 3-2-3 as functions of radial position (r). Figure 3-2-6 68 Idealized wet sphere model. Df: diameter of dry sphere, D p : diameter of swollen sphere. Figure 3-2-7 71 Idealized cylindrical unswollen fibre model. Df: diameter of dry cylindrical fibre, L: fibre length. Figure 3-2-8 77 Vlll Fibre radial velocity (V r ) vs. radial position (r) in a hydrocyclone vising Cox's equation. (1 mm with 0.17 mg/m, 0.68 mg/m, and 3 mm with 0.17 mg/m, 0.68 mg/m) Figure 3-2-9 78 Fibre radial velocity (V r ) vs. radial position (r) in a hydrocyclone using Cox's equation. (1 mm with 0.17 mg/m, 0.51 mg/m, and 3 mm with 0.17 mg/m, 0.51 mg/m) Figure 3-2-10 80 Idealized cylindrical wet fibre model. Df: diameter of dry cylindrical fibre, D p : diameter of swollen cylindrical fibre, L: fibre length. Figure 3-2-11 86 Li et al.'s ideal cylindrical fibre. Figure 3-2-12 89 Fibre coarseness value vs. specific surface for wheat straw pulps and aspen pulps. Figure 3-2-13 89 Microphotographs of TMP fractionation. Data from Rehmat [85]. Figure 3-2-14 90 Microphotographs of nylon fibres. (1 mm, 0.68 mg/m) Figure 3-2-15 91 Relationships between specific surface and specific volume for refined chemical pulps. Data of [19,90,103] Figure 3-3-1 92 Calculated Reynolds number using Aidun's drag coefficient for a non-swollen nylon fibre of various coarseness values moving inside a hydrocyclone. Based on Hsieh's data [51]. Figure 3-3-2 93 Calculated Reynolds number using both Aidun's and Cox's drag coefficients for a non-swollen nylon fibre of various coarseness values and fibre lengths moving inside a hydrocyclone. Based on Hsieh's data [51]. Figure 3-3-3 94 Calculated Reynolds number using both Aidun's drag coefficient and Cox's drag coefficients for a swollen nylon fibre of various coarseness values and fibre lengths moving inside a hydrocyclone. Based on Hsieh's data [51]. Figure 4-1-1 . .Il l Apparatus for fibre fractionation. Figure 4-2-1 112 Dimensional symbols used for the Bauer 3" Centri Cleaner. Figure 4-4-1 116 Microphotographs of nylon fibres.. Figure 4-4-2 118 Illustration of typical fibre properties distributions from the fibre quality analyzer (FQA): Histograms measuring fibre length, fibre curl and kink indexes. Based on data of nylon fibres length = 1 mm, coarseness = 0.68 mg/m. Figure 5-1-1 125 Feed, accepts, and rejects coarseness value vs. feed flowrate at various feed consistencies for Feed A. Figure 5-1-2 126 Differences in coarseness values between the rejects and the accepts for Feed A at various consistencies. Figure 5-1-3 127 Feed, accepts, and rejects coarseness values vs. feed flowrate at various feed consistencies for FeedG Figure 5-1-4 128 ix Differences in coarseness values between the rejects and the accepts for Feed C at various consistencies. Figure 5-1-5 129 Feed, accepts, and rejects coarseness values vs. feed flowrate at various feed consistencies for feedD. Figure 5-1-6 130 Differences in coarseness values between the rejects and the accepts for Feed D at various consistencies. Figure 5-1-7 131 Feed, accepts, and rejects coarseness vs. feed flowrate at various feed consistencies of Feed B. Figure 5-1-8 133 Separation efficiency for coarse fibres in the rejects for Feed A at various consistencies. Figure 5-1-9 134 Corrected separation efficiency for coarse fibres in the rejects for Feed A at various consistencies. Figure 5-1-10 134 Centrifugal separation efficiency for coarse fibres in the rejects for Feed A at various consistencies. Figure 5-1-11 135 Separation efficiency for fine fibres in the accepts for Feed A at various consistencies. Figure 5-1-12 136 Corrected separation efficiency for fine fibres in the accepts for Feed A at various consistencies. Figure 5-1-13 136 Centrifugal separation efficiency for fine fibres in the accepts for Feed A at various consistencies. Figure 5-1-14 137 Combined separation efficiency of Feed A at various consistencies. Figure 5-1-15 138 Corrected combined separation efficiency for Feed A at various consistencies. Figure 5-1-16 138 Centrifugal combined separation efficiency for Feed A at various consistencies. Figure 5-1-17 139 Separation efficiency for coarse fibres in the rejects for Feed D at various consistencies. Figure 5-1-18 140 Centrifugal separation efficiency for coarse fibres in the rejects for Feed D at various consistencies. Figure 5-1-19 141 Separation efficiency for the fine fibres in the accepts for Feed D at various consistencies. Figure 5-1-20 142 Centrifugal separation efficiency for fine fibres in the accepts for Feed D at various consistencies. Figure 5-1-21 142 Combined separation efficiency for Feed D at various consistencies. Figure 5-1-22 143 Centrifugal combined separation efficiency for Feed D at various consistencies. Figure 5-1-23 144 Separation efficiency for coarser fibres in the rejects for Feed A, D, SI, S2 at 0.9% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-24 144 Separation efficiency for coarser fibres in the rejects for Feed A, D, S1, S2 at 0.5% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-25 145 Separation efficiency for coarser fibres in the rejects for Feed A, D, SI, S2 at 0.3% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-26 146 Centrifugal separation efficiency for coarser fibres in the rejects for Feed A, D at 0.9% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-27 146 Centrifugal separation efficiency for coarser fibres in the rejects for Feed A, D at 0.5% consistency, L = mean fibre length, C = mean coarseness. Figure 5-1-28 147 Centrifugal separation efficiency for coarser fibres in the rejects for Feed A, D at 0.3% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-29 147 Centrifugal separation efficiency for fine fibres in the accepts for Feed A, D at 0.9% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-30 148 Centrifugal separation efficiency for fine fibres in the accepts for Feed A, D at 0.5% consistency, L - number mean fibre length, C = number mean coarseness. Figure 5-1-31 148 Centrifugal separation efficiency for fine fibres in the accepts for Feed A, D at 0.3% consistency, L = number mean fibre length, C = number mean coarseness. Figure 5-1-32 151 Feed, accepts, and rejects arithmetic average fibre lengths vs. feed flowrate at various feed consistencies for Feed B. Figure 5-1-33 151 Differences in the arithmetic average fibre lengths between the rejects and the accepts for Feed B at various consistencies. Figure 5-1-34 152 Feed, accepts, and rejects average arithmetic fibre lengths vs. feed flowrate at various feed consistencies for Feed E. Figure 5-1-35 153 Differences in the average arithmetic fibre lengths between the rejects and the accepts for Feed E at various consistencies. Figure 5-1-36 154 Feed, accepts, and rejects fibre length vs. feed flowrate at various feed consistencies of Feed A. Figure 5-1-37 155 Separation efficiency for short fibres in the rejects for Feed B at various consistencies. Figure 5-1-38 156 Separation efficiency for long fibres in the accepts for Feed B at various consistencies. Figure 5-1-39 156 Centrifugal separation efficiency for short fibres in the rejects for Feed B at various consistencies. Figure 5-1-40 .... ......157 Combined separation efficiency for short fibres in the rejects for Feed B at various consistencies. Figure 5-1-41 158 Separation efficiency for the short fibres in the rejects for Feed E at various consistencies. Figure 5-1-42 v .. 158 Separation efficiency for long fibres in the accepts for Feed E at various consistencies. Figure 5-1-43 159 Centrifugal separation efficiency for short fibres in the rejects for Feed E at various consistencies. Figure 5-1-44 159 Combined separation efficiency for short fibres in the rejects for Feed E at various consistencies. xi Figure 5-1-45 160 Separation efficiency for short fibres in the rejects for Feed B, E, SI, and S3 at 0.5% consistencies, L = number mean fibre length, C = number mean coarseness. Figure 5-1-46 ., 161 Separation efficiency for short fibres in the rejects for Feed B, E, SI, and S3 at 0.3% consistencies, L = number mean fibre length, C = number mean coarseness. Figure 5-1-47 1 164 Mass reject ratio vs. feed flowrate at various consistencies of Feed A. Figure 5-1-48 165 Mass reject ratio vs. feed flowrate at various consistencies of Feed C Figure 5-1-49 .....165 Mass reject ratio vs. feed flowrate at various consistencies of Feed D. Figure 5-1-50 166 Mass reject ratio vs. feed flowrate at various consistencies of Feed B. Figure 5-1-51 166 Mass reject ratio vs. feed flowrate at various consistencies of Feed E. Figure 5-1-52 167 Mass reject ratio vs. feed flowrate at various consistencies of Feed SI. Figure 5-1-53 167 Mass reject ratio vs. feed flowrate at various consistencies of Feed S2. Figure 5-1-54 168 Mass reject ratio vs. feed flowrate at various consistencies of Feed S3. Figure 5-1-55 168 Mass reject ratio vs. feed flowrate at 0.9% consistency of Feed A, Q D, SI, S2. Figure 5-1-56 169 Mass reject ratio vs. feed flowrate at 0.5% consistency of Feed A, Q D, SI, S2. Figure 5-1-57 169 Mass reject ratio vs. feed flowrate at 0.3% consistency of Feed A, Q D, SI, S2. Figure 5-1-58 170 Mass reject ratio vs. feed flowrate at 0.5% consistencies of Feed B, E, SI and S3. Figure 5-1-59 171 Mass reject ratio vs. feed flowrate at 0.3% consistencies of Feed B, E, SI, S3. Figure 5-1-60 171 Mass reject ratio vs. feed flowrate at various consistencies of Feed S3 with Tip II. Figure 5-1-61 173 Mass reject ratio vs. rejects crowding factor of Feed SI, S2, S3. Figure 5-1-62 174 Mass accept ratio vs. rejects crowding factor of Feed SI, S2, S3. Figure 6-1-1 182 Diagram of a non-uniform FD (finite difference) grid with a 42x32 control volume (CV) grid, X: axial position, Y: radial poshioa Y scale is expanded (X/Y = 1/5) to give a clearer illustration of the grid pattern. Figure 6-1-2 182 Grid divisions for computations. Figure 6-2-1 188 Pressure contour plots of Bauer 3" Cleaner at various feed flowrates. Figure 6-2-2 189 Bauer 3" Cleaner: computed pressure profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Figure 6-2-3 190 Axial fluid velocity contour plots of Bauer 3" Cleaner at various feed flowrates. Figure 6-2-4 191 X l l Bauer 3" Cleaner: computed axial fluid velocity profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Figure 6-2-5 192 Radial fluid velocity contour plots of Bauer 3" Cleaner at various feed flowrates. Figure 6-2-6 193 Bauer 3" Cleaner: computed radial fluid velocity profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Figure 6-2-7 194 Tangential fluid velocity contour plots of Bauer 3" Cleaner at various feed flowrates. Figure 6-2-8 195 Bauer 3" Cleaner: computed tangential fluid velocity profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Figure 6-2-9 196 Vector plots of radial and axial fluid velocity patterns of Bauer 3" Cleaner at various feed flowrates. Figure El-1 229 Pressure drop vs. feed flowrate at various feed consistencies using Feed A, Q D, B, E, SI, S2, and S3 with two different sizes of the rejects tip opening. Figure E2-1 231 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies for Feed A. Figure E2-2 231 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies for Feed G Figure E2-3 232 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies for Feed D. Figure E2-4 232 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed B. Figure E2-5 233 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed E. Figure E2-6 233 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed SI. Figure E2-7 234 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed S2. Figure E2-8 234 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed S3, Tip I. Figure E2-9 235 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed S3, Tip II. Figure E3-1 237 Thickening ratio vs. feed flowrate at various consistencies for Feed A. Figure E3-2 238 Thickening ratio vs. feed flowrate at various consistencies for Feed G Figure E3-3 238 Thickening ratio vs. feed flowrate at various consistencies for Feed D. Figure E3-4 239 Thickening ratio vs. feed flowrate at various consistencies for Feed B. Figure E3-5 239 Thickening ratio vs. feed flowrate at various consistencies for Feed E. Figure E3-6 240 Thickening ratio vs. feed flowrate at various consistencies for Feed SI. Figure E3-7 240 Thickening ratio vs. feed flowrate at various consistencies for Feed S2. Xlll Figure E3-8 241 Thickening ratio vs. feed flowrate at various consistencies for Feed S3, with Tip I. Figure E3-9 241 Thickening ratio vs. feed flowrate at various consistencies for Feed S3, with Tip II. Figure E3-10 242 Thickening ratio vs. feed flowrate at 0.9% consistency of Feed SI, S2 (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-11 242 Thickening ratio vs. feed flowrate at 0.5% consistency of Feed SI, S2 (Tip I), L = mean fibre length, C = number mean coarseness. Figure E3-12 243 Thickening ratio vs. feed flowrate at 0.3% consistency of Feed SI, S2 (Tip I), L = number mean fibre length, C = mean coarseness. Figure E3-13 243 Thickening ratio vs. feed flowrate at 0.9% consistency of Feed A, C, D (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-14 244 Thickening ratio vs. feed flowrate at 0.5% consistency of Feed A, Q D (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-15 244 Thickening ratio vs. feed flowrate at 0.3% consistency of Feed A, Q D (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-16 245 Thickening ratio vs. feed flowrate at 0.5% consistency of Feed SI, S3 (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-17 245 Thickening ratio vs. feed flowrate at 0.3% consistency of Feed SI, S3 (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-18 246 Thickening ratio vs. feed flowrate at 0.5% consistency of Feed B, E (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-19 t 246 Thickening ratio vs. feed flowrate at 0.3% consistencies of Feed B, E (Tip I), L = number mean fibre length, C = number mean coarseness. Figure E3-20 247 Thickening ratio vs. feed flowrate at various consistencies of Feed S3, with Tip I and II. Figure E4-1 249 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed SI with Tip I. Figure E4-2 250 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed S2 with Tip I. Figure E4-3 250 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed S3 with Tip I. Figure E4-4 251 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed A. Figure E4-5 251 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed G Figure E4-6 252 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed D. Figure E4-7 252 Volumetric reject ratio vs. feed flowrate at 0.9% consistencies for Feed A, D, SI, S2, L = number mean fibre length, C = number mean coarseness. Figure E4-8 253 xiv Volumetric reject ratio vs. feed flowrate at 0.5% consistencies for Feed A, D, SI, S2, L = number mean fibre length, C = number mean coarseness. Figure E4-9 253 Volumetric reject ratio vs. feed flowrate at 0.3% consistencies for Feed A, D, SI, S2, L = number mean fibre length, C = number mean coarseness. Figure E4-10 254 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed B with Tip I. Figure E4-11 254 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed E with Tip I. Figure E4-12 255 Volumetric reject ratio vs. feed flowrate at 0.5% consistency for Feed B, SI, S3, L = number mean fibre length, C = number mean coarseness. Figure E4-13 255 Volumetric reject ratio vs. feed flowrate at 0.3% consistency for Feed B, SI, S3, L = number mean fibre length, C = number mean coarseness. Figure E4-14 256 Volumetric reject ratio vs. feed flowrate at various consistencies of Feed S3 with Tip II. Figure E4-15 256 Volumetric reject ratio vs. feed flowrate at 0 consistency with Tip I, and Tip II. N O M E N C L A T U R E a acceleration (m/ s2) A accepts flowrate (kg/min) Ap projected area of a particle (m2) AD apparent density factor BCTMP bleached chemithermomechanical pulp BKP hardwood kraft pulp C coarseness (mg/m) C A average accepts coarseness value Cl , Qi , Gel, Ce2, k constants Cc coarseness value of a coarse fibre Cb drag coefficient GnA average coarseness value of the rejects CmR average coarseness value of the accepts CF coarseness value of a fine fibre CPPA Canadian Pulp and Paper Association C R average rejects coarseness value CSF Canadian standard freeness CTMP chemithermomechanical pulp D largest diameter of the hydrocyclone (m) DI inlet diameter (m) D2 length of the vortex finder (m) D3 length of the cylindrical section (m) D4 overall length of the hydrocyclone (m) D5 vortex finder diameter (m) D6 underflow diameter (m) D f dry fibre diameter (m) Do dry fibre diameter (=Df) (m) D p particle diameter (m) fnCA number fraction of coarse fibre in the accepts fnFA number fraction of fine fibre in the accepts fnCF number fraction of coarse fibre in the feed fnFF number fraction of fine fibre in the feed fnCR number fraction of coarse fibre in the rejects fnFR number fraction of fine fibre in the rejects fnLA number fraction of long fibre in the accepts fnSA number fraction of short fibre in the accepts fnLF number fraction of long fibre in the feed fnSF number fraction of short fibre in the feed fnLR number fraction of long fibre in the rejects fnSR number fraction of short fibre in the rejects fmCA mass fraction of coarse fibre in the accepts fmFA mass fraction of fine fibre in the accepts fmCF mass fraction of coarse fibre in the feed fmFF mass fraction of fine fibre in the feed fmCR mass fraction of coarse fibre in the rejects fmFR mass fraction of fine fibre in the rejects fmLA mass fraction of long fibre in the accepts fmSA mass fraction of short fibre in the accepts xvi fmLF fmSF fmLR fmSR F F B F C F D F Q A H S S F L L A Lc L F L L LNfibres L R L S L S S F Min MNfibres Mov Mun M p M v n N NRe U V \ w p PAPRICAN AP r R RPM SCAN SEM SE m C/R SEmC/Rc orr SEmC/Rc tr SE m F/ A mass fraction of long fibre in the feed mass fraction of short fibre in the feed mass fraction of long fibre in the rejects mass fraction of short fibre in the rejects feed flowrate (kg/min) centrifugal force (kg m/ s2) buoyant force (kg m/s2) drag force (kg m/s2) fibre quality analyzer high specific surface fibre overall length of hydrocyclone (m) average accepts fibre length length of coarse fibre length of fine fibre length of long fibre total length of n fibres in the feed average rejects fibre length length of short fibre low specific surface fibre mass flowrate of feed (kg/s) total mass of n fibres in the feed mass flowrate of overflow (kg/s) mass flowrate of underflow (kg/s) particle mass (kg) virtual mass (kg) exponent on virtual mass density function crowding factor Reynolds number of a hydrocyclone, based on the feed inlet diameter, or Reynolds number of a suspended particle based on particle diameter axial velocity (m/ s) radial velocity (m/s) particle radial velocity (m/ s) tangential (swirl) velocity (m/ s) pressure (Pa) The Pulp and Paper Research Institute of Canada pressure drop (Pa) radial coordinate (m) rejects flowrate (kg/min) revolutions per minute Scandinavian pulp and paper testing standards scanned electron microphoto separation efficiency on mass basis of coarse fibres in the rejects corrected separation efficiency on mass basis of coarse fibres in the rejects centrifugal separation efficiency on mass basis of coarse fibres in the rejects , separation efficiency on mass basis of fine fibres in the accepts XVII SEmF/Aeon- corrected separation efficiency on mass basis of fine fibres in the accepts SEmF/Actr centrifugal separation efficiency on mass basis of fine fibres in the accepts SEmS/R • separation efficiency on mass basis of short fibres in the rejects S E m L / A separation efficiency on mass basis of long fibres in the accepts SEmC/RF/A combined separation efficiency on mass basis of coarse fibres in the rejects and fine fibre in the accepts SEmS/RL/A combined separation efficiency on mass basis of short fibres in the rejects and long fibre in the accepts t time (sec) TMP thermomechanical pulp WRV water retention value x axial coordinate (m) XA accepts consistency XF feed consistency XR rejects consistency y radial distance measured from centre-line (m) yw radial distance measured from the wall (m) Greek Symbols a specific volume (mVkg) a t the turbulence dissipation e turbulent dissipation rate (m2/s3) 8e destruction rate of turbulent dissipation rate (m2/s4) K turbulent kinetic energy (m2/s2) XR length scale (m) v kinematics viscosity (m2/s) vt turbulent kinematics viscosity (m2/s) u, viscosity of water (cp) 6 cone angle of the hydrocyclone p water density (kg/m3) pf dry fibre density (kg/m3) pp apparent density of a particle (kg/m3) pfw density of dry fibre wall (kg/m3) a specific surface (mVkg) oK, o e constants CO angular velocity (m/ s) \|/ sphericity XVIU A C K N O W L E D G M E N T S I would like to express my sincere gratitude to those who have assisted me in completing this work. I would like to thank my supervisor, Dr. Richard Branion for his guidance, and advice throughout the course of this project. The efforts of my committee members, Professors Richard Kerekes, Ken Pinder and Steven Rogak are gratefully acknowledged. Sincere thanks to Dr. Elida Sevilla for her significant assistance. I also gratefully acknowledge the invaluable discussions with Dr. Norman Johnson from Los Alamos National Laboratory. This work would not have been possible without the financial support of the Network of Centers of Excellence for Mechanical Pulps, PAPRICAN, and Forest Renewal British Columbia (via a grant to Professor Martha Salcudean) Special thanks are also due to Professor Peter Englezos and members of his Papermaking Chemistry Group for equipment support. Many special thanks to Peter Pang, a good friend and fellow Ph.D. student, for the lively exchange of ideas and words of encouragement. The help of the technical, staff and students of the Pulp and Paper Centre at the University of British Columbia was highly essential to the successful completion of the present study. In particular, I would like to thank Brian MacMillan, Tim Paterson, Peter Taylor, Lisa Brandly, Brenda Dutka, Rita Penco, Judy Mackenzie, Tezim Rehmat and John Senger, for being there to help with any problems that I encountered while studying there. Also the wonderful technical and administrative staff at the Chemical and Biological Engmeering Department: Horace Lam, Helsa Leong, and Lori Tanaka. Thanks are also due to following people for all of their assistance from Paprican: Phil Allen, John Hoffman, and Norm Roberts. Last, most of all, I would like to pay special tribute to my family for their unconditional love and unselfish support. I owe a great deal to my parents Ting-Hsio Ho and Yu-Tsai Hsieh who have been behind me throughout this long journey. I can't thank them enough for their patience, thoughtf ulness and understanding during all this period. Chapter 1. INTRODUCTION 1 Chapter 1 INTRODUCTION Hydrocyclones, also known as centrifugal cleaners, have been used extensively in the pulp and paper industry to remove undesirable particles and unsatisfactorily pulped fibres from pulp suspensions. In addition, they can be used to classify pulp suspensions into fractions having different fibre properties (e.g. specific surface, fibre length, coarseness, fibre wall thickness, etc) [5, 6, 28,45, 46, 49, 53, 56, 63, 65, 81, 84, 85, 92,108,110]. In general, a hydrocyclone consists of a cylindrical section followed by a conical section (see Figure 1-la); however, some hydrocyclones (such as the cleaner most used in this study) consist only of a conical section (see Figure 1-lb). There are two exits: an upper exit which is called an overflow (or accepts) exit and a bottom exit which can also be called an underflow (or rejects) exit. For a forward cleaner, the overflow is called the accepts flow while the underflow exit is called the rejects flow. The opposite terminology is the case for a reverse cleaner. For a through-flow cleaner, both exits are from the apex, for an example see Figure 4-3-1, Section 4.3, Chapter 4. Forward cleaners are used for the rejection of particles which have a density greater than that of the suspending water. These particles move to the wall and are dragged down towards the reject tip by the downward flow at the wall. Reverse cleaners are used for the rejection of particles which have a lower density than water. These particles move towards the center and go out through the vortex finder. In the through flow cleaners, which operate as reverse cleaners, the low density contaminants move inwards toward the central reject oudet, the rest of the flow comes out through the outer, peripheral, accept outlet [7] which is an annular Chapter 1. INTRODUCTION 2 ring around the reject outlet. This type of cleaner consumes less energy than the other two types. OVERFLOW (MOV) OVERFLOW UNDERFLOW UNDERFLOW (MUN) (a) W Figure 1-1 Illustration of the geometry and dimensional symbols used of the hydrocyclones in this thesis. In the customary operation of a hydrocyclone, see Figure 1-2, the suspension to be treated is injected tangentially through a feed opening(s), which is (are) located near the top of the device. Under the influence of the centrifugal force field developed by the swirling fluid, movement of the solid particles relative to the liquid is created. This relative motion between a particle and the suspending fluid depends on (1) the size, shape (specific surface), density, and concentration of particles, (II) the density and viscosity of the suspending fluid. Therefore, in a suspension containing particles with different densities, some of the particles move towards the outer wall of the hydrocyclone and others to the core. Due to the classification of particles that Chapter 1. INTRODUCTION 3 can occur within a hydrocyclone, the compositions of the accepts and rejects can be different from each other and from the feed. Thus hydrocyclones can be used to separate pulp suspensions into fractions having different properties. Figure 1-2 Diagram illustrating the main flow structures in a hydrocyclone. It has been observed that hydrocyclones can separate pulp slurries into rejects and accepts streams that have different values of specific surface, fibre length distribution, fibre coarseness, etc., and that papers made from such fractions have different strengths. Earlier works from our research group [84] have found that hydrocyclones could separate fibres into rejects and accepts streams that had different values of mean coarseness and fibre length. In addition, the handsheets, which were made from these streams, showed different strengths. Chapter 1. INTRODUCTION 4 1 2 Arithmetic Av. Length (mm) 1.0 0.8 0.6 0.4 0.2 O The Rejects V The Accepts 40 50 TMP 0.65% consistency 60 70 80 Feed Flowrate (kg/min) 90 100 Figure 1-3 Arithmetic average fibre length of the accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. indicates the initial feed fibre length. Redrawn from [85]. 0 6 0 Coarseness (mg/m) 0.55 0.50 0.45 A 0.40 A 0.35 A 0.30 0.25 40 50 O The Rejects V The Accepts TMP 0.65% consisstency 60 70 80 Feed Flowrate (kg/min) 90 100 Figure 1-4 Coarseness values of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. indicates the initial feed coarseness. Redrawn from [85]. Chapter 1. INTRODUCTION 5 2.5 Burst Index (kPa m /g) 2.0 1.5 1.0 0.5 0.0 40 50 O The Rejects V The Accepts TMP 0.65% consistency 60 70 80 Feed Flowrate (kg/min) 90 100 Figure 1-5 Burst index values of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. -<— indicates the initial feed burst index. Redrawn from [85]. 1 Q 0Tear Index (mNt m2/g) 8.0 A 6.0 4.0 2.0 0.0 40 — i — 50 O The Rejects V The Accepts — i — 70 TMP 0.65% consistency 60 80 Feed Flowrate (kg/min) 90 100 Figure 1-6 Tear index values of the feed, accepts and rejects for TMP fractionation in the same hydrocyclone used in this study. •<— indicates the initial feed tear index. Redrawn from [85]. Chapter 1. INTRODUCTION 6 Figures 1-3 —1-6 demonstrate these differences. In spite of some inconsistencies, when comparing the various properties with the initial feed properties, probably due to poor sampling or to fines shifting from rejects to accepts, the rejects fibre lengths were always less than the accepts fibre lengths, with one exception the rejects coarseness was greater than the accepts coarseness. Similarly the accepts burst and tear indices were always great than the rejects. Many other tests have shown similar results [85]. In our group's work on wood pulp fibres the presence of fibre fines was a confusing factor. Sometimes the fines reported to the accepts stream and sometimes to the rejects stream. This resulted in some difficult to explain freeness results [85]. To eliminate such confusion the experimental work done in this thesis used synthetic (nylon) fibres of known fibre length and coarseness. There was no fines component to these fibre suspensions. Moreover in the wood pulp fractionation experiments fibre length distribution differences were noted among the feed, accepts and rejects streams. Some theoretical support for such length based fractionation is discussed in Chapter 3, section 3.2.2. However, it is also possible that some fibre property other than length governs fibre fractionation in hydrocyclones, e.g. fibre coarseness. If coarse fibres tended to be longer or shorter than fine fibres then length differences would be observed between the rejects and accepts streams but these differences might only result from a relationship between fibre length and fibre coarseness: coarseness differences being the root cause of the fractionation. To resolve this problem we chose to use simple two or three component rnixtures of the nylon fibres mentioned above. Chapter 1. INTRODUCTION 7 1.1 Fibre Fractionation It has been revealed, via a theoretical analysis and by experiment that a hydrocyclone can separate pulp suspensions into fractions having different specific surfaces [45, 46, 84]. Since it has been shown that specific surface is inversely related to fibre coarseness [45, 46, 84], a hydrocyclone can separate pulp suspensions into fractions having different values of fibre coarseness. In addition, it has been found experimentally that the fibre length distributions of the accepts and rejects streams coming out of a hydrocyclone are different [45,46, 84]. Fractionation of a stream of pulp into fractions containing pulp fibres of different characteristics is desirable for a variety of reasons. 1.1.1 Why Fractionate? The principal and historical reason for using hydrocyclones to fractionate pulp is to fractionate out (remove) particles of dirt, plastic contaminants, shives and lint [9, 34, 36, 37,109, 111]. This is done in such a way that rejection of the undesirables is maximized while as little useful fibre as possible is rejected. Bliss [5, 6, 7, 8] has summarized other reasons for fractionation of fibres using hydrocyclones. Fie listed the following as goals to be sought in fibre fractionation. Production of stronger sheets at the same freeness, producing pulps that gave equivalent sheet strengths at higher freeness, reduction in the amount of fines, reduction of the refining power requirements, removal of undesirable pulp components, separation of chemical pulps from mechanical pulps and separation of hardwood fibres from softwood fibres. After a successful fractionation the longer and stronger fibre fraction might be refined to produce sheets having higher strengths than the unfractionated pulp but at the same freeness as the unfractionated pulp. If this were possible then the upgraded pulp (refined fraction) could be Chapter 1. INTRODUCTION 8 used to replace another, more expensive furnish component without an overall adverse effect on drainage. If the sheet strength of paper made from the unfractionated pulp was adequate, fractionation, and subsequent refining could result in one of the exit streams from the hydrocyclone having equal sheet strength potential but at higher freeness and with a lower fines content. Thus on machine drainage might be improved as could be first pass retention. Bliss [5] presented four fractionation schemes. In the first of these the accepts from the fractionation stage would be sent to papermachine A while the rejects went to paperaiachine B. For this scheme to be useful two, or more, papermachines, which could produce marketable products from each of the accepts and rejects streams from the fractionation, would have to be available In the second scheme the accepts and rejects from the hydrocyclone would go to different layers of a multilayer sheet (e.g. liner and filler). For this scheme to be useful ply bonding between the different layers would have to be acceptable. Vollmer [105], for example, has noted that the bending stiffness of multiply board could be improved by using coarse fibres in the interior layer and fine fibres in the surface layers. In the third scheme one fraction would be discarded. This is the conventional way of using hydrocyclones to get rid of dirt, shives etc. Another example in this category is the discarding of extremely fine fines, ink and clay in recycle pulp production. In the fourth scheme, the accepts stream would go directly to the papermachine and the rejects stream then upgraded by refining. The upgraded rejects would then be mixed with the accepts and be sent to the papenmchine. Such a scheme was contemplated as a way of reducing refining energy requirements because only the fraction of the pulp that needed refining would be refined. Chapter 1. INTRCDUCTION 9 Kure et al. [63] have pointed out that thick-walled fibres in the surface of a sheet of paper cause printing problems. Thus their separation for upgrading by refining would be desirable. Such separation could be accomplished by hydrocyclones. Another reason for fibre fractionation is to characterize pulps for prediction of their paper making potential. To do this a laboratory device, such as a hydrocyclone or system of hydrocyclones, would be required that could separate fibres into fractions having different properties, such as specific surface, coarseness, fibre length distribution, etc., that could be used in characterizing pulps [109, 111] as, for example a Bauer McNett Fibre Classifier does. A detailed discussion on the desirability and usefulness of fibre fractionation can be found in the literature review in the following chapter. 1.2 Objectives The goal of this work was to contribute to the understanding of the behaviour of fibres in a hydrocyclone. This was attempted via a theoretical analysis of the fluid mechanics of particles, including fibres, that are subjected to centrifugal forces (see Chapter 3) and experimental measurements to support or refute the conclusions of the theoretical analysis (see Chapter 5). In particular we knew at the outset of this work that coarse fibres, fibres with thick walls and fibres with low specific surface tended to be rejected in passage through a hydrocyclone. See Chapter 2. Thus we wanted to see if consideration of the radial component of particle velocity in a centrifugal field would indicate why coarse fibres with low specific surface tended to be rejected in a hydrocyclone. Some earlier work by our research group focussed on the computational fluid dynamics (CFD) of flow in a hydrocyclone [66, 67, 68, 94]. Initially, for this thesis, it was planned to Chapter 1. INTRODUCTION 10 continue to work on CFD analysis of hydrocyclones. Later, such work was relegated to being a minor component of the thesis since another group at UBC [43] was doing the same sort of investigation, using a more sophisticated CFD model and we were skeptical about some of the results we were getting from our own CFD programs. However, the work of using our C F D program is extended here and some of these results are presented in Chapter 6. An attempt was made to qualitatively relate our CFD results to the results we obtained experimentally. Application of a CFD model to the calculation of fibre separation efficiencies, based on fibre trajectories in a hydrocyclone, requires analysis of a force balance on a wet fibre in a centrifugal field. Thus, one of our principal objectives was to develop a mathematical explanation for how fibre properties influence the radial velocity component of a fibre in a centrifugal field. The magnitude of that velocity is a major factor in determining whether or not a fibre will be accepted or rejected, in a hydrocyclone. We believe that our model of a wet fibre based on measurements of specific surface and volume is a unique feature of this work See Chapter 3. Finally to clarify the effects of fibre coarseness and fibre length on fibre fractionation in a hydrocyclone experiments using nylon fibres of known coarseness and fibre length were done. These were used to qualitatively confirm some of the proposed theories and to see if nylon fibre mixtures of known fibre length and coarseness fractionated in the same way as wood pulp fibres. See Chapter 5. To our knowledge no one else has used geometrically well defined, synthetic fibres in assessing fibre fractionation in hydrocyclones. In doing this part of the work some attention was given to developing equations to calculate separation efficiencies that could be used in reporting how successful a hydrocyclone would be in directing coarse (short) fibres to the rejects and fine (long) fibres to the accepts. See Chapter 3 for the derivation of the equations and Chapter 5 for their application. Chapter 2. LLTERA TURE RE VIE W 11 Chapter 2 L I T E R A T U R E R E V I E W There are many papers dealing with the ability of hydrocyclones to separate shives, dirt and other contaminants from pulp suspensions, however, this literature review is mainly focussed on separating pulp into streams, both of which might be useful in making paper, that have different fibre properties. Malhotra et al. [66,67, 68], Sevilla et al. [94,95] and He et al. [43] have published papers on the use of a CFD model for computing fluid velocity profiles and particle trajectories in a hydrocyclone. Literature on the topic of CFD for hydrocyclones is reviewed there. They found reasonable agreement between the CFD predicted values and those obtained from their own experiments or from the literature. The same programs they used [66, 67, 68, 94, 95], with some modifications, were used in this thesis. For a more detailed summary of these CFD models see Chapter 6. In order to show how the use of hydrocyclones for fibre fractionation developed, this literature review is presented in chronological order of the appearance of the various references [20]. A few other papers are included that do not deal with fibre fractionation but which provide information that is used in this thesis. An abridged rearrangement of this literature review on fibre fractionation arranged, for convenience, under subject headings, rather than chronologically, is provided in Appendix A. Aidun [1] investigated the free, gravitational settling of fibres. He did his experiments using mostly synthetic fibres, which had different specific gravities in various fluids. He Chapter2. LITERATURE REVIEW 12 proposed experimental relationships between drag coefficients and Reynolds number for fibres having a ratio of fibre length to diameter greater than 90. (See also Chapter 3) In a 1956 paper Boadway and Freeman [13] described a centrifugal pulp cleaner for removing shives. In that paper it was recognized that the ability of the cleaner to separate undesirables from the pulp depended on the size of the particles to be separated and on the dimensions of the hydrocyclone. McCuUoch [70] studied the effects of Vorjects (a type of hydrocyclone), primarily used for shive removal, on groundwood pulp quality. He applied several paper strength tests to handsheets made from the feed, accepts and rejects streams sampled at various rejects ratios. His results showed that the burst strength, breaking length and tear strength of handsheets were the greatest for the accepts stream, lower for the feed stream and much lower for the rejects stream Boadway [14] presented some theories of particle separation by a fluid vortex in a hydrocyclone. He emphasized the importance of understanding the mechanisms by which suspension classification could be achieved. It was observed that the smaller the hydrocyclone diameter the higher the removal efficiency for particles. He also pointed out that if the particles were assumed to be cylindrical rods, the separation efficiency varied with the diameter of the rods. Since fibre coarseness is related to fibre diameter, therefore, in theory, a hydrocyclone should be able to fractionate based on differences in fibre coarseness. In 1963 Boadway [15] described the use of hydrocyclones in separating coarse, stiff fibres and shives from groundwood. He believed that a hydrocyclone tended to fractionate fibres via a mechanism based on differences in their fibre diameters rather than on differences in their lengths. Microphotographs showed clearly that shives were preferentially rejected by a hydrocyclone and that the material in the rejects was coarser and less fibrillated than the material Chapter2. LITERATURE REVIEW 13 in the accepts or in the feed to the hydrocyclone. He noted that the rejects tended to be free of fines, possibly because the type of cleaner used involved the injection of elutriation water the result of which was that the fines would make several passes through the separation zone and thus have a greater probability of being accepted. One of the purposes of Boadway's investigation was to develop a fibre classifier based on the use of a series of hydrocyclones of progressively smaller diameters. The accepts from stage 1 would be the feed for stage 2 etc. When a single stage hydrocyclone was operated with the accepts being recycled continuously to the feed tank the level of coarse material appearing in the rejects decreased with time. The evaluation of coarseness was subjective based on the appearance of stock in the photomicrographs and on visual observations made on handsheets. Boadway also noted that smaller diameter hydrocyclones were capable of rejecting material that could not be rejected by larger diameter hydrocyclones. He worked at consistencies of the order of 0.1% to avoid inter-fibre interference as the fibres moved inside the hydrocyclone. In 1963, Pesch [83] discovered that summerwood fibres settled under the influence of gravity in water, nearly three times faster than springwood fibres. This observed difference in sedimentation rate led him to develop a process, which could separate southern pine pulp into springwood and summerwood fractions, using hydrocyclones. This fractionation could be used to improve paper qualities. He discovered that pulp from the accepts contained mainly springwood fibres and paper which was made from the accepts had higher tensile strength properties and density. The rejects contained mainly summerwood fibres and paper, which was made from the rejects, had increased bulk, porosity and tear. The most distinctive fractionation was obtained when the feed pulp was diluted to 0.1 —0.2% consistency. Chapter 2. LITERATURE REVIEW 14 Jones et al. [53] carried on further studies in this area of springwood-summerwood separation in 1966. Primary experiments were done on longleaf pine (Pinus pakstns) and slash pine (Pinus ccmbaea). Compared to other species, they observed that these species showed more effective separation of the ribbon-like springwood and the thick-walled summerwood than other species. The separation of the hydrocyclone was considered satisfactory if the accepts contained 70% springwood fibres and the rejects contained 70% summerwood fibres. The quality of paper made from combinations of the fractionated pulps showed little improvement when the contents of springwood or summerwood of a pulp were increased to over 70%. A single-stage fractionation process could result in 65 ~ 70% springwood fibres in the accepts and 65 ~ 70% summerwood fibres in the rejects. Many different centrifugal cleaners were tested; a Bauer 3 inch diameter Centri-Cleaner performed best in separating springwood fibres and summerwood fibres. They concluded that the smaller diameter cleaners were more efficient in separation. Several variables were investigated by these authors; consistency and temperature of the slurry, reject tip opening diameter, pressure drop across the cleaner, and the degree of mechanical damage done to the fibres prior to passage through the hydrocyclone. Their results showed that as the consistency of the feed pulp increased, within the range 0.05% ~0.25%, the separation efficiency decreased. Never-dried pulp separated better than re-slurried, machine-dried pulp. The accepts contained fibres that had a greater degree of refining than the rejects. They also indicated that there was better separation between beaten and unbeaten fibres than between springwood and summerwood fibres. Bleaching reduced separation efficiency. As the temperature increased, the mass amount of pulp from accepts decreased, the mass amount of springwood in the accepts increased, the mass amount of pulps from the rejects increased, but no significant changes were observed in the mass amount of summerwood leaving via the rejects. Chapter 2. LITERA TURE RE VIE W 15 Increasing the tip size increased the amount of pulp rejected and decreased the amount of pulp accepted. They noted that the rejects had higher freeness values than the accepts. Due to this observation and the knowledge, according the theory of El-Hosseiny and Yan [31], that freeness tends to vary inversely with specific surface this means that the low specific surface fibres tended to be rejected. Therefore, Jones et al. [53] implied that hydrocyclones could separate fibres based on differences in specific surface. Physical properties of handsheets were tested with different springwood contents to evaluate the influence of fibre composition. The optimum balance of strength properties appeared to be at a springwood content of 65 ~ 70%. Increasing the springwood content decreased sheet porosity and increased smoothness. Handsheets which were made from the accepts had higher burst, lower tear, and lower porosity than those made from the feed pulp or from the rejects. Handsheets which were made from the rejects had higher tear factors than those which were made from the feed pulp or from the accepts. The springwood-rich sheets had the highest print blackness and poorest print uniformity. The summerwood-rich sheets gave a more uniform print but print blackness was low. It was shown that the fines in the springwood-rich accepts contained a lot of macerated fiber debris which lowered the freeness values. But these fines contributed a positive effect on sheet strength and fibre bonding. Jones et al. [53] stated that a 50 : 50 ratio of accepts to rejects flow split produced the best separation. Stephens and Pearson [99] examined the effects of feed concentration, feed cleanliness (shive content), feed pressure, pressure drop, elutriation and reject rate on the separation efficiency of three sizes of hydrocyclones (ie 3-in. diameter, 4-in. diameter, and 12-in. diameter Bauer 623 Centri-Qeaners) using Eucalypt groundwood. Their results, using the 3-in. and 4-in. hydrocyclones, showed that at a fixed pressure condition, the separation efficiency decreased with increasing the pulp concentration, particularly in regard to the separation of shives. Chapter! LITERATURE REVIEW 16 Increased feed pressure and pressure drop were associated with increased levels of both reject rate and separation efficiency (reject rate was calculated as the amount of O.D. reject material divided by the O.D. solids in the input stream times 100). The smaller, 3-in. hydrocyclone performed more efficiently than the 4-in. unit for large shives separation. The wet and dry strengths of paper sheets which were made from the accepts had higher values than the corresponding values for sheets which were made from the feed and from the rejects using both the 3-in. and 4-in. hydrocyclones. They detected that highly fluctuating reject flows occurred when the input pressure was below 40 psi. Their experiments were all conducted between 40 to 60 psi. in Bauer 623 Centri-Geaners. Their results showed that the rejects consistency was higher than the feed consistency. The pressure drop was affected primarily by the feed flowrate; and the shive separation efficiency increased as the pressure drop decreased. Regardless of nozzle size, feed pressure, or pressure drop, the lower the concentration of the pulp the better the separation efficiency for all types of unsatisfactory material at a fixed reject rate. Besides, the separation efficiency improved for all unsatisfactory particles as the reject rate increased. Three reject orifice sizes were examined at a fixed feed concentration and flowrate. The largest nozzle produced the greatest reject rate. It consumed less power and provided the best separation of shives, specks and dirt. However, it also rejected an uneconomical amount of usable fibre. Their results indicated that paper sheets, which were made from the rejects, had very low values of breaking length and burst factor, but the tearing strength was appreciably high. Therefore, they speculated that fibre fractionation was based on fibre flexibility in a hydrocyclone. They concluded that the less flexible material had a higher probability of being rejected. Chapter2. LITERATURE REVIEW 17 Marton and Robie [69] investigated the sedimentation behavior of mechanical pulp suspensions (i.e. stone, and refiner groundwood). They measured the settling rates, fibre properties (i.e. fibre length, coarseness, and specific surfaces), and handsheet strengths of the fractions, which they got from a Bauer McNett classifier. Their research did not relate to fibre fractionation in hydrocyclones, but it did provide information on some common phenomena i.e. gravitationally driven fibre settling (sedimenting) and which has some things in common with how centrifugal force influences fibres moving in a hydrocyclone. They observed that fibre length strongly correlated with fibre coarseness. A multiple regression analysis was used to determine the correlation of each factor (length, coarseness, and specific surface area) with settling rate. Their results indicated that fibre coarseness was the most important variable affecting the settling rate, followed in order by specific surface area and fibre length. High values of the handsheet tear factor were associated with fibres having low settling rates. They believed that thin, flexible particles were more resistant to settling than thick and stiff particles. Cox [26] studied the motion of long slender solid bodies in a viscous fluid. Neglecting fluid inertia effects, he derived an equation describing the force per unit length acting on the solid body by the fluid as an asymptotic expansion in terms which included the ratio of the body's length to its cross-section. He obtained expressions for the drag on slender cylinders for cases in which the axis of the cylinder was and was not parallel to the direction of motion. See Chapter 3. Seifert and Long [93] evaluated different methods for fibre fractionation. The methods were compared on a cost-benefit basis and from a practical perspective. They noted that utilization of a conventional hydrocyclone (3-in diameter centrifugal cleaner) at a 25% reject rate, Chapter2. LITERATURE REVIEW 18 as a fractionator resulted in a concentration of long fibres in the accepts and of short fibres in the rejects. Hill et al. [44] studied the separation of shives in screens and hydrocyclones using an optical shive analyzer to provide the data. The slope of a plot of shive removal efficiency against rejects ratio gave the number of shives per kg of rejects divided by the number of shives per kg of feed. The higher the value was above one the better the rejection of shives. Two sizes of hydrocyclone were tested in this approach. For the smaller hydrocyclone, when the ratio of shives in the rejects to shives in the feed was plotted against shive length, the shive removal effectiveness decreased as shive length increased for both TMP and stone groundwood. In the case of the larger hydrocyclone, the ratio increased as shive length increased up to a maximum value and then decreased as shive length was further increased. Corson and Tait [24] used multiple regression analysis on some experimental data obtained in a Bauer 606-110-P, Centri-Cleaner which had a cyclone diameter of 6 inches. Six independent variables were varied; these included inlet pulp consistency, inlet pulp freeness (CSF), reject tip outlet diameter, the pressure drop across the cleaner, the inlet shive content of the pulp and a parameter (b) which characterized the fibre length distribution of the pulp entering the cleaner. The dependent variables considered were weight % rejection of fibre, volumetric ratio of reject flow to feed flow, accepts consistency, accepts freeness, accepts parameter b value, accepts shive content, rejects consistency, rejects parameter b value and rejects shive content. The test data were obtained using refiner mechanical pulps of Pinus radiata from which latency had been removed. The tests were done at 50°C. The fibre length distributions could be represented by a modified Rosin-Rammler equation [23]. Thus W = ae-bx •••(!) Chapter2. LITERATURE REVIEW 19 where W = fraction of fibres having length >x x = fibre length a, b = constants for a particular fibre sample The parameter b, which affects the fibre length distribution, was shown, for the accepts stream to be a function of the pressure drop across the hydrocyclone and the feed freeness of the pulp. Parameter b for the rejects stream depended upon the inlet consistency and the inlet fibre length distribution or upon the inlet consistency, reject tip diameter and inlet freeness, depending on whether or not the inlet fibre length distribution was included as an independent variable in the regression analysis. In any event passage through a hydrocyclone was shown to affect the fibre length distributions of the accepts and rejects streams. Accepts freeness values were lower than feed freeness values. Wood and Karnis [109] investigated how to get a lint-free newsprint sheet using a hydrocyclone. Lint is material of low specific surface and hence bonding potential. Knowing that a hydrocyclone could classify the fibres into fractions of different specific surface, they built a fractionation device (the Domtar K W Specific Surface Fractionator), which employed a hydrocyclone to separate fibres. This device could produce pulps having different values of specific surface via a cascading process. In addition, an inverse correlation between freeness and specific surface was noted. It was found that the rejects from hydrocyclones operating on TMP (Thermochemical Pulp) appeared to contain material with fibres, which were stiff, and of lower specific surface and which also showed essentially no surface fibrillation nor delamination. Their results were in agreement with the works of Jones et al. [53] and Stephens et al. [48, 89] who observed that the less flexible a fibre was the more likely it was to be rejected by a hydrocyclone. Chapter 2. LITERATURE REVIEW 20 Karnis and Wood [110] defined an index using the Domtar fractionator, which determined a pulp's linting propensity. Two operations to reduce the quantity of lint candidate fibre were also suggested: (1) increasing the specific energy used to produce the mechanical pulp, (2) passing through a hydrocyclone at a high reject rate plus a high consistency refining of the rejects. Wood and Karnis [110] carried on further study of the distribution of specific surface in paperrnaking pulps. They observed that the total amount of surface area wouldn't be changed as pulp passed through a hydrocyclone. Three fundamental pulp properties-specific surface, specific volume, and fibre length were studied in deteirnining how fibres separate in a hydrocyclone. Data were obtained by using the Domtar fractionator, which fractionation was described in Wood and Karnis [109]. Their results showed that for mechanical pulps, which were unbeaten, the rejects had increased coarseness and decreased specific volume, but the specific surface remained unchanged compared to the feed. For beaten chemical pulps (or mechanical pulps), the rejects had lower specific surfaces than the feed. The specific volumes of the rejects decreased slightly and the coarseness of the rejects showed no change relative to the feed. Therefore, they concluded that unbeaten fibres were separated on the basis of specific volume, and beaten fibres were separated on the basis of specific surface in a hydrocyclone Some other experiments were carried out on the effects of the two fibre properties: specific surface, and fibre length. The rejects and feed were passed through a Bauer McNett fibre classifier to measure any difference in fibre length between the rejects and feed. No significant difference was found in the average fibre length between the rejects and feed when the feed had consistencies of 0.052% and 0.313%. Consistency influenced the effectiveness of specific surface separation, consistencies higher than 0.15% gave a less efficient separation. Chapter2. LITERATURE REVIEW 21 They assumed that it was because of the fibre-fibre interactions. Their results also showed that the consistency only had a small effect on the fibre length differences. Wood and Karnis [110] also examined a bleached, beaten, softwood pulp to establish whether fractionation was based on fibre length differences or specific surface differences using both the Bauer McNett classifier and the Domtar Fractionator. From their experiments, they indicated that passage of a pulp suspension through a hydrocyclone had little effect on mean fibre length as expressed by Forgacs [32]. A plot of specific surface vs. fibre length showed that as the fibre length decreased, the specific surface barely increased. They also noted that the consistency over the range 0.05 ~ 0.30% did not affect the fibre length distribution in the rejects, but did affect the specific surface distributions from the Domtar fractionator. Larger tips yielded more selective separation as regards specific surface. Bliss [5, 6] investigated secondary fibre fractionation to improve strength/freeness characteristics in one fraction, and how to save refining energy or minimize the production of fines during refining by using a hydrocyclone (76 mm Black Clawson, 1-3-SR, Contra-Clone, reverse cleaner). He presented scanning electron microphotos (SEM) of TMP after fractionation in a hydrocyclone, which showed the very different characteristics of the accepts and rejects. The rejects were much coarser than the accepts in appearance. Also, the rejects had higher freeness than the accepts. Since freeness is related to specific surface, his results also agreed with Wood and Karnis [109] in that hydrocyclones separated fibres on the basis of fibre specific surface. He also stated that generally the rejects contained the less refined, longer, stiffer and lower specific surface area fibres, while the accepts contained most of the extremely fine, well refined, shorter fibres, and other material which was higher in fibre specific surface area. Chapter 2. LITERATURE REVIEW 22 After fractionation, the handsheets, which were made from the rejects were lower in burst index, breaking length, tear index and fold than those which were made from the accepts or the feed. After refining, the rejects were significantly higher in burst index, breaking length, and corrected fold, but lower in tear index than the feed at equal freeness. He also pointed out two disadvantages of hydrocyclones as fractionators; they consume energy, and they only operate well at low feed consistency. Four fractionation schematics were investigated by Bliss: • the separated fractions go to separate paper machines. • the separated fractions go to different layers of a multi-layer sheet. • one fraction is discarded (e.g. shive or dirt removal). • selective refining of a fraction to improve its papermaking character. Sending the fractions to separate paper machines, or to separate layers of a multilayer sheet seemed to be the most practical use for fractionated fibre streams. Shive and dirt removal in hydrocyclones is already widely practiced. Bliss [5] also studied the fractionation of deinked ledger stock by passing it through a 76 mm hydrocyclone. It was shown that the rejects contained heavy contaminants, stiff, whole, unrefined, low specific surface area fibres, and summerwood. The rejects had the highest consistency, and freeness. The accepts contained light contaminants, flexible, well refined, high specific surface area fibres, fines, and springwood. The accepts also had the lowest consistency, and freeness. After fractionation the rejects were refined and recombined with the accepts in proportion to the flow split in the hydrocyclone. A plot of freeness vs. specific refining energy showed no refining energy difference between the proportionately recombined pulp and the Chapter2. LITERATURE REVIEW 23 feed pulp, but paper, which was made from the recombined pulp, was enhanced in strength properties. According to his results, the rejects could be upgraded to become usable fibres. Some tests were done to evaluate the effects of changing the dimensions of a hydrocyclone on fibre fractionation. It was found that inlets substantially larger in area than those normally used for reverse cleaners resulted in significantly less fractionation. Substantially smaller inlets fractionated no better than the standard, but had lower capacities at equal pressure drops. Outlets smaller than those normally used for reverse cleaners reduced capacity but with no improvement in fractionation. A 3 level, 4 factor statistical experimental design was employed to assess the effects of flow split (i.e. the volumetric ratio of the accepts flowrate to the feed flowrate), the pulp split (i.e. the mass ratio of accepts flowrate to feed flowrate), pressure drop, accepts freeness and reject freeness, feed consistency and feed temperature on fibre fractionation. Regression equations were fitted to the data, neglecting those relationships that were not statistically significant. It was found that feed flowrate was dependent on both flow split and pressure drop. Accepts freeness was affected by flow split, pressure drop, feed consistency, and feed temperature; rejects freeness was affected by flow split, pressure drop, and the product of feed consistency and flow split. The pulp split was influenced by flow split, feed temperature, product of flow split and pressure, product of flow split and feed consistency, and product of pressure drop and feed consistency. Besides those parameters, the refined feed and the refined rejects freeness also significantly affected paper strength properties. The equations generated by Bliss' statistical model can be used to predict all parameter values at specified values for the operation of a hydrocyclone to achieve particular paper strength values. Figure 2-1 provides the Bauer McNett distributions for the feed, accepts and rejects streams in Bliss' [5] fractionation of deinked ledger stock Note that most of those fines still Chapter! LITERATURE REVIEW 24 remaining in the feed pulp stock after the deinking process, reported to the accepts. Figure 2-2 presents the Bauer McNett distributions for the feed and rejects streams. For this kind of pulp again it was clear that a separation occurred based on differences in freeness (specific surface). Burst and breaking length were greatest for sheets made from the accepts and lowest for sheets made from the rejects. Tear values were highest in the feed and lowest in the accepts but there wasn't much difference. Not much separation based on differences in fibre length was noted, although the rejects had less fines than the feed. 1 p 1 ll 1 — — -—— +14 -14+35 -35+65 -65+150 -150 l I Feed vzza Rejects 1888883 Accepts Data of Bliss 1983, Hydrocyclone: 76 mm Black Clawson 1-3-SR Contra Cone Reverse Cleaner Figure 2-1 Bauer McNett fractions for deinked ledger stock for feed, accepts and rejects. Underflow freeness could be used as a parameter for assessing fractionation. Given a constant value for flow split, as pressure drop increased the rejects freeness increased. At constant flow split and constant pressure drop the rejects freeness increased as feed consistency Chapter 2. LITERATURE REVIEW 25 decreased. At constant pressure drop and constant consistency the rejects freeness increased as the flow split value decreased. The equations generated by Bliss' statistical model permit calculation of all of these parameters. 20 10 +14 Feed mm Rejects -14+35 -35+65 Bauer McNett -65+150 -150 Data of Bliss 1983, Hydrocyclone: 76 mm Black Clawson 1-3-SR Contra Cone Reverse Cleaner Figure 2-2 Bauer McNett fractions for recycled corrugated boxes for feed and rejects. Ricker and House [88] investigated the thickening of pulp suspensions in a hydrocyclone. By using three different pulps in a Bauer-606-110P hydrocyclone, they studied the feed flowrate, product flow distribution, feed concentration and temperature. According to their results, hindered sedimentation of fibres controlled the thickening process, and the thickening efficiency was inversely proportional to fluid viscosity in dilute suspensions. For pulps of comparable hydrodynamic density (the density of fibre and associated water within and on the exterior of the fibre), fibre specific surface area dominated both thickening and classification of fibres. Their results and Wood et al. [109, 110, 111] both suggested that Chapter 2. LITERATURE REVIEW 26 hydrocyclone could classify pulps based on the specific surface. As the specific surface increased, the drag force increased, thus decreased the migration of high specific surface fibres to the underflow. Ricker et al. defined a critical flow rate through a hydrocyclone, below which no fluid solid separation occurred. They believed, as a result of their studies, that this critical flow rate was primarily dependent upon fibre length. Mukoyoshi and Ohsawa [74] have discussed the separation efficiency of a hydrocyclone in terms of settling velocities of wood fibres and vessel elements from various bleached, hardwood kraft pulps (BKP) by using a Bauer 600 Centri-Cleaner. They also measured the settling velocities of model fibres and model vessel elements of known geometric shapes made from P V C and duminum foil. The vessel elements of the wood fibres, which they used in their experiments, were assumed to be round, empty tubes, which had been flattened. Their results showed that the amount of rejected material was greater for those fibres and vessel elements having high settling velocities. The settling velocity of the vessel elements was influenced by their projected area and axis ratio (ratio of length to diameter). As the projected area of the vessel elements increased or the axis ratio decreased, the setting velocity increased. Model vessel elements, which were made of various materials, were also examined. With a fixed projected area and axis ratio, the setting velocity was proportional to the apparent density and the film thickness of these elements. The actual fibres, which were investigated in their report, originally were cylindrical but had flattened into a ribbon shape. Their model fibres were assumed to be cylindrical in shape and did not retain or expand in water. They found that the settling velocities of BKP fibres were linearly proportional to the product of the apparent density and the diameter of the fibres. For Chapter 2. LITERATURE REVIEW 27 the model fibres, the setting velocity was strongly affected by the fibre diameter, and only barely affected by the fibre length. Ohtake et al. [77] published a paper on flow visualization techniques for studying hydrocyclone fluid mechanics. They observed that the existence of a flow towards the conical apex of the hydrocyclone in the liquid phase at the outer edge of the air core. As a result of its presence they commented that large tracheids, which were located near the wall of the hydrocyclone might move upward towards the vortex finder exit while small fibres and/or fibre fragments might tend to be rejected. No evidence was given for the conjecture. Bliss [7] examined the effects of fibre fractionation on multilayer sheet formation. He noted that in general the rejects stream from a hydrocyclone contained the less refined, longer and stiffer, low specific surface area fibres plus other material that had higher specific surface values. The rejects (underflow) stream contained pulp that was much higher in freeness. Paper which was made from the rejects stream performed somewhat lower in burst, breaking length, tear and corrected fold than that made from the accepts. If the rejects pulp was refined, the resulting pulp produced paper that was significantly higher in burst, breaking length and corrected fold and slightly lower in tear than the feed pulp when compared on the basis of equal freeness. Note that in one component of the experimental works of Ho et al. [45, 46], it was found that the rejects (rejects tip opening = 3/16") stream contained most of the fines and had lower freeness values (CSF) than the accepts or feed. At higher flowrates the rejects had higher CSF than the accepts. In yet another experiment using a larger reject tip opening (1/4") the rejects CSF was always higher than the accepts CSF. Mohlin [72] defined a fibre-bonding index, in terms of the tensile index of handsheets made from a Bauer McNett 16-30 mesh fraction of mechanical pulps (i.e. pulp passes a 16-mesh Chapter2. LITERATURE REVIEW 28 screen but is retained on a 30-mesh screen). The value obtained for the 16-30 mesh fraction was considered to be representative for the whole long fibre fraction. Several criteria involving fibre-bonding ability were discussed. Mohlin [72] noted that as fibre bonding ability improved, surface roughness decreased with increased sheet density, and fibre rising decreased. Fibre rising is based on placing a drop of water on a sheet of paper, drying it at 120°C then image analyzing the raised portion of the sheet. Fibre rising was expressed as the sum of the lengths of all fibres risen from the surface over a certain surface area. The importance of low fibre rising in printing papers increases with the introduction of more and more multicolour offset printing. Fibres that were only loosely bonded to the sheet surface (i.e. the ones that would rise during the above treatment) tended to be thicker (coarser) than fibres that were well bonded in the sheet. Because the summerwood had poor bonding ability, the fibres with a high tendency to rise would tend to be the summerwood fibres. Differences in fibre bonding index were observed between the feed, rejects and the accepts of hydrocyclones in a TMP pulp mill. The screened pulp entering the cleaner had a fibre bonding index value of 8.0; the rejects bonding index value was 5.3 and the accepts bonding index was 8.9. Therefore, it was shown that the hydrocyclone could separate out material, which had lower bonding ability, the stiffer, thick-walled summerwood fibres present in the rejects, decreased the tensile strength of the handsheets that were made from the rejects. Wood et al. [108] established a method of how to use a hydrocyclone to characterize the linting propensity (fines) generated in mechanical pulping processes. Based on their previous investigation, they noted that fibre separations in a hydrocyclone were based on the specific surface differences. Thus, they extended this concept in fractionating the fines component of mechanical pulp to improve paper quality. Wood et al. [108] observed that when a hydrocyclone was operated under constant conditions, with a feed containing a large proportion of low Chapter2. LITERATURE REVIEW 29 specific surface material, the rejects had higher consistency and a higher tHckening factor (ratio of rejects consistency to feed consistency) than when there was more high specific surface material in the feed. Therefore, Wood et al. [108] concluded that the reject rate or thickening factor could be used as a criterion to rank pulps regarding their low specific surface material contents. Gavelin and Backman [37] also studied the subject of fractionation with hydrocyclones. Based on earlier work of Mohlin [72], they noted that a hydrocyclone could separate stiff and coarse fibres with less bonding ability from soft pliable fibres with higher bonding ability. Gavelin and Backman used softwood kraft pulps for their experiments, which were supposed to have the same coarseness. They measured drainage time, sheet density, air permeability, and tensile strength of handsheets, which were made from both the feed and rejects. The ratios of each of these characteristics in the rejects to the corresponding characteristics in the feed were related to fibre coarseness. Thus fibre suspensions with higher coarseness values drained faster than those with lower coarseness values. Sheets which were made from coarser fibres were lower in density, higher in air permeability and weaker in tensile strength. Their results indicated that the rejects drained faster than the feed for newsprint groundwood pulp. Thus the rejects had higher freeness and were lower in specific surface than the feed. The difference in drainage rate between rejects and feed increased as the pressure drop across the hydrocyclone increased. This implied that hydrocyclones rejected more low specific surface fibres at a higher pressure drop. Because of their results, Gavelin and Backman agreed that the criterion for separation in hydrocyclones was fibre coarseness. Another important article on the fractionation of pulps in hydrocyclones has been written by Paavilainen [81]. Her study involved the fractionation of softwood kraft fibres using hydrocyclones, a Johnson fractionator and a Jacquelin apparatus. At the outset she noted that Chapter2. LITERATURE REVIEW 30 softwood fibres as raw material for pulping had widely varying properties. The differences between springwood and summerwood fibres were particularly marked. The fibre lengths of springwood fibres were said to be somewhat shorter than those of summerwood fibres. In the experimental work involving hydrocyclones Paavilainen [81] used both bleached and unbleached, softwood kraft pulps which had been screened in the pulp mill. She later rescreened them to remove shives, thus her pulps could be regarded as fines free. Summerwood comprised 25% of the pulp; its kappa number was 32. The hydrocyclone employed was a Bauer 601, which had a diameter of 75 mm Some tests were done using a single stage of hydrocyclone treatment. In these tests the pulp consistency was 0.10% (a rather low value in terms of hydrocyclone operating energy efficiency) and the stock temperature was 7°G She believed, because of Jones et al. [53] and Alho [2] (not read by the present author) that fractionation was unlikely to occur to a significant extent if the consistency was > 0.3 %. In Paavilainen's work reject ratios of approximately 20, 50 and 80% were achieved by reject nozzle tip size/cleaner pressure drop combinations of 4.6 mm/150 kPa, 6.2 mm/100 kPa and 11.2 mm/180 kPa. The separation efficiencies for these tests were assessed by measuring fibre length and coarseness using a Kaajani FS100 analyzer. Handsheets were formed and measurements of tensile index, air resistance, tear index and relative bonded area were made. Table 2-1 provides a summary of the results. The data displayed in Table 2-1 indicated that in all instances the accepts fraction had equal or higher fibre length, and lower coarseness than the feed, which in turn had higher fibre length and lower coarseness than the rejects fraction. The differences between rejects and accepts mean fibre lengths and coarseness values were not large. As the reject ratio increased the difference between feed fibre length and rejects fraction fibre length decreased as expected, because at 100% rejects the feed and rejects streams would be the same. The maximum Chapter 2. LLTERA TURE RE VIE W 31 difference between accepts and rejects fibre length was observed at the lowest reject ratio. Conversely as the rejects ratio decreased one would expect that the difference between accepts and feed fibre length would diminish, however these differences did not change by much as rejects ratio was varied and showed no pattern. Note that the mean fibre lengths of the rejects were lower than those of the accepts and the coarsenesses were higher even though there was more summerwood fibre, which is longer than springwood, found in the rejects stream. T A B L E 2-1 Paavilainen's hydrocyclone fibre fractionations data. REJECTED OR ACCEPTED (%) FIBRE L E N G T H (mm) COARSENESS (mg/m) RELATIVE B O N D E D AREA (%) Original Pulp - 2.60 0.192 12.6 Reject Target 20% Rejects 21.3 2.44 0.202 8.3 Accepts 78.7 2.65 0.190 18.5 Reject Target 50% Rejects 55.2 2.50 0.198 9.9 Accepts 44.8 2.60 0.185 13.4 Reject Target 80% Rejects 80.6 2.52 0.199 10.0 Accepts 19.4 2.66 0.164 25.8 Chapter! LITERATURE REVIEW 32 As the rejects ratio increased the rejects coarseness tended to approach the feed coarseness. As the rejects ratio decreased the accepts coarseness approached the feed coarseness. The maximum difference between rejects and accepts coarseness occurred at the highest reject ratio. As a result of her investigation Paavilainen [81] concluded that hydrocyclones tended to separate thick-walled fibres as rejects and thin-wailed fibres as accepts. The rejects fibres had higher coarseness and thus a sheet which was made from the rejects would have better tearing resistance and higher porosity than one made from the accepts or from the feed. Besides, her experimental results showed that the multistage fractionation produced totally different properties of the rejects or accepts when compared to the original pulp. Handsheets made from the accepts fractions had greater % relative bonded areas than sheets made from the corresponding rejects fractions. The % relative bonded area data of Table 2-1 imply that sheets made from the accepts fraction had greater levels of interfibre bonding and therefore should be stronger than sheets made from the rejects fraction. This was borne out by the tensile index data which showed that the accepts always produced stronger sheets. The tensile index values for the accepts sheets were higher and those for the rejects sheet were lower than those of the unfractionated pulp. The highest tensile index values were found for sheets made from the least coarse pulp, which was the accepts at a reject ratio of 80%. The lowest tensile index values were noted for sheets made from the coarsest pulp, which was the rejects stream at a reject ratio of 20%. The volume of air passing through the sheets per unit time was always lower for sheets made from the accepts implying that their air resistance was higher and that they formed a less permeable, less porous, denser sheet. The unbeaten accepts (at an 80% reject ratio) had higher tear index values than the rejects. After beating to various degrees in a PFI mill however, the tear index of this type of pulp decreased. For all the other cases (feed, Chapter2. LITERATURE REVIEW 33 20% rejects, 50% rejects) as the number of revolutions, to which the pulp was exposed in the PFI mill, increased the tear index values rose to a maximum than declined. As the number of PFI mill revolutions increased the rejects developed higher tear indices than the accepts. The lower the ratio of rejects to feed the higher was the tear index of sheets made from the rejects streams. Paavilainen [81] noted in comparing the behavior of bleached and unbleached pulps that the bleaching process had no effect on the ability of the hydrocyclone to separate springwood from summerwood fibres. She also observed that in order to get a summerwood rich rejects stream and a springwood rich accepts stream, the reject ratio had to be less than 50% if the summerwood content of the feed was below 30%. She found that the least coarse pulp, having the highest fraction of springwood, that made the strongest (in tensile index) sheet, was the accepts from the hydrocyclone at a rejects ratio of 80%. However the rejects from the hydrocyclone at a rejects ratio of 20% put the coarsest pulp, having the highest summerwood content, into the rejects stream In addition, she noted that for a summerwood content of less than 30% the reject ratio for best fractionation should be less than 50%. Paavilainen [81] also investigated the effects of multistage cleaning on fibre fractionation by passing a pulp through a hydrocyclone cleaner, collecting the accepts and rejects streams in separate containers, then passing the rejects stream through the cleaner again at a different pressure drop. Finally the rejects were again collected and passed through the cleaner yet again at the same pressure drop as in the previous passage. In these multistage trials it was demonstrated that the summerwood content of the pulp, which was 20% in the unfractionated pulp, rose to approximately 40%, 60% and 70% in the rejects after one, two and three stages of cleaning. The accepts from a single pass through the hydrocyclone contained about 6% summerwood fibre. This value did not change appreciably Chapter2. LITERATURE REVIEW 34 upon further passes through the hydrocyclone. Since summerwood fibres tend to be coarser than springwood fibres the hydrocyclone in Paavilainen's experiments was rejecting on the basis of differences in fibre coarseness. Cell wall thicknesses and fibre widths on the fibres in the feed, rejects and accepts streams were also measured. The mean cell wall thickness of the feed fibres was 5.6 unx The cell wall thicknesses of the accepts were 4.0 —4.7 urn and those of the rejects were 6.6, 8.0 and 9.2 pm after one, two and three stages of cleaning. The mean fibre width of the feed fibres was 43.6 pm; the accepts fibres had widths of 44.0 —50.5 urn; the rejects fibres had widths of 41.2, 39.0 and 36.7 urn after one, two and three stages of cleaning. Paper strength tests done on handsheets made from samples of feed, accepts and rejects from multistage cleaning showed that the accepts had a higher tensile index than the feed and that the rejects had lower tensile index than the feed. The sheets made from the rejects of the third stage had lower tensile index than those from a single stage. At high levels of refining (in a PFI mill) the third stage rejects had higher tear index than the first stage which in turn was higher than that of the feed. The lowest tear index was for the accepts at these higher refining levels. When Bendsten smoothness was plotted against tensile index different relationships could be seen for each of the unfractionated feed, stage 1 accepts, stage 1 rejects and stage 3 rejects. For a given value of tensile index the smoothness values (ml/min) were lowest for the accepts, next lowest was the feed, followed by the stage 1 rejects. The highest values were noted for the stage 3 rejects. Plots of light scattering coefficient against apparent sheet density resulted in linear, but distinctly different, relations for the feed pulp, the stage 1 accepts, stage 1 rejects and stage 3 rejects. Chapter 2. LLTERA TURE RE VIE W 35 Rehmat and Branion [84] introduced a theoretical analysis, based on a force balance on a fibre in a centrifugal field, that led to the conclusion that the radial velocity of a fibre in a hydrocyclone is lower the higher the fibre's specific surface. This theory then was supported by the observations of Wood and Karnis [109] that fibres of low specific surface tended to be rejected by a hydrocyclone. These workers experimentally studied fibre fractionation of IMP using a Bauer 3 inch diameter Centri-Cleaner and observed that the rejects mean fibre length was less than the mean fibre length of the accepts. The fibre coarseness of the rejects was greater than the coarseness of the accepts. Burst and tear strengths of handsheets made from the rejects were lower than for sheets made from the accepts. Fibre fractionation was affected by hydrocyclone feed flow rate. Similar results were observed with CTMP, with the exception of fibre coarseness, which did not exhibit much difference between, accepts and rejects. In 1997, Karnis [56] proposed a new fractionation index, which could be applied to all fractionation processes and thus could be used to characterize hydrocyclones. His fractionation index (FI), which expresses a fractionation efficiency, was defined as: FI = 1 - X i / X u 0<FI<1 where X j and X J J are the average values of property X in streams I and II. He assumed that the average value of the fibre properties in either stream I or II was the value of the property associated with the 50% weight fraction greater than this specific property that was being considered. He also defined that the fraction with lower value of X as fraction I for all types of fraction. When X l = X n then FI = 0, and there was no separation. The distribution characteristics of property X were plotted in a probability diagram as the weight of fibres with Chapter 2. LITERATURE REVIEW 36 property value greater than the particular value of the property against the average value of the particular property in any given fraction. He believed that separation in a hydrocyclone occurred on the basis of specific surface differences. Hence, fraction I contains the low specific surface fibres (LSSF), and fraction II contains the high specific surface fibres (HSSF). Based on Karnis et al's early work, the high specific surface fraction (HSSF) would be found in the accepts. In his distribution plot, as the fibre flow of the low specific surface fraction (LSSF) increased, the reject rate increased. He also found that the fractionation index was independent of the size of the hydrocyclone but was strongly influenced by the cone angle. The smaller the cone angle, the better was the efficiency under the same operating conditions. From his experimental observations, hydrocyclones fractionated mechanical pulps on the basis of specific surface, because mechanical pulps usually have a broad specific surface area distribution and, on a relative basis, a narrower coarseness, wall thickness or diameter distribution. For unbeaten chemical pulps, usually the distributions of external surface area and diameter are quite narrow, thus the separation was on a basis of fibre wall thickness (coarseness). He examined the distributions of fibre length in a 76 mm hydrocyclone. His plot showed that as the rejects tip opening increased, the reject ratio increased. The fibre length distribution changed a little during a hydrocyclone separation. The underflow fraction contained more long fibres than the feed and accepts, because in general the long fibres also had a lower specific surface. But if the size of rejects tip opening relative to the length of the fibre was small, the long fibres could be caught in the upward spiral flow in the hydrocyclone (wall effect), thus the long fibres could end up in the overflow (accepts). However, for reject ratios greater than 16%, the fibre length distribution was less influenced by the reject ratio [84]. Karnis speculated that these results were caused by his postulated wall effect. Chapter 1 LITERATURE REVIEW 37 A three-stage hydrocyclone fractionation (in a cascade manner) was also investigated. It was arranged so that the rejects from the first stage became the feed to the second stage, then the rejects from the second stage became the feed to the third stage. The accepts of each stage were treated independently. He found that in the 3 stages, the fibre length of the rejects in the first stage was the shortest, the fibre length of the rejects in the third stage was the longest. The reject ratio of each stage was about the same. The rejects in the third stage had the smallest average specific surface value, and the rejects in the first stage had the largest average specific surface value. As Karnis had earlier concluded the long fibres had lower specific surface, these results showed agreement with his viewpoint. Sandberg, Nilsson and Nikko [92] investigated fibre fractionation to improve the quality of printing paper in a TMP pulp mill. They used a two-stage fractionating hydrocyclone (Noss Radiclone A M 80) system Microscope pictures, which are provided in their paper, showed that the accepts contained fines and long fibre, while the rejects contained more coarse material and a lesser amount of fines. Paper properties were also measured on handsheets, which were made from the feed, the rejects and the accepts. The results indicated that the handsheets which were made from the accepts had the maximum values of tensile index, tear index and light scattering, while the rejects had the minimum values. In addition, the rejects were coarser then either the feed or the accepts, and the accepts were less coarse than the feed. In their study, handsheets which were made from the rejects had very poor qualities. Thus it was confirmed that a hydrocyclone had great potential to remove inappropriate fibre material. Hoydahl and Dahlqvist [50] noted that the surface smoothness of a paper sheet was important to print quality and that the presence of thick-walled fibres in the sheet surface was detrimental. Thus the separation of such fibres for further refining should result in reducing Chapter2. LITERATURE REVIEW 38 their wall thickness. Return of these thinner walled fibres to the furnish should then result in a smoother sheet. They also observed that hydrocyclones, to some extent, tended to accept fibres that should be rejected because of their negative contribution to surface smoothness. Such fibres were referred as low energy mtterioL They noted that fractionating hydrocyclones of a special design exist to separate such material. They presented a plot which showed that the fibre wall thickness distributions of the feed pulp to, and the pulp rejected by, one of these fractionating hydrocyclones were significantly different. More very thick fibres were observed in the rejects than in the feed. Fibre wall thickness distributions for rejects ratios of 4% and 14% were not very different. They also showed that the fibre perimeters for the feed and rejects were the same. Refining of the thick-walled fibres reduced their fibre wall thickness Vollmer [105] has discussed fibre fractionation using a hydrocyclone (supplied by Celleco) as a means of improving the strength characteristics of multiply paper and board. In her work a STFI Fibre Master was used to measure the fibre length, and fibre thickness distributions. Vollmer [105] noted that in order to use a hydrocyclone, or any other fibre fractionation device, for fractionation, the distribution of fibre properties, e.g. fibre thickness, should be broad. Therefore, if the distribution of the pulp to be fractionated was narrow there would be little probability of achieving much separation. She indicated that hardwood pulps were unlikely to be fractionated for this reason. Ffowever others [28, 65] revealed that Eucalypt pulps could be fractionated by a hydrocyclone. After she fractionated the pulp, she sent the rejects to the core and the accepts to the surface layers to form a three-ply sheet. The results showed that the surface smoothness was improved when compared to a sheet made from the same pulp but not fractionated. Chapter2. LITERATURE REVIEW 39 Demuner [28] investigated, amongst other devices, the use of a Noss Radiclone AM80-F for the fractionation of an E C F (Elemental Chlorine Free), Eucalypt market pulp at a feed consistency of 0.5%. Eucalypt pulps have a rather narrow distribution of fibre properties and thus represent a challenge to any fibre fractionation process. The feed pulp was directed to stage 1 of a 2-stage system The rejects from stage 1 became the feed to stage 2 while the accepts from stages 1 and 2 were combined to become the accepts from the system The rejects from the system were the rejects from stage 2. From his experimental observations, which are shown in Table 2-2, Demuner [28] pointed out that the average fibre length was lower in the accepts than it was in the rejects. This seems to be characteristic of the Noss fractionating cleaner [63, 92] and is the opposite of what others and we have observed [45,46, 81, 84,85] using another type of commercial hydrocyclone. Demuner [28] did not observe any significant differences in coarseness among the feed, accepts and rejects. Fines were concentrated in the accepts. There were some chemical composition differences as well between feed, accepts and rejects. Perhaps this implied that different types of fibres were separated during the fractionation. Refining the accepts and rejects streams in a PFI mill showed for the accepts fraction, that for a particular number of PFI mill revolutions, the tensile index of the accepts was significantly greater than the tensile index of the feed pulp. Refining of the rejects resulted in a lower, but not by much, tensile index than that observed for the feed pulp. Demuner [28] plotted values of air resistance (Gurley), apparent sheet density, light scattering coefficient, Bendsten roughness, dynamic drainage time and water retention value versus tensile index. The air resistance of the accepts pulp was greater than that of the feed pulp and the air resistance of the rejects pulp was lower at a particular value of tensile index. The apparent sheet density of the accepts pulp was greater than that of the feed pulp while the feed Chapter2. LITERATURE REVIEW 40 and rejects apparent densities were approximately the same at a particular value of tensile index. The light scattering coefficients of the accepts pulp were higher than the feed pulp scattering coefficients and the rejects pulp scattering coefficients were lower at a particular value of tensile index. The accepts Bendsten roughness was lower than the feed pulp roughness and the rejects roughness was higher at a particular value of the tensile index. Dynamic drainage times for the accepts were longer than those of the feed pulp which in turn were longer than those of the rejects at a particular value of tensile index. Water retention values of the accepts were higher than those of the feed pulp at a certain tensile index but the water retention values of the feed and rejects didn't show significant differences except at low values of tensile index. Table 2-2 Demuner's hydrocyclone fibre fractionation data for Eucalyptus pulp. Property Feed Pulp Accepts Pulp Rejects Pulp Weighted Average Fibre Length (mm) 0.67 0.64 0.69 Fibre Coarseness (mg/lOOm) 7.8 7.8 7.9 Number of Fibres per Gram (millions) 22.7 24.2 21.6 Fines Content from Dynamic Drainage Jar (%) 10.9 19.5 7.1 Pentosans Content (%) 16.6 16.8 15.3 Carboxyl Content (meq/lOOg) 5.8 5.9 5.7 Chapter2. LITERATURE REVIEW 41 Demuner [28] concluded that the hydrocyclone he used was indeed capable of separating a stream of Eucalypt fibres into two streams containing fibres having different characteristics. Kure et al. [63] published a paper on fractionation of fibres (mechanically pulped Norway spruce) using a Noss Radiclone hydrocyclone system In this 2-stage system, stage 1 consisted of 8 hydrocyclones and stage 2 consisted 4 hydrocyclones. The accepts from stage 1 were the system accepts. The rejects from stage 1 became the feed to stage 2 and the rejects from stage 2 became the system rejects. The accepts from stage 2 were mixed with the incoming, unfractionated feed to be the feed to stage 1. The incoming unfractionated feed consistency was 1%, the consistency of the combined incoming feed and the accepts from stage 2 was 0.6%. The system reject ratio was varied. The mcoming feed mass flowrate of fibres ranged from 3.5 ~ 4.0 oven dry kilograms per minute. The objective of their work was to separate thick walled fibres from the thin walled fibres, then refine the thick walled fibres so that print quality and smoothness of the resulting paper sheets could be improved. Their data are reproduced in Tables 2-3, and 2-4. In all of the cases they studied -• the rejects mean fibre length was greater than the accepts mean fibre length. This finding seems to be typical of what's been observed using Noss Radiclone fractionating hydrocyclones [28,92]. • the CSF values for the rejects were higher than for the accepts (this is in accord with the idea that hydrocyclones tend to reject material of low specific surface). • the fibre wall thicknesses were greater for the rejects than for the accepts as measured on the + 50 mesh Bauer McNett fraction (this is in accord with findings that hydrocyclones tend to reject coarse material). • fibre perimeters were not significantly different between rejects and accepts. Chapter! LITERATURE REVIEW 42 • the % of fibres having microscopically observable breaks in the fibre circumference (indicative of fibre damage) was higher in the accepts than in the rejects, indicating that fibre flexibility plays a role in fibre fractionation. • shive content was substantially higher in the rejects than in the accepts. • scattering coefficients, for sheets made from the various hydrocyclone fractions, were higher for the accepts than for the rejects. • considering the Bauer McNett distributions (see Figures 2-3 and 2-4) of the feed, accepts and rejects it was found that the pass 200 mesh fraction (fines) was higher for the accepts than for the rejects. The +30 mesh fraction (long fibres) was higher for the rejects than for the accepts; this was also true for the -30+50 and -50 +100 fractions. They studied two pulps a newsprint pulp (from Mill A) and a super-calendar magazine pulp (SGA from Mill B). For the newsprint pulp (data of Table 2-3) as the system reject ratio rose the difference between the rejects and accepts CSF values increased, for the S G A pulp the opposite was observed. For both pulps as the reject ratio increased the difference between the rejects and accepts fibre lengths increased. As reject ratio increased the difference between the amount of fines in the accepts and in the rejects increased for both types of pulp. With one exception, as the reject ratio increased the difference between rejects and accepts fibre wall thickness tended to decrease for both types of pulp. Refining of the rejects stream resulted in decreasing the mean fibre wall thickness. Increasing the specific energy of refining (kWh/ton) resulted in decreasing fibre wall thickness at both low (3.5%) and high (21%) refining consistencies. At a given specific energy low consistency refining produced slightly thinner fibres than refining at high consistency. Chapter 2. LITERATURE REVIEW 43 Table 2-3 Kure et al.'s [63] hydrocyclone fibre fractionation data for a newsprint pulp. Feed Accepts Rejects Accepts Rejects Accepts Rejects System Reject Ratio (%) 10 10 17 17 25 25 CSF (ml) 130 141 596 129 632 120 652 Mean Fibre Length (mm) 1.36 1.34 1.51 1.27 1.49 1.31 1.63 Fibre Wall Thickness (um) 2.78±0.1 2 2.46±0.10 2.99±0.13 2.58±0.12 3.04±0.15 2.57±0.10 2.95±0.15 Fibre Perimeter (um) 94.7±3.1 95.9±3.1 93.9±3.2 96.3±3.5 94.2±3.0 92.7±2.9 94.2±3.0 Fibres With Broken Circumference (%) 28.5 32.4 29.0 33.8 24.0 31.0 28.7 Shive Weight (%) 0.14 0.05 0.57 0.03 0.83 0.06 0.41 Bauer McNett 4-30 (%) 49.6 47.6 50.7 44.1 46.6 44.3 52.5 Bauer McNett -30+50 (%) 17.6 16.5 22.2 17.7 24.8 16.2 23.1 Bauer McNett -50+100 (%) 10.8 10.9 11.9 12.0 13.5 11.5 12.6 Bauer McNett -100+200 (%) 5.0 5.3 4.5 5.9 4.5 5.9 4.1 Bauer McNett -200 (%) 17.0 19.7 10.7 20.3 10.6 22.1 7.7 Scattering Coefficient 24.6 28.4 24.5 25.8 23.6 26.1 24.1 Chapter 2. LITERATURE REVIEW 44 Table 2-4 Kure et al.'s [63] hydrocyclone fibre fractionation data for a super calendar magazine pulp. Feed Accepts Rejects Accepts Rejects Accepts Rejects System Reject Ratio (%) 5 5 10 10 15 15 CSF (ml) 32 31 425 29 398 26 349 Mean Fibre Length (mm) 1.27 1.26 1.43 1.24 1.43 1.20 1.50 Fibre Wall Thickness (lim) 2.01±0.09 2.06±0.09 2.4010.11 1.96±0.10 2.3410.10 2.0010.08 2.1910.09 Fibre Perimeter (um) 81.8±3.0 84.1±3.1 79.0±2.6 79.7±3.0 83.8+2.8 89.2+3.0 83.812.8 Fibres With Broken Circumference (%) 28.5 32.4 29.0 33.8 24.0 31.0 28.7 Shive Weight (%) 0.01 0.00 0.08 0.05 0.08 0.01 0.07 Bauer McNett +30 (%) 40.9 39.1 43.9 37.8 48.1 36.9 51.6 Bauer McNett -30+50 (%) 13.7 12.5 22.1 12.7 19.2 12.4 18.4 Bauer McNett -50+100 (%) 9.2 9.4 12.4 8.9 11.0 9.1 10.6 Bauer McNett -100+200 (%) 5.5 5.7 4.5 4.8 4.9 4.6 4.6 Bauer McNett -200 (%) 30.7 33.3 17.1 35.8 16.8 37.0 14.8 Scattering Coefficient 31.8 32.2 25.4 31.7 28.3 31.8 25.6 Chapter! LITERATURE REVIEW 60 +30 -30+50 -50+100 -100+200 -200 Bauer McNett Distributions Newsprint Pulp l l Accepts 10% Reject Ratio Rejects 10% Reject Ratio Accepts 17% Reject Ratio 1888888 Rejects 17% Reject Ratio Accepts 25% Reject Ratio rrrrm Rejects 25% Reject Ratio r I Feed Figure 2-3 Data of Kure et al. [63] newsprint pulp. 60 S? 30 4 +30 -30+50 -50+100 -100+200 -200 Bauer McNett Distributions SC-A Magazine Pulp i l Accepts 5% Reject Ratio PZ&n Rejects 5% Reject Ratio ESSSi Accepts 10% Reject Ratio KS£££Sj Rejects 10% Reject Ratio E S S Accepts 15% Reject Ratio rrrrm Rejects 15% Reject Ratio Feed Figure 2-4 Data of Kure et al. [63] S G A magazine pulp. Chapter! LITERATURE REVIEW 46 Besides, refining of the rejects caused the fibre wall thickness distribution to shift towards lower values. Almost all of the thickest fibres disappeared during refining. Refining the rejects resulted in improved tensile index, improved Parker Print Surf and increased light scattering. All of these variables changed linearly with increases in refining specific energy. The light scattering coefficient and the Parker Print Surf were unaffected by refining consistency, but at a given specific energy the tensile index was higher for low consistency refining. Li et al. [65] studied the hydrocyclone fractionation of Eucalypt, bleached kraft pulps. They proposed that fibre fractionation in a hydrocyclone was governed by drag forces, centrifugal forces and flocculation effects, the latter, in turn, being dependent upon consistency. In their work they decided to avoid any complicating effects of the presence of fines by working only with a prescreened (Bauer McNett fibre classifier), long fibre, pulp fraction from which the fines had been removed. To avoid flocculation effects they chose to work at a pulp consistency of 0.05%, which as previously noted, was too low for real commercial application. Thus their objective was to shed some light on the mechanism of fibre fractionation and the motion of pulp fibre fractions in hydrocyclones. Li et al [65] used an A K W (Ambeger Kaolinwerke) hydrocyclone having a maximum diameter of 40 mm (1.5 inches); a 16x3 mm2 feed inlet, a 6 mm diameter rejects tip opening and a 13 mm diameter vortex finder (accepts outlet). Note that this hydrocyclone was very small in comparison to almost all of those used in the other works cited in this review. The operating pressure drop was 310 kPa (45 psi) and the feed flowrate was 2.5 mVhr. The mass flowrate of fibres in the rejects was approximately equal to the mass flowrate of fibres in the accepts. Fibre lengths were measured using a Kajaani FS-200; other fibre properties were measured by confocal microscopy. Chapter! LITERATURE REVIEW 47 Since the apparent density of a fibre moving under the influence of centrifugal and drag forces in a hydrocyclone affects the fibre trajectory, Li et al. [65], as did our group (see Chapter 3), defined [84], an apparent density for a water swollen fibre which was modelled as a straight circular cylinder. Li et al.'s [65] apparent density was a function of water density, fibre coarseness (which is a function of dry fibre density), dry fibre diameter, dry fibre lumen diameter and wet fibre diameter. The appropriate fibre dimensions for use in calculating an apparent fibre density, and ultimately fibre trajectory in a hydrocyclone, were estimated using confocal microscopy. As these authors note this was not a simple task and we note that not everybody has access to a confocal microscope. The model utilized by our group used wet fibre specific surface and volume as parameters to be estimated in the calculation of wet fibre trajectories in a hydrocyclone. Use of water retention value (WRV) is another possibility. These parameters are somewhat more accessible but still require some specialized equipment (Robertson and Mason [90]). See Chapter 3, Section 3.2.1.2 for more details As a correlating parameter Li et al. [65] recommended, and used in their research, an apparent density factor (AD) which was a function of dry fibre diameter and dry lumen diameter. A D can also be related to fibre thickness and to Runkel ratio, which latter was defined as twice the fibre wall thickness divided by the lumen diameter. Their experimental data indicated that the rejects from their hydrocyclone were slightly longer (mean fibre length = 0.92 mm) than the accepts (0.88 mm). Rejects fibre coarseness in the rejects was 0.081 mg/m while that of the accepts was 0.073. Fibre wall cross-sectional area in the rejects was 90 um2; that of the accepts was 66 um2. Accepts sheet bulk was 1.86 cm3/g, rejects sheet bulk was 1.95. Accepts tensile index was 31.3 Nm/g, rejects tensile index was 23.8. Accepts tear index was 6.11 Nm 2/g, the rejects value was 4.9. Thus Li et al.'s [65] results were similar to those noted by others in that their, all be it unusual, hydrocyclone tended to reject Chapter 2. LITERATURE REVIEW 48 long, coarse, thick walled fibres and that sheets made from the rejects were less dense and weaker than sheets made from the accepts. From the confocal microscope images it was observed that 35% of the fibre in the accepts were collapsed compared to only 17% in the rejects. Plots of the distribution functions of A D showed that the rejects tended to have higher values of AD; than the accepts for all fibres and for collapsed and uncollapsed fibres individually. Li et al. [65] also calculated grade efficiency curves in terms of A D that is they plotted the fraction of material having a certain value of A D that was rejected against A D . Ho et al. [45, 46] presented papers in which they reported some revisions to their theory explaining why hydrocyclones fractionate on the basis of specific surface differences. See Chapter 3. In them the results of some studies on the hydrocyclone fractionation of nylon fibres having known values of coarseness and fibre length were reported. (See Chapter 5) Experimentally we observed that when a feed stream containing a 50% : 50% or 25% : 75% (mass basis) mixture of nylon fibres having a common fibre length but different coarseness values, was put through a 76 mm commercial hydrocyclone, an accepts stream was produced that was more concentrated in the lower coarseness fibres and a rejects stream that was more concentrated in the higher coarseness fibres. Using a 50% : 50% and a 75% : 25% (mass basis) of nylon fibres having the same coarseness but different fibre lengths we found that the longer fibres tended to report to the accepts stream and the shorter fibres to the rejects stream. (See Chapter 5) Using a TMP (at 0.9 % consistency) a 6 stage fractionation was made using a Bauer 600 3 inch Centri Cleaner. The accepts from stage 1 contained more long fibres than the rejects from stage 1. Rejects from stage 1 tended to contain a lot of fibre fragments, shives ray cells and fines. The rejects from stage 6 contained both earlywood and latewood fibres which showed Chapter 2. LTTERA TURE RE VIE W 49 some signs of fibrillation. Two hydrocyclone configurations were studied: a 1/8 and a 3/16 inch reject tip opening. In all cases the rejects mean fibre length (Kajaanf) was shorter than the mean accepts fibre length. Accepts Canadian standard freeness (CSF) values were always greater than those of the rejects. Bauer McNett distributions showed that there was a large amount of pass 200 mesh material (fines) in the rejects. Burst and tear indices were always in the order accepts >feed > rejects. The difference between the mean fibre length of the accepts and the mean fibre length of the rejects was always greater with the 1/8 inch reject opening. The same was true of the difference between the accepts and rejects freeness values and for the difference between accepts and rejects burst index. It was also observed that, except for the case of single stage fractionation with the 1/8 inch opening, that the difference between the accepts and rejects tear index was greater with the 1/8 inch opening. (For more details see the M.ASc thesis of Rehmat [85]) Using BCTMP, Ho et al. [45, 46] using the same basic hydrocyclone (Bauer 600 Centri-Cleaner), but with rejects tip openings of 3/16 and 1/4 inches, observed that the mean fibre lengths of the feed (0.6 % consistency) and accepts were more or less the same (low reject ratio) but the rejects fibres were shorter than the feed and accepts fibres over a wide range of feed flow rates. With the 3/16 inch reject tip opening at low feed flow rates the CSF values of the accepts were higher than those of the rejects but at high flow rates the opposite was seen. With the 1/4 inch opening the rejects CSF values were higher than the accepts values at all flow rates. Wong [106] investigated the hydrodynamic behaviour of individual pulp fibres. His experimental results were obtained by using a rotating cylindrical tank (a centrifuge), which was built to measure the velocity of various fibres in water under the influence of various centrifugal Chapter 2. LITERATURE REVIEW 50 fields. He proposed the following equations relating drag coefficient to Reynolds number (based on fibre diameter) for Kraft pulp and TMP. Kraft: C D = n * for 0.007 < Re < 1.0 R e-0.571 TMP: C D = 7 * for0.007<Re<1.0 Re" 0 7 6 3 He observed that the shape of the fibres did not affect their migration rate (radial velocity) in the centrifuge. Curved and kinked fibres moved at almost the same rate as straight fibres. Fibres did not rotate regardless of their initial orientation; they remained in that orientation, relative to the radius of the centrifuge, during the entire settling process in the rotating tank Most fibres did not orient themselves with their long axis perpendicular to the direction of motion. Wong's thesis contains an extensive review of the literature on drag coefficients for cylinders including fibres. Rehmat [85] investigated fibre fractionation in different hydrocyclones. She concluded, from her experimental results, that fractionation of various kinds of mechanical and chemical pulps had occurred and that there were differences in coarseness and fibre length between the accepts and rejects streams. Sheet strength properties were usually stronger for pulps made from the accepts than for sheets made from the rejects. For tests preformed on recycled pulp, her results showed that the rejects fibres were shorter than the accepts fibres. Sheets which were made of accepts fibres were stronger than those made of the rejects. Microscopic examinations of the accepts and rejects fibres showed that chemically pulped fibres tended to report to the accepts and mechanically pulped fibres tended to report to the rejects. Multistage fractionations of mechanical and chemical pulps were performed too. Her results showed that for tests performed with mechanical pulp, the rejects fibres were coarser and shorter than those reported to the accepts. Fines were found in the rejects. She also used a Chapter 2. LITERATURE REVIEW 51 different hydrocyclone (supplied by Celleco) to fractionate chemical pulps. In those tests, she stated that fibre fines and earlywood fibres reported to the accepts and latewood fibres reported to the rejects. She examined the refining of fractionated chemical pulps. Those tests illustrated that earlywood fibres developed more improvement at lower refining intensity than latewood fibres. They also showed that rejected latewood fibres could be upgraded to usable fibres through refining. Chapter3. THEORETICAL ANALYSIS 52 Chapter 3 T H E O R E T I C A L ANALYSIS A variety of forces act upon a particle suspended in a fluid inside a hydrocyclone. These forces include buoyant, drag, and centrifugal forces which are believed to be significant, and others, such as gravity, which are typically not significant. Under the influence of the centrifugal force, a particle, such as a fibre, which is denser than the suspending fluid, tends to move toward the wall where it enters a region of flow in which the axial velocity is directed towards the reject opening at the tip of the conical section. Thus particles closer to the wall will tend to exit via the rejects opening. Particles having a high, outward, radial component of velocity will, in a given residence time, travel farther and thus be more likely to get into the reject bound, wall flow region. Qn the other hand, the slower particles will tend not to get to the wall region of downward flow in the allotted residence time and will be dragged inwards, eventually proceeding towards the vortex finder, which is usually located at the opposite end of a hydrocyclone. Experimentally it has been demonstrated that hydrocyclones tend to reject coarse, low specific surface, high wall thickness wood pulp fibres. See Chapter 2. It has also been demonstrated that hydrocyclones, depending on the hydrocyclone design parameters, tend to reject short or long fibres. See again Chapter 2. In this Chapter we look at the equations of motion of particles (including fibres) which are moving primarily under the influence of centrifugal and drag forces. Specifically we wanted to find out how specific surface, specific volume, fibre coarseness, fibre diameter and fibre length would affect the radial velocity of a Chapter3. THEORETICAL ANALYSIS 53 particle in a centrifugal field. Since we did not have access to a convenient technique for measuring fibre wall thickness, since we were not working with wood pulp fibres, but with nylon fibres, which had no lumens, and since fibre thickness (diameter) can be deduced from specific surface, specific volume and coarseness values, we did not further consider fibre wall thickness. 3.1 Principles of Hydrocyclone Operation Figure 1-2 illustrates a hydrocyclone and indicates the spiral flow patterns, which exist inside it. Fluid enters tangentially at the inlet, then spirals downwards in the outer part of the hydrocyclone towards the apex of the conical part. As the volume available for flow diminishes the flow then turns upwards, at the inner radii, towards the vortex finder. There are also some short-circuit flows close to the vortex finder. In these, part of the inlet flow moves across the roof of the hydrocyclone towards the vortex finder, then downwards over the outer surface of the vortex finder and finally radially inward across the bottom of the vortex finder and into the vortex finder. These short-circuit flows do not penetrate very far down into the part of the hydrocyclone below the vortex finder. For a forward cleaner, the accepts is the overflow and the rejects is the underflow, and for a reverse cleaner, the overflow is the rejects and the underflow is the accepts. Some experimental velocity profiles from the data of Kelsall [59] are presented in Figure 3-1-1, which shows the velocity components in the tangential, axial, and radial directions. Various other researchers have produced measured [27, 51, 52, 62, 80, 89] or computed velocity profiles [11,12,43, 68,94] which are qualitatively similar to those of Kelsall. In the hydrocyclones, the tangential velocity is highest near the center, and lowest near the wall. All of the velocity components are equal to zero at all solid surfaces. The axial Chapter3. THEORETICAL ANALYSIS 54 velocities have both positive and negative values. In this thesis positive values indicate that the flow is moving towards the overflow while negative values indicate the flow is directed towards the underflow. For the radial velocities, positive values indicate motion in an inward direction, and negative values indicate motion in an outward direction. Bradley [17] and Kelsall [58, 59] noted that the radial fluid velocities tended to be much smaller in magnitude than the tangential and axial velocities. Figure 3-1-1 (a) Axial velocity profile (b) Radial velocity profile (c) Tangential velocity profile of a hydrocyclone. Kelsall [59] Chupter3. THEORETICAL ANALYSIS 55 3.2 Equations of Motion in a Centrifugal Field In this section, the objective is to establish equations of motion for particles (including fibres) moving in a centrifugal field as found in a hydrocyclone. Having established such equations we can use them to get a qualitative idea of how various fibre properties affect the trajectory of these particles in such a centrifugal field. In particular we would like to be able to explain why accepted fibres tend to have higher specific surfaces than rejected fibres as observed in the experimental works of Wood and Karnis [110] and the current experiments. The equation of motion for particles in a centrifugal field will be similar to that for motion in a gravitational field, except that the gravitational acceleration g must be replaced by the centrifugal acceleration rco2, where r is the radius of rotation and CO is the angular velocity. However, in the centrifugal field the acceleration is now a function of the radial position (r) of the particle, unlike in a gravitational field in which it is generally assumed constant with respect to particle position. The particle velocity can be calculated from a force balance in the radial direction on the particle in a centrifugal field. There is a centrifugal force (F^, which plays a major role in a hydrocyclone, a buoyant force due to fluid displacement by the particle (FB) and a drag force (Fj^, resulting from fluid friction and pressure differences, which acts in a direction opposite to the direction of motion of the particle. Any effects of the axial and radial components of fluid velocity are ignored in the following analysis. Also ignored were any fibre-fibre interactions. — Fc (3.2.1) (3.2.2) M P a (3.2.3) Chapter3. THEORETICAL ANALYSIS 56 pvr2 F D = C D ^ A p (3.2.4) where, Mp = particle mass V r p = radial vebcityof particle a - radial particle acceleration t = time p = the fluid density p P = the apparent density of a particle Q, = a drag coefficient Ap = the projected area of the particle on a plane perpendicular to the direction of the particle motion. In a centrifugal field, as it would occur in a tubular centrifuge, the particle acceleration is: a = rco2 (3.2.5) where, r = radial position of particle CO = the angular velocity of the fluid In a centrifuge rco2 is constant and the flow is described as a forced vortex. In a hydrocyclone part of the flow field tends to be in the form of a forced vortex, but part of it is in the form of a free vortex [98]. Let's now proceed initially by assuming a forced vortex. Then, combining Equation (3.2.1) to (3.2.5), Equation (3.2.6) can be obtained. dV r dt 1 - -P -,2 c o P y : rco z - u r r p A p (3.2.6) 2 M n p It has been noted (Coulson et al., [25], page 116) that when a particle is accelerating with respect to the fluid in which it is suspended, that a certain mass of fluid outside of the particle Chapter3. THEORETICAL ANALYSIS 57 will be accelerated along with the particle. Allowance for this additional "virtual mass" (N/L) should be included in the force balance under discussion. Thus Equation (3.2.1) becomes dV ( M p + M V ) ^ = F C - F B - F D (3.2.7) Mp and M,, are neither functions of V r nor t, thus the effect of including virtual mass in solving Equations (3.2.6) or (3.2.7) will be in the form of a correction involving particle density and fluid density. Thus whether or not virtual mass is considered should not affect the role of other particle properties such as specific surface, specific volume, particle diameter, etc. on a particle's radial velocity in a centrifugal field. If the left hand side of Equation (3.2.7) is set equal to zero then virtual mass plays no role at all. In the customary analysis of particle motion in a gravitational field, in which a particle is moving in a relatively non-viscous medium, such as water, it can be shown by calculation or by measurement that such a particle would rapidly accelerate to a terminal velocity at which the forces acting on the particle balance one another. It then continues to move at a constant velocity, assuming the forces remain unchanged. In fact, in a centrifugal field the centrifugal acceleration (rco2) is a function of radius (r) thus as a particle moves radially it encounters a dV r different accelerating force. Let's set, equal to zero regardless; by making the assumption dt that it is small in magnitude in comparison with the terms on the right hand side; then Equation (3.2.6) can be solved. Not setting the left hand side of Equation (3.2.6) equal to 0 is discussed in more detail below. The following equation for the particle's radial velocity was obtained: 2 _ ' P V = 2M. ( ^ i - P - rco2 (3.2.8) Chapter3. THEORETICAL ANALYSIS 58 3.2.1 Spherical Particles 3.2.1.1 For An Unswollen, Spherical Particle (a) Left Hand Side of Equation (3.2.6) Set Equal to 0 The choice of a sphere as a model particle in a work concerned with fibre fractionation may seem odd. However we are not necessarily looking for an equation that would accurately predict the trajectory of a particle in a hydrocyclone but rather for one that would indicate qualitatively, if not quantitatively, the effects of changes in fibre properties on fibre trajectory. The reasons then for using a sphere model are: • There is much more drag coefficient data available for spheres than for cylinders. • A sphere is symmetrical and thus could not display any preferred orientation in a flow. • Cylindrical fibres could be represented by some sort of equivalent spheres. See Figure 3-2-1 below. • Fibre fines and fibre fragments could have a shape that could be represented by an equivalent sphere. Figure 3-2-1 shows the friction factor (drag coefficient) vs. Reynolds number for particles having various shapes characterized by sphericity (*P). Sphericity is defined as the ratio of the surface area of a sphere having the same volume as the particle to the surface area of the particle. The sphericities of the nylon fibres used in this study range from 0.212 to 0.396. These values are within the range of sphericities covered by Figure 3-2-1, thus considering fibres in terms of equivalent spheres does not seem unreasonable. Chapter3. THEORETICAL ANALYSIS 59 Figure 3-2-1 Fraction factor (drag coefficients) vs. Reynolds numbers for particles of different sphericities. Brown at al. [21]. To begin let's choose a spherical particle which does not, unlike wood pulp fibres, swell in the suspencling fluid medium. The nylon fibres used in the experimental part of this thesis do not swell appreciably in water. Soszynski [98] measured the moisture uptake of nylon fibres in humid air and found it to be less than 2%. See also Chapter 4, Section 4.4. The mass of the model particle (Mp,) is: M p = f ( D 3 p ) P p (3.2.9) Its projected area (Ap) is: A p = ^ D 2 p (3.2.10) where, D p = particle diameter P p = particle apparent density. Combining Equations (3.2.8), (3.2.9) and (3.2.10) leads to Chapter3. THEORETICAL ANALYSIS 60 V ^ = T ^ ( l - A ) « o 2 (3.2.11) p 3 p C D p p For spheres at low Reynolds number (NpJ the drag coefficient (Q,) is given by N „ D p V r p p where, (JL = fluid viscosity. The upper limit of validity for Equation (3.2.12) is usually quoted to be Np^ = 0.1, but extending that limit to 1.0 does not result in much error. For example if one uses the Equation (3.2.13) C D = - ^ - ( l + 0.15N°Rf7) (3-2.13) which is noted by Clift et al. [22] to be a good fit of experimental drag coefficient data for N ^ , between 0 and 800, and calculates Q, at N R . = 1 the value is 27.6, using Equation (3.2.12) gives Q , = 24 . At N R . = 2, the values are 14.9 and 12 respectively. Combining Equations (3.2.11) and (3.2.12) gives V =5£pJL(i__P_) r C 02 for 0 <N R e <1 (3.2.14) p 18ix P p ; Equation (3.2.14) implies that the greater the particle diameter the greater the radial velocity of the particle. Thus large diameter spheres would tend to have a higher probability of being rejected in a hydrocyclone than would small diameter spheres. The specific surface area (a) of a particle is defined as the surface area per unit mass of particle. For spheres then Chapter3. THEORETICAL ANALYSIS 61 Thus V R = ? 2 (1 --2-)ru)2 for 0 < N R E < 1 (3.2.16) P oppM- P P From Equation (3.2.16) it is seen that as specific surface increases the radial velocity of a spherical particle decreases. Thus high specific surface particles should have a lower probability of being rejected than low specific surface particles. The centrifugal force term rco2 in the above equations can be rewritten, in terms of tangential fluid velocity, (V,) as rco 2=-^- (3.2 17) r Assuming the particle has the same tangential velocity as the fluid, then 2(p - p ) v 2 1 V R = V P P , for 0 < N R E <1 (3.2.18) W>1 r a 2 Below we estimate that the particle Reynolds number in a hydrocyclone could go from 0 to as high as 240 (See Figure 3-2-5, page 67). Thus Equation (3.2.11) would not be valid over the whole flow region. There is a number of equations for drag coefficient as a function of that are valid over wider ranges of N R , than equation (3.2.12) (Gift et al. [22]). One of these (Kellyetal.[57]) is C o = ^ (3.2.19) This is not the equation that best fits the data over a wide range of Reynolds number but use of those equations requires the solution of non-linear equations. In the solution of such non-linear equations the role of specific surface is difficult to establish. Use of Equation (3.2.19) is justified because it fits the experimental data well over a range 2 <N R e < 500. Thus combined Chapter3. THEORETICAL ANALYSIS 62 with Equation (3.2.12) we have covered the range of particle Reynolds numbers that we would expect to find in a hydrocyclone. Substituting Equation (3.2.19) into (3.2.11) leads to D U 4 ( p - p ) 0 7 1 ( r c o 2 ) ° 7 1 V f p = 0.15 p ^ P 0 , 7 0 2 9 V for2 <N R £ <500 (3.2.20) u p In terms of specific surface (s) 1.18(p-p) 0 7 1 u O - V p V ' 2 9 V r J a U 4 1 for 2 <N R e <500 (3.2.21) Equation (3.2.20) and (3.2.21) show again that as particle diameter increases and specific surface decreases the radial velocity of a particle in a centrifugal field increases. If virtual mass is deemed to be important, it needs to be included as in Equation (3.2.7). The recommended mass of water to be accelerated along with the particle is the mass of water occupying Vi the particle volume [25]. Thus M v = ^ D 3 p P (3.2.22) However, if the terms on the left hand side of Equation 3.2.7 are set to zero, as was done above, Equation 3.2.7 reduces to Equation 3.2.8 and virtual mass does not have an effect on the particle's radial velocity. From here on virtual mass is ignored in this thesis. (b) Inclusion of the Left Hand Side of Equation (3.2.6) In the above analysis the left hand side of Equation (3.2.6) (i.e. —-J-) was set to 0 to dt simplify the analysis. If this were not done then differentiating either of those equations, would lead to an equation giving the position (r) of a particle as a function of time. It is [25] Chapter3. THEORETICAL ANALYSIS 63 d 2 r dr + a — - n r = 0 dt2 dt (3.2.23) This Equation (3.2.23) can be solved if Stokes law is applicable, i.e. if Equation (3.2.12) is relevant. The solution [25] is at r = B 1 e" 7 {B 1 e- k t +B 2 e k t } (3.2.24) from which V =e 2 p k— v 2 y k -B 2 e k t -f a^ k + -v 2 y B i e - k t (3.2.25) i a k + -where B, =—-^-r. and B 2 - — xx 1 2k 1 2k In addition, the initial conditions for Equation (3.2.7) are that at t = 0, r = xx and V r = 0. a = 18|i D 2 p p K p n = 1--P- co k = A / a 2 / 4 + n Equation (3.2.23) and (3.2.24) assume that co is constant which it would be in the case of a tubular centrifuge. However, for a hydrocyclone CO depends on the radial position. For example, Figure 3-2-2 (drawn from data of Hsieh [51]) is a plot of CO vs. r for some experimental data obtained in a hydrocyclone. The 4 parameter logistic equation fitted to Hsieh's data is Chapter3. THEORETICAL ANALYSIS 64 shown on the Figure 3-2-2. Note that co was high near the core of the hydrocyclone but dropped off significantly as r increased. 1000 ct) (Rad/s) 800 600 400 200 811.9963 10 15 20 25 30 Radius Position (10'3 m) 35 40 Figure 3-2-2 Relation between angular velocity (co) and radial position (r). Data from Hsieh [51], page 137, for a hydrocyclone. The above equations can be numerically integrated starting with r = ^ = 0.005 m and V r = 0 at t = 0 and using Equation (3.2.24) to compute V r p in the next time interval. Then the new value for r was computed from r=V r p At (3.2.26) The Equation fitted to the data of Figure 3-2-2 was used to compute co. This procedure was used to produce Figures 3-2-3 ~ 3-2-5 in which V r p , r and N^. are shown as functions of position (r) or time (t) for some of the nylon fibres used in the experimental part of this thesis. Chapter 3. THEORETICAL ANALYSIS 65 The particle diameter used in those calculations was the diameter of a sphere having the same volume as the fibre in question. The numerical calculation was continued until the particle reached a radius of 40 mm which was close to the hydrocyclone wall for the set of data chosen. 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 Radial Velocity (m/s) • 1 mm, 0.17 mg/m v 1 mm, 0.17 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) Radial Velocity (m/s) • 3 mm, 0.17 mg/m » 3 mm, 0.17 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) Radial Velocity (m/s) 0.5 0.4 0.3 0.2 0.1 • 1 mm, 0.68 mg/m T 1 mm, 0.68 mg/m, left-side = 0 0.01 0.02 0.03 Radius Position (m) 1.8 Radial Velocity (m/s) 1.6-1 1.4 1.2-1 1.0 0.8 0.6 0.4 0.2 0.0 • 3 mm, 0.68 mg/m • 3 mm, 0.68 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) Figure 3-2-3 Radial velocity (V ) vs. radial position (r) of spherical particles having the same volumes as nylon fibres having various fibre lengths and coarseness values. Figure 3-2-3 demonstrates radial velocity (V r ) vs. radial position (r) of spherical particles having the same volumes as nylon fibres having various fibre lengths and coarseness values. In each plot one curve is for Equation (3.2.6) and the other is for Equation (3.2.6) with the left hand side set equal to 0. Figure 3-2-3 shows that setting the left hand side of Equation Chapier3. THEORETICAL ANALYSIS 6 6 (3.2.6) equals 0 only resulted in differences in velocity near the hydrocyclone core. The greater the fibre mass, the greater the difference between the two curves in each plot. So for the heavier particles setting the left hand side of Equation (3.2.6) = 0 can have significant effects as this procedure underestimates the radial velocity. Figure 3-2-4 demonstrates radial position vs. time for the various particles used, again with and without setting the left hand side of Equation (3.2.6) equals 0. For all but the longest, coarsest fibre there was no appreciable difference as a result of including or not including the left hand side of Equation (3.2.6). Since this latter particle would have the greatest inertia it is to be expected that it would not move as far in a given time as would an identical particle whose inertia was ignored. Radial Position (m) « 1 mm, 0.17 mg/m • 1 mm, 0.17 mg/m, left-side = 0 Radial Position (m) 0.0 0.5 1.0 1.5 2.0 2.5 Time (sec) Radial Position (m) 0.00 0.25 0.50 0.75 1.00 Time (sec) 1.25 1.50 0.25 0.50 0.75 Time (sec) Radial Position (m) • 3 mm, 0.68 mg/m T 3 mm, 0.68 mg/m, left-side = 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Time (sec) Figure 3-2-4 Radial position of a spherical particle as a function of time. Chapter 3. THEORETICAL, ANALYSIS 67 Figure 3-2-5 indicates that setting the left hand side of Equation (3.2.6) equals 0 does not have a great effect on particle Reynolds number over most of the centrifugal field. It does, however show that many of the Reynolds numbers calculated were above the range of validity of Stokes law, thus calling into question the validity of the numerical integration procedure. • 1 mm, 0.17 mg/m T 1 mm, 0.17 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) • 3 mm, 0.17 mg/m T 3 mm, 0.17 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) 70 60 60 H 40 30 20 10 260 200 150 100 50 • 1 mm, 0.68 mg/m T 1 mm, 0.68 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) • 3 mm, 0.68 mg/m • 3 mm, 0.68 mg/m, left-side = 0 0.01 0.02 0.03 Radial Position (m) Figure 3-2-5 Reynolds numbers (NRe) for the various particles described in Figure 3-2-3 as functions of radial position (r). 3.2.1.2 A Water Swollen, Spherical Particle Now let's consider the motion of a swollen, spherical particle through a fluid in a centrifugal field. To do this adopt the Robertson and Mason [90] concept of a particle as a swollen solid, having a dry density of p f that carries with some immobilized water that has the Chapter3. THEORETICAL ANALYSIS 68 density of water (p). If such a particle was a fibre (fibres are discussed below in Section 3.2.2), this water could be in the fibre lumens or in the fibre walls or even entrapped on the fibre surfaces as a result of fibrillar projections from the surface. Figure 3-2-6 is an idealized diagram of such a particle. In Figure 3-2-6, D f represents the diameter of the spherical particle component of the water/particle composite as it would be in the dry state, and D p represents the effective diameter of the spherical particle in its swollen state. Robertson and Mason [90] utilized this sort of swollen particle model in developing a permeability technique for measuring specific surface (surface area per unit dry mass of particle) and specific volume (volume of swollen particle per unit dry mass of particle). They considered that water associated with their fibres, causing them to swell, was immobile compared to the water flowing around these fibres in a packed bed. In our case the particles are moving and the water is assumed to be immobile. Figure 3-2-6 Idealized wet sphere model. D 5: diameter of dry sphere, D p : diameter of swollen sphere. In our swollen sphere model D p defines a surface inside of which water and solid move together. The velocity of the swollen sphere at this surface relative to the fluid outside of this surface is assumed to be zero (i.e. no slip at the boundary). The mass of the model particle (Mp) is: M p = ^ ( D p - D 3 ) p + | D 3 p f (3.2.27) Chapter3. THEORETICAL ANALYSIS 69 Its projected area (Ap) is: A P = - D 2 P P 4 P (3.2.28) The apparent density (pp) of this sphere is: (pf -p) P P =P + (3.2.29) The specific surface (c), (wet surface area of particle per unit dry mass of solids) of this sphere is: a -PfDf (3.2.30) The specific volume (a, wet volume of particle per unit dry mass of solids) is: a = P f D f 3 (3.2.31) In terms of specific volume the apparent density is P P =P+" oc (3.2.32) Combining Equations (3.2.6), (3.2.27), (3.2.28), (3.2.29), (3.2.30) and (3.2.31) leads to n _ 4 rco2Df3 V = r p 3 D j p Q , (Pf ~ P ) (3.2.33) or, in terms of specific surface (a) 8rcoz(pf -p ) C D p p f a (3.2,34) V, Since co = — , where V t = the tangential velocity of the fluid, r = radial position of the particle, Equation (3.2.19) can be rewritten as: Chapter3., THEORETICAL ANALYSIS 70 y 2 = 8 ( P L Z P ) ^ (3.2.35) p * C^pPfO r Using Equation (3.2.12) for the drag coefficient in the range 0 <N R e <3 1 D r V 2 V r = J - ± l I « _ ( p f - p ) (3.2.36) r p 18 r D p u V K f V ) V ' or, in terms of specific surface (a) and specific volume (a) V r = 2 V - ( p f ~ 2 p ) a f o r O < N R e < l (3.2.37) r u P f a The virtue of Equation (3.2.37) is that it gives the radial velocity in terms of a and a which can be measured using the Robertson and Mason technique [90]. It also requires a measurement of dry particle density. Equation (3.2.36) requires knowledge of wet and dry particle diameters which could be obtained by microscopy. It too requires knowledge of the dry particle density. If Equation (3.2.19) is used for the drag coefficient i . i 8 ( P f - P r r> i x a 4 3 P ° 7 1 p ° " 9 (yi V 7 1 -.0.43 v r J a for 1 <N R e <500 (3.2.38) .1.14 Equation (3.2.38) also indicates that as specific surface increases the radial particle velocity decreases. In both Equations (3.2.37) and (3.2.38) while s appears in the denominator, a appears in the numerator. Is there a relationship between s and a? Yes there is for these ideal particles. It is expressed by Equations (3.2.30) and (3.2.31). For more about this see below in Section 3.2.4. Chapter3. THEORETICAL ANALYSIS 71 3.2.2 For An Ideal, Cylindrical Fibre Model 3.2.2.1 Unswollen Ideal Cylindrical Fibre Model Now let's consider a force balance on an idealized unswollen fibre considered to be a straight, cylinder, see Figure 3-2-7. The mass of this model fibre is given by: Massof DryFibre= M p = (^)D f 2 Lp f (3.2.39) where, pf = the dry fibre density L = the fibre length D f = the diameter of dry fibre Figure 3-2-7 Idealized cjlindrical unswollen fibre model. D f : diameter of dry cylindrical fibre, L: fibre length. When a sphere was used as a model particle the question of orientation was not important since a sphere is symmetrical. However with a fibre it becomes necessary to consider the orientation of the axis of the fibre to the direction of flow. First assume that the fibre is moving so that its length axis is perpendicular to the radial direction of the flow. There is some basis for this assumption in the observations, made by Wong [107] using a high speed video camera capuiring fibre images in the centrifugal fields developed in a rotating tank. Recall that this sort of centrifugal field has a constant value for ? and can be considered to be rigid body Cbapter3. THEORETICAL ANALYSIS 72 motion, whereas in a hydrocyclone there is fluid shear and ? varies with r as illustrated in Figure 3-2-1. Wong observed that fibres inserted into the centrifugal field in his rotating tank tended to retain their original orientation in moving radially outward under the influence of the field. We have no such observations made in a hydrocyclone with which to support or reject our assumption. Thus it remains an assumption. The projected area of the fibre then is assumed to be A p = D f L (3.2.40) Consequently, the specific surface (a) of a unswollen fibre (based on the idealized fibre model) is given by: a = —^— (3.2.41) The specific volume (a) of a unswollen fibre (based on the idealized fibre model set-up) is given by a = — (3.2.42) Pf Combining the equations above (Equations (3.2.39), (3.2.40), (3.2.41), (3.2.42)) with the particle force balance in a centrifugal field (Equation (3.2.6)) and assuming that the left hand side of Equation (3.2.6) = 0, the radial velocity of the unswollen model fibre can be re-written as: rcDf(Pf-P)rco2 ( 3 2 4 3 ) r p 2 pQ, or y 2 = ^ 2 ( P f - P ) ( 3 2 4 4 ) CoPPfO Cbapter3. THEORETICAL ANALYSIS 73 Aidun [1] defined a particle Reynolds Number in terms of fibre diameter, thus the characteristic dimension of the fibre to use in the Reynolds Number of the equation of a unswollen fibre is D f , and N R I = ^ V (3.2.45) He also fitted the following equations to his drag coefficient data: Q = 7 . 7 N £ 8 1 3 for 0.007 <N R e <0.1 (3.2.46) C D = 10.48N^e68 for 0.1 <NR f i <2.0 (3.2.47) Aidun's correlations were obtained using fibres of various materials all of which had lengths greater than 5 mm However, he could not get useful results for fibres which had ratios of the length to width less than 90. The nylon fibres used in this thesis had fibre lengths of 1 and 3 mm Their L / D f ratios ranged from 36 to 235. Wood pulp fibres, particularly mechanical pulp fibres, tend to have fibre lengths less than 5 mm Their L / D f ratios are of the order of 60 [81]. Besides, most of the fibres used by Aidun [1] did not swell in water. Wong [106] studied the motion of various fibres, including the same kind of nylon fibres used in this thesis, in a centrifugal field. His results were correlated by equations similar in form to Equations (3.2.46) and (3.2.47). His equations for wood pulp fibres were Kraft: Q , =113NR c 5 7 1 for 0.007 <NRe <1.0 (3.2.48) TMP: C D = 7 4 N R 0 / 6 3 for 0.007 <N R e < 1.0 (3.2.49) Thus qualitatively there would be no differences in the way a fibre property affected the radial velocity, as a result of using Wong's equations instead of Aidun's. Quantitatively the values of some of the exponents on the various terms would change. Chapter3. THEORETICAL ANALYSIS 74 In the above analysis fibre length does not appear in any of the equations for the particle's radial component of velocity, since it always cancelled out in deriving the velocity equation. Nevertheless it was known that hydrocyclones could fractionate fibres into streams having different mean fibre lengths; see Chapter 2. After doing the above analysis and some searching we found that Cox [26] had proposed a drag coefficient based on a purely theoretical analysis for cylinders. It involves the fibre length to width ratio (L/D f) and thus provides a means of introducing fibre length into the analysis. The range of the Reynolds number for which it is valid was not specified, but it must be from 0 to some small value since his derivation was based on creeping flow. His drag coefficient equation for a circular cylinder (slender body) moving perpendicular to its axis in a viscous fluid is: 8TT N Re K%0 + 0.19315 (3.2.50) Now suppose that the fibre is oriented so that its axis is parallel to the radius instead of perpendicular to it. Then 7tDf2 Using Equation (3.2.43) and (3.2.55) in Equation (3.2.8) leads to V 2 =• (3.2.51) n 2 L ( P f - p ) r c o 2 Q>P (3.2.52) Cox has also provided an Equation for the drag coefficient of a cylinder moving parallel to its axis. It is 16uL 16L l n ( — ) - 0.807 N R e D f l n ( — ) - 0.807 (3.2.53) Chapter3. THEORETICAL ANALYSIS 75 Substituting Aidun's drag coefficient equations (Equation (3.2.46), (3.2.47)) and V t = rco (Vt = tangential fluid velocity assumed to be = to the tangential particle velocity) into Equation (3.2.44), for the radial velocity of the unswollen, cylindrical fibre oriented perpendicular to the radial direction in a centrifugal field yields: _0 .26 (p f - P rD f 1 A84TM.52 r^Tl \0 M u ° - V 1 6 v r j for 0.007 <N R e <0.1 (3.2.54) and 0.84 or V = Z 1 4 ( p L - p J ^0.68pl,2p0,6 v r J .1.52 for 0.007 <N R e <0.1 (3.2.55) 0.24(p f-PrD f" 0^,2p0.24 v2 v r J for 0.1 <N R e <2.0 (3.2.56) or _ l - 4 l ( p f - p ) ' 0.76 0^.52pU8p0.24 v r J .1.28 for 0.1 <N R e <2.0 (3.2.57) Equations (3.2.54) to (3.2 57) show that as specific surface increases or as fibre diameter decreases the fibre's radial velocity diminishes. Coarseness (Q is another fibre property; it is defined as the mass of dry fibre per unit of fibre length. So for an unswollen, cylindrical fibre 4 L 4 f K f - 2 -a p{ (3.2.58) Thus in terms of coarseness Equations (3.2.55) and (3.2.57) become 0 . 3 l ( p f - P ) 0 - 8 4 C ° 7 6 i4°-68Pai6Pr V, = V r j for 0.007 <N R e <0.1 (3.2.59) and V , = 0 .28 ( P f -p ) 0 7 6 C a 6 4 (I0.52p0i4p0.64 fW2 \ 0 7 6 v r J for 0.1 <N R e <2.0 (3.2.60) Chapter3. THEORETICAL ANALYSIS 76 Equations (3.2.59) and (3.2.60) show that as coarseness increases the radial velocity of the fibre increases, thus coarse fibres travel further in a given time than do fine fibres. As a consequence coarse fibres are more likely to reach the wall region of a hydrocyclone and be rejected. This conclusion is in accord with the experimental results reviewed in Chapter 2 and is in accord with my own experimental results reported in Chapter 5. Substitution of Cox's drag coefficient Equation (3.2.50) into Equation (3.2.44) for determining the radial velocity yields: v = 1 (p f -p ) [ ln(L/D f ) + 0.19315]D2 V t 2 r p 16 u r y - - > or V r = ( P f - p ) N L / D f ) + 0 . 1 9 3 1 5 ] ^ up 2 r a 2 or V _ 1 (p f -p ) [ ln(L/D f ) + 0.19315]CV2 r" 4TX up f r Equations 3.2.61 —3.2.63 indicate that other things being equal a long fibre would move faster than a short fibre. Figure 3-2-8 plots fibre radial velocity using Equation (3.2.61) above, vs. radial position in a hydrocyclone using the relation between co and r of Figure 3-2-2 and converting CO to V t by using Equation (3.2.17). Figure 3-2-8 shows that as L goes from 1 mm to 3 mm with constant coarseness value of 0.17 mg/m, there is a slight change in V r as a function of r; at a fixed value of r the longer fibre moves faster. Similarly when considering 1 and 3 mm fibres at a constant coarseness of 0.68 mg/m the same effect is seen but the magnitude of the difference in behaviour of the two kinds of fibres is bigger. Thus longer fibres tend to move faster than short ones and so are more likely to be rejected. This is in agreement with the experimental observations of some of the research reviewed in Chapter 2, but is contrary to the observations noted in Chapter 5 of this thesis. It is also contrary to the conclusions of Cbapter3. THEORETICAL ANALYSIS 77 Mukoyoshi and Ohsawa [74] who observed that fibres having low L / D ratios tended to be rejected in a hydrocyclone. According to Rehmat [85] whether or not a hydrocyclone tends to accept or reject long fibres also depends on the hydrocyclone geometry. V r (m/s) 0.18 -| I . i.. 0.16 - Oo 0 1 mm, 0.17 mg/m, Df = 12.77 nm, a = 273.56 m2/kg V 1 mm, 0.68 mg/m, Df = 27.66 \im, a = 126.30 m2/kg 0.14 -o • 3 mm, 0.17 mg/m, Df = 12.77 nm, a = 273.56 m2/kg 0.12 - <0 0 3 mm, 0.68 mg/m, Df = 27.66 nm, a = 126.30 m2/kg 0.10 - v vO w 0.08 - 0 V 0.06 - vO 0.04 -0.02 -m D O ° D CD° 0 D ° 8 8 ( 1 1 V 0.00 -0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 Radial Position (m) Figure 3-2-8 Fibre radial velocity ( V r ) vs. radial position (r) in a hydrocyclone using Cox's equation. (1 mm with 0.17 mg/m, 0.68 mg/m, and 3 mm with 0.17 mg/m, 0.68 mg/m) When comparing fibres having a common fibre length of 1 mm but coarseness values of 0.17 mg/m and 0.68 mg/m it can be seen that there is a much more significant difference than what was seen when comparing fibre lengths at equal coarseness. This is also true of the 3 mm fibres at the two different coarseness values. Thus it would appear on theoretical grounds, if Cox' equation is valid, that coarseness differences would have more influence on fibre fractionation than fibre length differences. Chapter3. THEORETICAL ANALYSIS 78 The fibre properties used in preparing Figure 3-2-8 were the same as some of the fibres used in our experimental work as discussed in Chapter 5. Fibre length was increased by a factor of 3 from 1 mm to 3 mm and coarseness was increased by a factor of 4 from 0.17 to 0.68 mg/m. To make sure our conclusion that coarseness is more important than length in affecting particle trajectory was not a result of an excessive increase in coarseness, Figure 3-2-9 was drawn wherein the coarseness also was increased by a factor of 3. The conclusion remains the same that changes in fibre coarseness have much greater effects than changes in fibre length. Vr (m/s) I __P 0.14 -.  oo O 1 mm, 0.17 mg/m, Df = 12.77 um, o = 273.56 m2/kg 0.12 -V 1 mm, 0.51 mg/m, Df = 23.81 (im, a = 146.72 m2/kg 0.10 -• 3 mm, 0.17 mg/m, Df = 12.77 nm, a = 273.56 m2/kg ° V v o <X> o 3 mm, 0.51 mg/m, Df = 23.81 nm, a = 146.72 m2/kg 0.08 -w 0.06 - o V v o 0.04 -0.02 -0.00 -•0 v O m a o o D v ° C D ° O o O O V y ° 8 8 8 e § I I I 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 Radial Position (m) Figure 3-2-9 Fibre radial velocity (V ) vs. radial position (r) in a hydrocyclone using Cox's equation. (1 mm with 0.17 mg/m, 0.51 mg/m, and 3 mm with 0.17 mg/m, 0.51 mg/m) That our experimental observations in terms of fibre length are opposite to these theoretical conclusions can be possibly attributed to the presence of turbulence in our hydrocyclone or to Cox's equation not completely specifying the drag force in our hydrocyclone. Chapter3. THEORETICAL ANALYSIS 79 Note that the hydrocyclone used in the calculations of this chapter was the one used by Hsieh [51] because measured velocity data were available for it. The hydrocyclone used in most of our experiments was a different one and had different dimensions. Now consider the case of a fibre moving so that its axis lies along the radius of the centrifugal field instead of being perpendicular to it. Combining Equations (3.2.52) and (3.2.53) gives y = l ( p f - p ) D 2 r c o 2 p 8 \y in terms of fibre diameter, or v = 2(p f -p)rco 2 ln(—)-0.807 (3.2.64) ln(—)- 0.807 (3.2.65) in terms of specific surface, or y = 1 ( P f - P )Ctco 2 P 271 U P f in terms of coarseness. ln (—)- 0.807 T V (3.2.66) Equations (3.2.64) ~ (3.2.66) again show how a fibre's radial velocity in a centrifugal field is affected by fibre diameter, length to diameter ratio, specific surface and coarseness. Comparing Equations (3.2.64) ~ (3.2.66) to Equations (3.2.61) ~ (3.2.63), one can see that the only difference is in the terms in the square brackets and in the values of the numerical constant. While Wong [107] has noted that fibres in a centrifugal field, that have their axes parallel to the direction of motion, tend to move faster than those which are oriented perpendicular to the direction of motion, we are not aware of any useful drag coefficient data correlations for such fibres that could be used to extend the valid Reynolds number range of Equations (3.2.64) to (3.2.66). Chapter3. THEORETICAL ANALYSIS 80 In equations (3.2.56) — (3.2.67) viscosity (p) appears in the denominator. Thus an increase in viscosity should lead to a decrease in a fibre's radial velocity. Our above analysis is for a single fibre that is not affected by fibre-fibre interactions. However, we could relate it to situations, where such interactions occur, via a "pseudo viscosity". The consistency of fibre suspensions can be related to a "pseudo-viscosity", thus as consistency increased, "pseudo viscosity" would increase. Therefore, one would expect that low consistencies would be associated with higher fibre radial velocities and hence more fibres would be rejected at low consistencies than at high consistencies. This was found in our experiments with nylon fibre as can be seen in Chapter 5. 3.2.2.2 Swollen Ideal Cylindrical Fibre Model Next, let's consider a force balance on an idealized wet fibre considered to be a straight, cylinder of dry fibre surrounded by the required amount of water that would be necessary to produce a given value of fibre specific volume (a). See Figure 3-2-10. We do not envision the model fibre as a dry fibre surrounded by a shell of water. The diagram is drawn that way to show how the calculations were made. This model is not very realistic as a model of a wood fibre, see below, but using this model we can calculate the appropriate values of the specific surface and volume, which are measurable quantities, assuming that an appropriate expression for F D is available. Figure 3-2-10 Idealized cylindrical wet fibre model. D f : diameter of dry cylindrical fibre, D p : diameter of swollen cylindrical fibre, L: fibre length. Chapter3. THEORETICAL ANALYSIS 81 The mass of the model fibre is given by: Massof dryfibre=MD = ( - ) D 2 L p f (3.2.67) Mass of waterwithinfibre= M = (—)(Dp - D f 2 ) L p (3.2.68) where, p = the water density p f = the dry fibre density L = the fibre length D f = the diameter of dry fibre D p = the diameter of wet fibre Accordingly, the total wet fibre mass is given by M p = M p f + M p w =( | ) [pD 2 p + (p f -p)Df]L (3.2.69) If the fibre is moving so that its length axis is perpendicular of the radial direction of the flow, then the projected area (Ap) of a cylindrical fiber (idealized fibre model) could be written as: A p = D p L (3.2.70) and the apparent density of the wet fibre (p ) is proposed as: P P = P + § r ( P f - p ) (3-2 7 1) p In the idealized fibre model, as in Figure 3-2-10, the contribution to the specific surface of the cylindrical particle, of the ends of the cylinder are ignored. Table 3.2.1 provides the justification for this showing that the effect of the ends of the cylinder is insignificant compared to the rest of the surface of the cylinder. Let's define A is the surface area of a cylinder without the ends, and A' is the surface area of a cylinder with the ends. Chapter3. THEORETICAL ANALYSIS 82 Table 3-2-1 Comparison of the Calculated Total Surface Area of a Fibre Cylinder With (A) and Without (A) the Ends. Fibre Length (mm) Avg. Fibre Width (mm) A (mm2) A' (mm2) A/A' 1 0.02 0.0628 0.0634 0.991 3 0.02 0.1885 0.1891 0.997 Consequendy, the contribution of the fibre ends to specific surface can be safely ignored and the specific surface (a) of a swollen fibre (based on the idealized fibre model set-up) is given by. 4 D „ DfPf (3.2.72) The specific volume (a) of a swollen fibre (based on the idealized fibre model set-up) is given by: Dl a = D 2 p f (3.2.73) The apparent density of the wet fibre (pp) (based on the idealized fibre model setup) can also be written as: PP =P + -a 1-Pf (3.2.74) Coiribining Equation (3.2.72) and (3.2.73), D P can be shown as: 4oc D = — P c (3.2.75) Chapter3. THEORETICAL ANALYSIS 8 3 Introducing Equation (3.2.75) into Equation (3.2.74), the apparent density could also be presented as: P P = P + 1--P- (3.2.76) Combining the equations above (Equation (3.2.69), (3.2.70), (32.71), (3.2.72), (3.2.73), (3.2.78)) with the particle force balance in a centrifugal field (Equation (3.2.1) to (3.2.6)) and assuming that the left hand side of Equation (3.2.6) = 0, the radial fibre velocity can be re-written as: V. 2 = 27trco ( P f -p ) (3.2.77) C D p p f a Use Aidun's equations (Equations (3.2.46) and (3.2.47)) for the drag coefficient and a Reynolds number based on the swollen particle diameter (Dp) D p V r P N R e = - (3.2.78) Substituting Aidun's drag coefficient equations (Equation (3.2.48), (3.2.49)) and V t = rco (Vt: tangential velocity) into Equation (3.2.77), for the radial velocity of the idealized wet fibre model oriented perpendicular to the radial direction in a hydrocyclone yields: 2 . 5 2 ( p f - P r « ° „ 1.52 - 0.16. . 0.68 ,. 0.84 s p u P f (pf -p) V 2 V r J 2.52 p 0.16^0.68 v r / 0.84 1 (on (3.2.79) .0.84 for 0.007<NRe <0.1 V. = 1 . 3 9 ( p f - P r a 0.52 fyl \0 7 6 , s 1 2 8 p 0 . 2 4 ^ O 5 2 p 0 7 6 1.39 p 0.24^0.52 (Pf-P) v r J 0.76 Pf fW2 \ v r y j ,0.76 / \0.52 (3.2.80) for 0.1<NR e <2.0 Chapter3. THEORETICAL ANALYSIS 84 It should be noted that Equation (3.2.79) and (3.2.80), indicate that fibres with high values of specific surface have lower radial velocities than fibres with low values of specific surface, thus the low specific surface fibres are more likely to be rejected. This agrees with Karnis and Wood's experimental findings [56,110]. Note that, fibre length does not appear, as it cancels out of the equations. Thus, Equations (3.2.79) and (3.2.80) show that the radial velocity has an inverse relationship with specific surface (a) but fibre length does not appear in these equations. This indicates that hydrocyclones can fractionate fibres on the basis of specific surface differences. These equations also show that fibres having high values of specific volume/ specific surface ratio are more likely to be rejected. However, there also may be some kind of a secondary effect where fibre length plays an important role; using Cox' equations for fibre drag coefficients does result in showing how fibre length can play a role. See below. Combining Equations (3.2.58), (3.2.72)) and (3.2.73), the following equation was obtained: C = ^ £ (3.2.81) a In addition, if Equation (3.2.81) is introduced into Equation (3.2.79) and Equation (3.2.80), then Equations (3.2.79) and (3.2.80) can be re-written in terms of coarseness as: 0.32 ( p f - p H C 0 7 6 ( V. -.0.08 - 0.16 ..0.68 - 0.84 V r J 0.27(Pf-prC Vr p a0.12p0.24^ 0.52p0.52 ,0.76^ 0.64 (y2 "\0 7 6 v r J for 0.007<NRe <0.1 (3.2.82) for 0.1<NR e<2.0 (3.2.83) Equation (3.2.82) and Equation (3.2.83) also indicate that the coarser fibres, which move with higher radial velocities, will be preferentially rejected. Chapter3. THEORETICAL ANALYSIS 85 Substitution of Cox's drag coefficient (Equation (3.2.50)) into Equation (3.2.77) for re-solving the radial velocity yields: for fibres moving with their axes perpendicular to the radial direction 0.06(pf - p ) D In + 0.19315 _ { / p ) _ V.2 up fa (3.2.84) 0.25( P f-o) or fr / > In + 0.19315 a V p) V2 (3.2.85) 0.0l( P f -p) or V. = fr / > In [LA] + 0.19315 r (3.2.86) It is worth noting that Equation (3.2.86) also indicates that the coarser fibres have a preference to be rejected. For fibres having their axes parallel to the radial direction the radial velocity is of the same form, differing only in the term inside the square brackets and the numerical constant. Thus our conclusions about the effects of specific surface, specific volume/specific surface ratio and coarseness are qualitatively the same. Fibre Model of L i etal. [65] Li et al. [65] have proposed a somewhat different model of an ideal swollen, cylindrical fibre. It is diagrammed in Figure 3-2-11. Chapter3. THEORETICAL ANALYSIS 86 Figure 3-2-11 Li et al.'s ideal cylindrical fibre. D c is the outside diameter of a dry fibre containing a lumen which has diameter dD. When swollen in water D 0 becomes D w and d 0, becomes cv Fibre coarseness is designated as C (they used the symbol c). The apparent density (p.) of Li et al.'s swollen fibre is C + % ( D 2 w - ( D 2 - d 2 ) ) 4 — D 2 4 w C = > f w ( D 2 - d 2 ) 4 where p f w = density of the dry fibre wall. From Equations (3.2.87) ~ (3.2.88) (3.2.87) (3.2.88) Pa=P + = P + (p f w-p)[Do-d 2 ] D Do (Pfw-pXDo-d 2 ] Dl = p + k D (3.2.89) 2 ( p f w - p ) [ D o - d o ] D D Q and dG can be found by microscopy. Li et al. assumed that D G / D W was a constant = k This assumption was based on some experimental data of Stone et al. which indicated that when a fibre swelled it did so in terms of Chapter3. THEORETICAL ANALYSIS 87 increasing fibre wall thickness rather than in terms of increasing fibre diameter. Li et al. interpreted this to mean that k ~ 1. They defined an apparent density factor (AD) such that A D = ( P l z i ) (3.2.90) thus P a = k 2 ( P f w - P ) A D + p (3.2.91) Li et al. have used a dry fibre wall density (PfJ while we have used a dry fibre density (ignoring the presence of a lumen). Since a fibre of known dimensions must have the same mass using both measures of density and since the dry fibre diameter would be the same, i.e. D f = D„ then Pf = ( J 2 \ 1 — P „ (3-2.92) From Equations (3.2 88) and (3.2 90) one can see that 4 C TCPfwDo A D = ——^ - j - (3.2.93) Thus, A D can be related to fibre coarseness. Introducing Equation (3.2 81) A D = - ^ r (3.2.94) Thus, A D is shown to be related to fibre specific surface and volume. So we can conclude that the model of Li et al. is basically the same as the model we have used but involving some different terminology. Their model requires determination of D 0 and d c using a confocal microscope technique and assuming that a fibre doesn't change in outer diameter when it swells. Our model requires determining a and a using Robertson and Mason's water Chapter3. THEORETICAL ANALYSIS 88 permeability technique and requires no further assumptions. Both models require a measurement of p f w or pf. Relationships among Specific Surface, Specific Volume and Coarseness Above we have shown that for our swollen, cylindrical model fibre that c = ^ ^ - (3.2.72) D f 2 p f ^ ' D 2 a = - ^ - (3.2.73) D f 2 p f D = — (3.2.75) P a C = ^ (3.2.81) a Equation (3.2.81) implies that coarseness varies as 1/fJ2. In our theoretical model, the specific volume (a) and specific surface (a) are not independent. See Equation (3.2.72), Equation (3.2.73) and Equation (3.2.75). Figure 3-2-12 illustrates relationships between specific surface and coarseness value using experimental data and calculated data for wheat straw pulps and aspen pulps [19]. The calculated values were obtained using Equation (3.2.81) and inserting the measured values of a and a. The curves of Figure 3-2-12 support qualitatively Equation (3.2.81) in as much as the plots of C vs. l / o 2 are linear. But Equation (3.2.81) does not fit the data quantitatively, which might be due to our modelling a refiner treated fibre as a simple cylinder. Chapter3. THEORETICAL ANALYSIS 89 1 „ d c Coarseness (mg/m) 1.0e-6 H 8.0e-7 H 6.0e-7 4.0e-7 2.0e-7 i • Wheat Straw Pulps exp. data T Aspen Pulps exp. data O Wheat Straw Pulps cai. value 7 Aspen Pulps cai. value . — f 0 1e-6 2e-6 3e-6 4e-6 5e-6 6e-6 7e-6 1/c 2 (kg2/m4) Figure 3-2-12 Fibre coarseness value vs. specific surface for wheat straw pulps and aspen pulps Compare Figures 3-2-13 and 3-2-14, the former shows the complexity of TMP wood pulp fibres (data of Rehmat [85]); the latter the simplicity of nylon fibres, which are close to being cylinders, used in this thesis. Figure 3-2-D Microphotographs of TMP fractionation. Data from Rehmat [85]. Chapter3. THEORETICAL ANALYSIS 90 Figure 3-2-14 Microphotographs of nylon fibres. (1 mm, 0.68 mg/m) If one takes as typical fibre dimensions length = 1 mm and diameter = 30 ixm with a cell wall thickness of 12 jxm and uses a dry fibre density of 1500 kg/m 3, the value for specific surface calculated by Equation (3.2.41) is 88.9 mVkg (92.5 if one allows for a 6 p.m diameter lumen). This value is quite a bit lower than the usual values measured by Robertson and Mason's [90] permeability technique, which are in the range 200 — 6000 kg/m 2. While use of a simple cylinder as a model to represent a wood pulp fibre may not be very realistic, nothing better, that is simple enough to deal with in the way we have done in the above analysis, comes to mind. Figure 3-2-15 is a plot of the specific volume (a) vs. specific surface (a) for refined chemical pulps using data taken from various sources. Each curve represents a refining trial, the unrefined pulp is the lower left hand symbol for each curve and as one moves up the curve to the right the degree of refining increases. It can be seen that as a increases a initially increases and then tends to level off. These plots are probably more indicative of the degree of refining than they are of any mtrinsic relationship between o and a, but they seem to be the only kind of data available. One can use Equation (3.2.75) and values of a and a to calculate values for the Chapter3. THEORETICAL ANALYSIS 91 swollen fibre diameter D p , but if one does that the values obtained (3 ~ 30 pm) are less than typical dry fibre diameters. o oocs:pecific V o l u m e (™3fog) 0.005 A 0.004 A 0.003 A 0.002 A 0.001 A 1 1 1 1 1 1 0 1000 2000 3000 4000 5000 6000 Specific Surface (m2/kg) Figure 3-2-15 Relationships between specific surface and specific volume for refined chemical pulps. Data of [19,90,104] 3.3 Reynolds Number Of A Fibre Moving Ins ide A Hydrocyclone Aidun's [1] drag coefficients for fibres are valid over fibre Reynolds number ranges of 0.007 -0.1, and 0.1 ~2.0. Wong's [107] data cover the range 0.007 -1.0. If we knew a typical range of fibre Reynolds numbers inside a hydrocyclone, we could determine whether the cited drag coefficients were valid for use in hydrocyclones. To check this we did the following calculations. Using fluid velocity data given as a function of radial position from Hsieh [43], see Figure 3-2-2, the drag coefficients which Aidun suggested (Equation (3.2.49)), and assuming that Chapter3. THEORETICAL ANALYSIS 92 nylon fibres do not swell [98, 100], Equations (3.2.1 ~6, 3.2.39, 3.2.40, 3.2.41, and 3.2.42) were combined to obtain the radial velocities of nylon fibres. Then, using these values, the fibre diameter and the density and viscosity of water, the range of Reynolds numbers of the fibres could be determined. (Equation (3.2.45)) 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 Radial Position (m) Figure 3-3-1 Calculated Reynolds number using Aidun's drag coefficient for a non-swollen nylon fibre of various coarseness values moving inside a hydrocyclone. Based on Hsieh's data [51]. Figure 3-3-1 shows that the calculated Reynolds numbers of the selected nylon fibres in a hydrocyclone ranged from 0.08 to 1.3, which was low enough that Aidun's correlations [1] (Equation (3.2.46) and Equation (3.2.47)) could be used for calculating particle trajectories (based on Hsieh's data [51]). However, it is important to again point out that, these may not be valid for fibres that are shorter than 5 mm. In addition, the calculated Reynolds numbers were quite different when using Aidun's drag coefficients compared to using Cox's drag coefficients Chapter3. THEORETICAL ANALYSIS 93 [26] (Equation (3.2.50)); see Figure 3-3-2. Of course Cox's drag coefficients are probably invalid at Reynolds numbers greater than 1. Figure 3-3-3 demonstrates the Reynolds number for a swollen fibre of various coarseness values and fibre lengths using both Aidun's and Cox's drag coefficients assuming this swollen fibre has a specific volume (a) = 0.004 mVkg. This value for specific volume was chosen because it is in the middle of the range of values measured for wood pulp fibres. The diameter of the swollen fibre and the specific surface (a) could be calculated from Equation (3.2.73) and Equation (3.2.75), then the Reynolds number could be determined. It shows that whether a fibre swells or not has a significant effect on the Reynolds number. 20 16 12 8 H CD CD • • • D • J • — 0 -V n o • o 0.17 mg/m Aidun's C D 0.34 mg/m Aidun's C D 0.68 mg/m Aidun's C D 1 mm, 0.17 mg/m_Cox's C D 1 mm, 0.34 mg/m_Cox's C D 1 mm, 0.68 mg/m_Cox's C 0 3 mm, 0.17 mg/m_Cox's C D 3 mm, 0.34 mg/m_Cox's C D 3 mm, 0.68 mg/m Cox's C D 0.000 0.005 0.010 0.015 0.020 0.025 Radial Position (m) 0.030 0.035 0.040 Figure 3-3-2 Calculated Reynolds number using both Aidun's and Cox's drag coefficients for a non-swollen nylon fibre of various coarseness values and fibre lengths moving inside a hydrocyclone. Based on Hsieh's data [51]. Chapter3. THEORETICAL ANALYSIS 94 20 8 4 • o —O— 0.17 mg/m Aidun's CD swollen • p ' 0.34 mg/m Aidun's CD swollen n • m 0 0.68 mg/m Aidun's CD swollen O 1 mm, 0.17 mg/m_Cox's C,j_swollen • • V 1 mm, 0.34 mg/m Cox's Cu swollen CD D a 1 mm, 0.68 mg/m_Cox's C s^wollen O-O n o 3 mm, 0.17 mg/m_Cox's C s^wollen 0 3 mm, 0.34 mg/m Cox's C,^  swollen • • o 3 mm, 0.68 mg/m Cox's CD swollen • v wXr v • • w y > "" oo V X • 0 0 ° ooo^ gggj -o-&§ 1 1 r 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 Radius Position (m) Figure 3-3-3 Calculated Reynolds number using both Aidun's drag coefficient and Cox's drag coefficients for a swollen nylon fibre of various coarseness values and fibre lengths moving inside a hydrocyclone. Based on Hsieh's data [51]. 3.4 Separation Efficiency On Mass Basis (SE.J In thinking about fibre fractionation one needs some measure of how effective a hydrocyclone, as a fractionating device, is in sending particular fibres to one of two outlets, e.g. coarse fibres to the rejects and fine fibres to the accepts. One way of doing this is to define separation efficiencies. Separation efficiency on mass basis is defined as mass fraction of coarse fibres rejected (SEmC/R) or mass fraction of fine fibres accepted (SEmF/A). The method used to determine the mass separation efficiency is described below. First, let's consider that there is a total of N fibres in the feed, and they can be characterized as long or short; coarse or fine, therefore, Chapter3. THEORETICAL ANALYSIS 95 M , 'Nfibres = f n C F N Q L c + f n F F N G F L F (3.4.1) L Nfibres — f n C F L c N + f n F F L p N (3.4.2) •^Nfibres _ ^ n C r O ^ C ^ n F F ^ F ^ F Nfibres f n C F L c + f n F F L F (3.4.3) Numberof CoarseFibresintheFeed TotalNumberof Fibre; in the Feed (3.4.5) nFF — Numberof Fine Fibres in the Feed TotalNumberof Fibres in the Feed (3.4.6) where, M ^ r e s = total mass of N fibres in the feed LjMfibres = total length of N fibres in the feed Q = coarseness value of a coarse fibre Q = coarseness value of a fine fibre = length of long fibre 1^  = length of short fibre L c = length of coarse fibre Lj: = length of fine fibre fnCF = number fraction of coarse fibres in feed f,^ = number fraction of fine fibres in feed • Number Fractions Number fractions of the rejects and the accepts are defined as following: f n c R = number fraction of Coarse fibre in the Rejects fnFR = number fraction of Fine fibre in the Rejects f n c A = number fraction of Coarse fibre in the Accepts fnFA = number fraction of Fine fibre in the Accepts Chapter3. THEORETICAL ANALYSIS 96 I) Assume there are two components in the Feed each having the same fibre length but two different coarseness values (L = L c = Lp). Note that the average coarseness value of the rejects and the accepts and the average length of the rejects and accepts are calculated from the F Q A measurement, (more details in Chapter 4) f „ C R + U = l (3-4.7) f n C A + f n F A = l (3 A S ) AverageRejectsCoarseness= C R = f n C R C c + f ^ C p (3.4.9) AverageAcceptsCoarseness= C A = f n C A C c +f n F A Cp (3.4.10) There are 4 unknowns and 4 equations (3.4.7 — 3.4.10), then introducing Equation (3.4.7) to Equation (3.4.9), fnCR can be solved as: fnCR=^5^ (3-4.11) Introducing Equation (3.4.8) to Equation (3.4.10), fnCA can be solved as: f „ C A = - ^ L (3-4-12) Similarly, f ^ and f,^ can be solved as: (3-4.13) ^ F f n E R = ^ 1 ^ (3-4.14) II) Next assume there are two components in the Feed each having the same coarseness value but two different fibre lengths (C = Q = Q) . U + f n L R = l (3-4.15) Chapter3. THEORETICAL ANALYSIS 97 f n S A + f „ L A = l (3A16) AverageRejects Fibre Length = L R = f n S R L s + f n L R L L (3.4.17) AverageAcceptsFibreLength= L A = f n S A L s + f n L A L L (3.4.18) Introducing Equation (3.4.15) to Equation (3.4.17), fnSR can be solved as: Introducing Equation (3.4.16) to Equation (3.4.18), fnCA can be solved as: f " S A = r r r ^ (3-4-20) Similarly, f ^ and can be solved: f n L A = ^ ^ (3-4.21) f n L R =^f^ (3A22) • Mass Fractions Mass fractions of the feed, rejects and the accepts are defined as following: fmCF = mass fraction of Coarse fibre in the Feed froFF = mass fraction of Fine fibre in the Feed fm C R = mass fraction of Coarse fibre in the Rejects fnjR = mass fraction of Fine fibre in the Rejects fm C A = mass fraction of Coarse fibre in the Accepts f ^ = mass fraction of Fine fibre in the Accepts Considering a total of N fibres in the Feed, thus Chapter3. THEORETICAL ANALYSIS 98 Total mass fibres in the Feed = N f n C F C c L c + N f n F F C p L F (3.4.23) Mass coarse fibres in the Feed = N f n C F C c L c (3.4.24) Mass fine fibres in the Feed = N f n F F C F L F (3.4.25) where, fnCF N = Number of coarse fibres in the Feed fnFF N = Number of fine fibres in the Feed Q L C = mass of 1 coarse fibre CpLj: = mass of 1 fine fibre From Equation (3.4.23) and (3.4.24), the mass fractions of the coarse fibres in the Feed (fmCF) and the mass fraction of the fine fibres in the Feed (f^) can be obtained as: f = f n C F Q L ^ f r i +f r i 1 n C F V > C 1 - ' C o F F M 1 F f = f n F F C F L F ft 4 27) m F F f C L +f C L K ' nCFM) C n F F M ' F Similarly, the mass fractions of the coarse fibres in the Rejects (fmCR), the mass fraction of the coarse fibres in the Accepts (fmCA), the mass fraction of the fine fibres in the Rejects ( f ^ and the mass fraction of the fine fibres in the Accepts (t^^) can be obtained as: f mCR = 7 f n C R C c f L c (3-4.28) fnCR^-'cLc + f n F R Q ; L F f r A = L C A C C L C / 3 4 2 9 x m C A f r L +f C L 1 n C A V j C i - ' C nFAMF F f ^nFR^-'F^F / 3 4 3 0 X f C L +f C L f = W ^ L F (3 4 31) f C L +f C L K 1 n C A ^ C ^ C ^ 1 nFAM= ^  F Chapter3. THEORETICAL ANALYSIS 99 For Case (I) - two components of fibres in Feed having the same fibre length but two different coarseness values (L = Lj = 1^), the mass fractions of the coarse/fine fibres in the Feed, Rejects and Accepts can be simplified as: f m C F = — ( 3 . 4 . 3 2 ) ' n C F ^ C + ^ F F ^ r n C F ^ C + nFF F Lc* = f ^ r (3A34) r n C R ^ C + r n F R ^ F Lc, = ( !:CffC r (3A35) r n C A ^ C + r n F A * ^ F ^mFR ~ r ^ C ^ n C R ^ C + r n F R ^ F f = L F A Q / 3 4 3 7 \ m F A f c +f a K ' 1 n C A V j C ^ 1 n F A M = Similarly, the mass fractions of the short/long fibres in the Feed, Rejects and Accepts of Case (II)- two components of fibres in Feed having the same coarseness value but two different fibre lengths (C = Cc=Ce) can be obtained as: f S F = f " s p L s (3.4.38) fm L F = f / ^ f / . (3-4.39) ^nSF-^S + I n L F i j L f L ^ n S R ^ S + f n L R L L fm S R = r 7 T (3.4-40) f L m S A f L +f L K ' 1 n S A A " S nLA L Chapter3. THEORETICAL ANALYSIS 100 fm L R = r / n L ^ L , (3A42) t n S R i j S + r n L R i j L fm L A = f / " L ^ L - (3A43) ^nSA-^S + r n L A ' L L • Separation Efficiency on Mass Basis (SE,,,) Coarseness (Case I) The mass separation efficiency for separation by coarseness is defined as a ratio of the mass of coarse fibres in the Rejects divided by the mass of coarse fibres in the Feed (SEmC/R), or as the ratio of the mass of fine fibres in the Accepts divided by the mass of fine fibres in the Feed (SEJF/A). These are two definitions of separation efficiency, which one to use depends on the objective of the fractionation process - to reject coarse fibres, accept fine fibres or some of both. O T n Mass of CoarseFibres in the Rejects , ^ l t A \ SE m C / R = :—: — — (3.4.44) Mass of Coarse Fibre; in the Feed „ , . Mass of Fine Fibres in the Accepts ,„ . . . . SE m F / A = — : — (3.4.45) Mass of Fine Fibre; in the Feed Mass of Coarse fibres in the Feed = Fx F f m C F (3.4.46) Mass of Coarse fibres in the Rejects = RxRf m C R (3.4.47) Mass of Coarse fibres in the Accepts = Ax A f m C A (3.4.48) Mass of Fine fibres in the Feed = Fx F f ^ p (3.4.49) Mass of Fine fibres in the Rejects = Rxj^f^R (3.4.50) Mass of Fine fibres in the Accepts = Ax A f m F A (3.4.51) where, F = Feed flowrate Chapter3. THEORETICAL ANALYSIS 101 R = Rejects flowrate A = Accepts flowrate xF = Feed consistency xR = Rejects consistency xA = Accepts consistency Combine equations (3.4.44), (3.4.46) and (3.4.47), S E m C / R = R ' m C R (3.4.52) Introducing equations (3.4.32) and (3.4.34) to Equation (3.4.52), the mass separation efficiency of mass fraction of coarser fibres rejected can be obtained as: S E m C / R = r x (3A53) r ' X F t m C F l t n C R ^ - ' C + n F R ^ T / (Combining equations (3.4.45), (3.4.49) and (3.4.51), A Y f S E m F / A = A ( 3 . 4 . 5 4 ) F X F * mFF Introducing equations (3.4.33) and (3.4.37) to Equation (3.4.54), the mass separation efficiency of the mass of fine fibres accepted can be obtained as: S E m F / A = A x A f n F A C F ( 3 A 5 5 ) F X F * m F F V f n C A Q ; + I n F A ^ F ) In addition, substituting equations (3.4.11) and (3.4.14) to Equation (3.4.53), S E m C / R can be re-written as: F X F ^ mCpKOt. _ Q r^C + (O: ~ Q. )Q ) Substituting Equation (3.4.12) and (3.4.13) to Equation (3.4.55), S E m F / A can be re-written as: Chapter3. THEORETICAL ANALYSIS 102 FXptmFF ((O: - QL )Cp + ( C A - Cp ) C C ) Bradley [17] and Svarovsky [101] have described the calculation of separation efficiency for hydrocyclones. For a hydrocyclone that is only separating solids from liquid they defined a gross separation efficiency as Mass of Solids in the Re jects Rx R . . SE = " ~ — ; — • — (3.4.58) Mass of Solids in the Feed Fx F Now suppose that a hydrocyclone did not achieve any concentration of solids in the rejects compared to the feed concentration, for example if the solids density was equal to the liquid density, any separation of solids that would come about would be attributable only to flow-splitting. Thus xF = xR = xA and from Equation (3.4.58) SE = - | (3.4.59) R / F is finite and positive but it has not been achieved as a result of any centrifugal effects. So a corrected (for flow-splitting) separation efficiency was defined as [17,101] S E c o r r = | ^ - | = | ( ^ - l ) (3.4.60) Fx F F F x F Equation (3.4.60) takes care of the flow-splitting problem, however now suppose that the solids are easy to separate from the liquid and all of them were rejected. Then in terms of removing solids in the rejects stream we should have a separation efficiency of 1.0 or 100%, but SE C 0 I T would be (1.0 - R/F), a number less than 1.0. Thus SE c o r r is unsatisfactory for easy to separate solids. So they defined another corrected separation efficiency as SE„„ = SE corr R F X R _ y Xp 1 - * F 1 - * F (3.4.61) Chapter3. THEORETICAL ANALYSIS 103 1-R/F is the fraction of the feed flow from which solids were separated as a result of centrifugal effects. Equation (3.4.61) gives SE c t r = 0 when there is no separation and SE c t r = 1.0 when all the solids are rejected. Now let's reconsider our separation efficiency as defined by Equation (3.4.56). We are concerned in this thesis with fibre fractionation, as distinct from separation of fibres from water. Thus Equation (3.4.56) is our gross separation efficiency. We could achieve a gross separation efficiency for getting coarse fibres into the rejects of 1.0 (100%) by merely rejecting all of the fibres, including of course all of the coarse fibres, thus all of the feed fibres would report to the rejects and none would go to the accepts. We have then a number that indicates a perfect separation but in fact no fractionation would have occurred since the coarse and fine fibres in the rejects would be present in the same proportions as they were in the feed. We could define a corrected separation efficiency as S E „ C / R„„,, = r m C R -Rx f ™ Rx. Rx R ^ F ^ m C F FXp Fx F mCR f y 1 m C F (3.4.62) But this would suffer from the same defects as Equation (3.4.60) for solid liquid separation. By analogy define a SE c t r for fractionation as (i \ f m C F ' (3.4.63) Rx R S E C / R „ , = — -1 -Fx F If there were no fractionation fmCR would = fmCF and S E m C / R would be 0. For a perfect separation fm C / R would be 1.0. Thus all the coarse fibres would be in the rejects and all the fine fibres would be in the accepts. Do a mass balance on the coarse fibre fraction Fx F f m C F = Rx Rf m C R + Ax A f m C A (3.4.64) Chapter3. THEORETICAL ANALYSIS 104 For a perfect separation the rejects stream would be all coarse fibres thus fm C R would be equal to 1.0 and fm C A would be equal to 0. Then Fx F f m C F = Rx R (3.4.65) or fm C F = | ^ (3.4.66) Fx F Substituting fmCR =1.0 and for fmCF from Equation (3.4.65) into Equation (3.4.63) leads to Equation (3.4.67) S E m R / Q t r =1.0 (3.4.67) which is what it should be. In a similar manner separation efficiencies corrected for centrifugal effects on fibre fractionation can be defined for S E m F / , SE^/R^,. , SE^L/A^, etc. Fibre Length (Case II) The mass separation efficiency on fibre length is defined as a ratio of the mass of short fibres in the Rejects divided by the mass of short fibres in the Feed (SEmS/R), or as the ratio of the mass of long fibres in the Accepts divided by the mass of long fibres in the Feed (SE m L/ A). Mass of Short fibres in the Feed = Fx F f m S F Mass of Short fibres in the Rejects = Rx R f m S R Mass of Short fibres in the Accepts = Ax A f m S A Mass of Long fibres in the Feed = Fx F f m L F Mass of Long fibres in the Rejects = Rx Rf m L R Mass of Long fibres in the Accepts = Ax A f m L A Chapter3. THEORETICAL ANALYSIS 105 SE m S/R and S E m L / A can be solved by using similar methods to those described above for the mass separation efficiency based on coarseness. Therefore, S E m S / R = ^ X R f " S R L s r (3.4.68) FX Fl"mSFvfnSRLs + f nLR^L ) S E m L / A = r (3.4.69) ^ F f m L F V n S A ^ S + f n L A L l J Substituting equations (3.4.19), (3.4.22) to Equation (3.4.68) and equations (3.4.20), (3.4.21) to Equation (3.4.69), S E m S / R = R x R ( L L - L R ) L s ( 3 A 7 Q ) F x F f m S F ( l L L - L R J L S + l L R - L s j L L j S E m L / A = / / r A X R ^ A ) T " L d L L r U ) ( 3 A 7 1 ) F x F r m S F ( ( L A - L s J L L + ( L L - L A ) L s ) • Corrections to The Separation Efficiency Let's reconsider mass separation efficiency, for two possible cases, which were named Case A, and Case B. Case A represents no fractionation. Case B represents perfect fractionation (for a two component system). Case A - no separation, all fibres rejected (xA = 0). Thus from a fibre mass balance Fx F = A x A + Rx R = Rx R (3.4.72) Substituting Equation (3.4.72) into Equation (3.4.52), then S E r a C / R = ^ (3.4.73) *mCF Now consider a coarse fibre balance on the Feed, Rejects and Accepts streams. The following equations were obtained. Chapter3. THEORETICAL ANALYSIS 106 f m C F F X F = f m C A A x A + f m C R R x R (3.4.74) but xA = 0, so fmCpFxp =f m C R Rx R (3.4.75) Introducing Equation (3.4.72), Equation (3.4.75) can be re-written as: f m C F = f m C R (3-4.76) From Equation (3.4.73) and Equation (3.4.76), SE m C/R=l . But there would be no fractionation since all the fibres were rejected. Therefore, this definition of the mass separation efficiency (SE) is not too good and needs to be corrected. Case B - perfect separation, all coarse fibres to the rejects and all fine fibres to the accepts (or all short fibres to the rejects and all long fibres to the accepts) Since only coarse fibres are in the rejects, fm CR=l. Therefore, Rx S E m C / R = (3.4.77) Fx f F mCF Equation (3.4.77) could give a S E m C / R of less then 1, which is not practical for a perfect separation. So we corrected for mass reject ratio using the following two equations.. Rxp SE C / R _ =• Fx F Ax 4 f 1 mCR y \ ^ m C F ft \ SE F / A = 4 P -m corr mFA I - 1 ^ mFF J (3.4.78) (3.4.79) Fx F Next, let's apply these corrected mass separation efficiencies to the same two cases (Case A and Case B) again. Case A - all fibres rejected (fmCR = fmCF). S E m C / R c o r r = 0 (3.4.80) Equation (3.4.80) indicates no fractionation, which is as it should be. Cbapter3. THEORETICAL ANALYSIS 107 Case B - prefect separation (fmCR = 1). Equation (3.4.78) can be rewritten as: Rx SE C / R = R FX,; — 1 mCF (3.4.81) Again, applying the coarse fibres balance (Equation (3.4.74)). f m C F ^ X F — R"XR From Equation (3.4.82), the following equation can be obtained. Rx„ (3.4.82) f mCF — " Fx, (3.4.83) Therefore, SE C / R „ = FX,: Fxp Rx D — 1 Rx, Fx P (3.4.84) Equation (3.4.84) can be less then 1, which is not acceptable for a perfect separation. So, again, we need another correction to the mass separation efficiency. Let's try the centrifugal correction (SEmC/R t r i or S E m F / A ^ . SE „ C / R „ SE m F / A , =• Rx R Fx F 1 m C R k f mCF 1 Rx R Fx F A x A l"mFA Fx F k ^ mFF 1 A x A Fx F -1 (3.4.85) -1 (3.4.86) Considering the same two cases: Case A - all fibres rejected (fmCR = fmCF). S E m C / R c t r = 0 (3.4.87) Chapter3. THEORETICAL ANALYSIS 108 Equation (3.4.87) represents no fractionation, which is as it should be. Case B - prefect separation (fmCR = 1). Introducing equations fmCR = 1 and (3.4.83) to Equation (3.4.85) = 1 (3.4.88) Equation (3.4.88) now represents the perfect separation (all coarse fibres to the rejects, all fine fibres to the accepts). In addition, if all of the coarse fibres were in the rejects S E m C / R would be 1; if none of the coarse fibres were in the rejects S E m C / R would be 0. Similarly, if all of the fine fibres were in the accepts S E m F / A would be 1 and if none were in the accepts it would be 0. If we multiply SE m C/R, which indicates the degree of success in getting coarse fibres into the rejects, by S E m F / A , which indicates the degree of success of getting fine fibres into the accepts we have some sort of measure of overall effectiveness (SE m C/RF/A). This measure of efficiency at least fits at the end of the range, i.e. when separation is perfect (all coarse fibres in the rejects, all fine fibres in the accepts), S E m C / R F / A equals 1. If there were no coarse fibres in the rejects and no fine fibres in the accepts S E m C / R F / A would be 0. There would still be a perfect separation but into the wrong streams. Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 109 Chapter 4 EXPERIMENTAL MATERIALS AND METHODS In this chapter the equipment used and the suspended particles used in the experimental measurements are described. The objectives of the experiments were to see if nylon fibres of known fibre length and coarseness could be fractionated and if any fractionation that occurred would be qualitatively in accord with the predicted effects of fibre coarseness and fibre length as discussed in Chapter 3. Moreover we wanted to see if nylon fibres fractionated in a similar way to the wood pulp fibres that have been studied by our research group and by other workers. This work was done using the Bauer hydrocyclone. In addition we wanted to get some experimental data against which to compare the predictions of a CFD model for hydrocyclone flow as discussed in Chapter 6. 4.1 Hydrocyclone Test Equipment The experimental apparatus used for fibre fractionation is shown in Figure 4-1-1. One hundred liters of pulp suspension of synthetic fibres of the desired consistency was prepared in the slurry tank A fresh slurry was prepared for each different fibre feed and each consistency tested. The tank was equipped with an agitator to ensure that a constant consistency was preserved throughout the procedure. The pulp slurry in the tank was pumped into the Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 110 hydrocyclone. The accepts stream refers to the stream coming from the top of the hydrocyclone, while the rejects stream refers to the stream coming from the apex of the conical section of the hydrocyclone. A valve in the feed line controlled the flow into the hydrocyclone. Pressures of the feed and accepts line were monitored using electronic pressure sensors. A sampling device allowed diversion of the accepts flow into a sampling bucket. Rejects samples could be collected directly from the rejects spigot. Flowrates of the accepts and the rejects streams were measured. The feed flowrate was calculated to be the sum of the rejects and accepts flowrates. When not being sampled both accepts and rejects were re-circulated back to the storage tank. Samples were collected from the accepts and rejects at various pressure drops and analyzed for consistency, fibre length, coarseness, etc. Three samples, of about 200 ml each, were removed from the rejects flow at each flowrate to provide a measure of flowrate. The flowrate was calculated based on the time of took to collect the measured volume of sample. One of these samples was returned to the feed tank The other two were used for determining the consistency, fibre length, and coarseness. A similar procedure was used for sampling the accepts. Two of the three flowrate samples were returned to the feed tank. About 400 ml was taken from the third sample for consistency, fibre length, and coarseness analysis. The remainder of the third accepts flowrate sample was returned to the feed tank On one occasion, samples were taken from the feed tank before and after a five flowrate experiment. There were no significant differences in consistency, fibre length and coarseness for these samples. The temperature was measured (usually it was in the range of 25~35°C). It could be controlled if necessary by using a heating coil. Chapter* EXPERIMENTAL MA TERIALS AND METHODS 111 ACCEPTS ACCEPTS STREAMS Figure 4-1-1 Apparatus for fibre fractionation. 4.2 Hydrocyclone Used A 3-in (76 mm) commercial Bauer Qntri-Cleaner, shown in Figure 4-2-1, was used for fibre fractionation. It had a feed inlet inner diameter of 12.7 mm, a overflow inner diameter of 16 mm, and underflow inner diameters (reject tip openings) of 5.0 mm and 6.0 mm. Its overall diameter at the top was 76 mm, the vortex finder length inside the hydrocyclone was 50.7 mm, and the overall length of 810 mm. This hydrocyclone contained a volume of 1.5 litres, thus mean flow through residence times (= hydrocyclone volume/feed flow rate) at the flow rates used in this work were of the order of 1.2 to 2.6 seconds. These residence times are reported to give an order of magnitude estimate of particle residence time in the hydrocyclone. Actual particle residence time would require a more sophisticated calculation and tracer testing. It is Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 112 known that particles can orbit for lengthy periods in a hydrocyclone without being accepted or rejected. A C C E P T S R E J E C T S * Dimension used in CFD calculations in Chapter 6. Figure 4-2-1 Dimensional symbols used for the Bauer 3" Centri Cleaner. 4.3 Hydrocyclone Measurements • Flowmte With the accepts valve 100% open, the feed valve setting was varied to achieve a pressure drop of 8 to 40 psi (55 to 276 kPa) for the 3" Bauer cleaner in increments of approximately 8 psi (55 kPa). The accepts flowrate and rejects flowrate were measured by directing the flow to a pail during 5—10 seconds (timed using a stop watch) for each corresponding pressure and then weighing it on an electronic scale to get the mass flowrates. The reported values are the averages of three samples. The feed flowrate was calculated as Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 113 the sum of the accepts and rejects flowrates. The measurement was then converted to kg/min. • Pressure Drop (psi orkPa) The pressure in the rejects streams was atmospheric therefore P r = 0. The pressure drop across the hydrocyclone was defined as the difference between the feed line and the accepts line pressures measured immediately before the feed entry and immediately after the accepts exit [36]. Pressures were measured by electronic pressure sensors. • Consistency (%) Feed consistencies in the range 0 to 0.9% were prepared by weighing out the appropriate amount of fibre and adding the requisite amount of water. These consistencies were checked by measurement for each of the different feeds. The rejects and accepts consistency were also measured for each trial. The reported results are the averages of three The consistency measurement was based on TAPPI standard [103]. (Details see Appendix B) • Thickening Ratio (%) The thickening ratio is the ratio of the rejects consistency to feed consistency [36]. • Volumetric Reject Ratio (%) The volumetric reject ratio is the ratio of the reject flowrate to the feed flow rate [36] expressed as a %. AP = P f - P a (4.3.1) samples. VolumetridtejectRatio= Rejects Flowrate^ xl00% (4.3.2) Feed Flowrati Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 114 • Mass Reject Ratio (%) The mass reject ratio is the ratio of the rejects solids mass flowrate to the feed solids mass flowrate [36] expressed as a %. MassRejectRatio= RejectsConsisten yxRejectsFlowrate x l o o % Feed Consistent x Feed Flowrate • Separation Efficiency on Mass basis (SEm) Separation Efficiency was defined for a 2-component mixture of fibres (coarse and fine) as a ratio of the of the mass of the coarse fibres in the rejects to the mass of coarse fibres in the feed (SEmC/R) and as the ratio of the mass of the fine fibres in the accepts to the mass of fine fibres in the feed (SEJF/A). (See Section 3.4, Chapter 3) For the fibre length separation for a 2-component mixture of fibres (long and short), the separation efficiency was defined as the ratio of the mass of long fibres in the rejects to the mass of long fibres in the feed (SEmS/R) and as the ratio of the mass of short fibres in the accepts to the mass of short fibres in the feed (SEJL/A). (See Section 3.4, Chapter 3) 4.4 Synthetic (Nylon) Fibres Used Study of wood pulp fibre fractionation is complicated by the presence of fines and defects in the wood fibres caused by refining or other fibre processing operations [85]. To avoid these complexities and to simplify the description of fibre geometry, stiff, circular, nylon fibres of known length and coarseness were used in our experimental work. There were no fines in these nylon fibres, some of which are illustrated in Figure 4-4-1. (similar microphotographs of all of the nylon fibres used in this thesis can be found in Appendix C). These fibres were used Chapter4. EXPERIMENTAL MA TERMLSANDMETHODS 115 as supplied by the manufacturer making no attempt to eliminate any chemical additives used in their manufacture. The crowding factor is the number of fibres in a spherical volume of a diameter equal to the length of a fibre [60]. It is a parameter that can be related to fibre flocculation [60]. It can be calculated from Equation 4.4.1. The crowding factors for the 1 mm nylon fibres of coarseness 0.17, 0.34 and 0.68 mg/m used in this work were in the range of 2 to 26 (within the feed consistency range between 0.3 ~ 0.9%), and therefore, negligible flocculation between fibres would be expected according to the criterion of Kerekes and Schell [60], i.e. crowding factor less than 30. In the experimental work related to fractionation by coarseness the crowding factors of the rejects were in range of 20 to 130, while the crowding factors of the accepts were in the range of 10 to 47. The 3 mm fibres used in the experimental work on fractionation by fibre length (coarseness = 0.17 mg/m and the feed consistency between 0.3 ~ 0.9%) had higher crowding factors (range of 79 to 130), hence, flocculation could be expected. For these experiments the crowding factors of the rejects were in the range of 65 to 95, while the crowding factors of the accepts were in the range of 24 to 32. Other than calculating the crowding factors of the various fibre slurries, flocculation effects were ignored in this work. Neglecting any flocculation effects, fibres will tend to be rejected or accepted based on the balance of the two primary forces (centrifugal and drag) acting on them (See Chapter 3) 5C I 2 N = ^ n ^ _ (4.4.1) c ; where Q , = mass consistency as % L = fibre length (m) Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 116 C = coarseness (kg/ m) Nylon Fibre Nylon Fibre Length: 1.0 mm Length: 3.0 mm Coarseness: 0.17 mg/m Coarseness: 0.68 mg/m Figure 4-4-1 Microphotographs of nylon fibres. The synthetic fibres (nylon fibres) used in the fractionation study had average fibre lengths of 1 mm, and 3 mm, and coarseness values of 0.17 (1.5), 0.34 (3.0) and 0.68 (6.0) mg/m (denier), which correspond to fibre diameters in the range of 13 ~ 28 microns. Denier is another way of measuring coarseness used in the textile industry. The equivalent denier values for the nylon fibres are the numbers in brackets following the above coarseness values. Their properties are tabulated in Table 4-4-1. Chapter* EXPERIMENTAL MATERIALS AND METHODS 117 Table 4-4-1 Properties of nylon fibres and fibre suspensions used in the experiments. Fibre Length (mm) Mfr. FQA Density (kg/m3) Coarseness (mg/m) Mfr. FQA L/Dr Consistency (%) Crowding Factor1" (N) 0.9 26 0.17 0.167 78 0.5 15 0.3 9 0.9 13 1 1.07 1145 0.34 0.345 52 0.5 7 0.3 4 0.9 7 0.68 0.687 36 0.5 4 0.3 2 0.9 . 238 3 3.11 1145 0.17 0.169 235 0.5 132 0.3 79 *Based on feed suspension consistency, mean fibre length and mean coarseness The nylon fibres used were almost straight, cylinders exhibiting very few defects, and which swelled very little, less than 2% in water [93, 98]. It was also observed by the author, watching a nylon fibre wetting process through a microscope that no significant swelling of these fibres occurred when a dry nylon fibre was placed on a microscope slide and wetted with Chapter 4. EXPERIMENTAL MATERIALS AND METHODS 118 water. Therefore, it is reasonable to be neglect swelling. An example of the data recorded by a Fibre Quality Analyzer (FQA), which was used for measurement of fibre length, coarseness, curl and kink, is presented in Figure 4-2-2. • • • H I S T O G R A M ••' C U R L H I S T O G R A M 180-5. y. 98 -i f 88 -r o 78 \ C l u 68 i e n s a \ 43 \ y m \ 28 -i 18 -i 8 -i p. L= e . s e O 8 .88 18.80 s e a 8.8 8.1 8.2 8 .3 8.4 8.S 6.6 8.7 8 .8 8.9 1.8 i n d e x K I N K H I S T O G R A M 1.8-V. e.9-i r 8.6-i r e 8-7 i ci u 8 6-e a.s-i n <z 8.4^ y 8.3^ 8.2-i 8 . i - i e.e : L - e . s e K= 8,88 e.e e.5 i .e l .S 2.8 2.5 3 . ! i n d e x 18.88 28.88 Figure 4-2-2 Illustration of typical fibre properties distributions from the fibre quality analyzer (FQA): Histograms measuring fibre length, fibre curl and kink indexes. Based on data of nylon fibres length = 1 mm, coarseness = 0.68 mg/m. Note that, these nylon fibres had very narrow fibre length distributions. They exhibited essentially no curl nor did they have a significant amount of kinks. The mean fibre lengths and coarseness values (deniers) obtained from the F Q A agreed well with the data provided by the manufacturer. Chapter* EXPERIMENTAL MATERIALS AND ME THCDS 119 4.5 Fibre Mixtures, Consistencies and Reject Tip Openings Used Various feed suspensions consistencies and reject tip openings were used in the experiments. The details of the various experiments are provided in Tables 4-5-1 and 4-5-2 as is the nomenclature applied to the various feed slurries (i.e. Feed A, Feed B, etc.) Table 4-5-1 Characteristics of nylon fibres used in the experimental work, rnixtures are characterized as percentages on a mass basis. Coarseness (mg/m) Length (mm) Number Mean Coarseness (mg/m) Number Mean Length (mm) Feed 0.170 0.340 0.680 1.0 3.0 SI 100% 100% 0.170 1.0 S2 100% 100% 0.680 1.0 S3 100% 100% 0.170 3.0 A 50% ~ 50% 100% 0.268 1.0 B 100% 50% 50% 0.170 1.3 C 33-% 3 33-% 3 33-% 3 100% 0.287 1.0 D 25% - 75% 100% 0.403 1.0 E 100% 75% 25% 0.170 1.1 Chapter* EXPERIMENTAL MATERIALS AND METHODS 120 Table 4-5-2 Consistencies of the feeds and the reject tip openings used in the experimental work. Reject Tip 1(5.0mm) Reject Tip II(6.0mm) Feed 0.9 Consistency (%) 0.5 0.3 0 Consistency (%) 0.9 0.5 0.3 0 SI x X X -S2 x X X ~ S3 - X X X X X -A X X X B - X X --C X X X -D X X X --E ~ X X --Wl X -W2 ~ X 4.6 Fibre Property Measurements • Fibre Length and Coarseness A Fibre Quality Analyzer (FQA) was used to measure fibre length and coarseness for the experiments. Samples which were collected from both the accepts and rejects were de-watered, then rinsed with alcohol and filtered using a micro filtration system. Next, they were air-dried in a constant temperature/humidity room for 48 hours and then their moisture contents were determined. Chapter* EXPERIMENTAL MATERIALS AND METHODS 121 Samples were taken from the air dried fibres and weighed to within 0.01 mg (A), then transferred to vials. Water was added and they were soaked for at least an hour. After that, they were diluted to 4 L in a beaker; then the suspension weight was recorded to the nearest 0.1 g (B). Subsequently, sufficient sample, which was required by the F Q A in order to get the necessary fibre mass, was recorded to the nearest 0.1 g (D). The O.D. fibre weight in the sample (mg), was calculated as (A/B)xD. Then the sample was ready for the coarseness measurement. Each reported value of mean fibre length and mean coarseness is the average of three determinations. • Fibre Density The densities of the various nylon fibres used in these experiments were measured using a pyncnometric method. A known weight of nylon fibres was placed in a pre-weighed calibrated volumetric flask. The flask containing the fibres was filled to the mark with water and weighed again. From the known masses of fibres and water, the known density of water and the known total volume in the flask, the density of the fibres could be calculated, (details see Appendix D) Table 4-6-1 lists the average densities observed for the fibres tested plus their standard deviation. Comparison of the various groups to one another using a student t test showed no significant differences between the mean fibre densities. • Fibre Thickness Fibre thickness (diameter) can be calculated directly from the coarseness definition, i.e. the dry mass per unit length. (See Chapter 3, Equation (3.2.62)) c = f D 2 L p f _ 7 t D 2 p f L 4 It can also be scaled from the microphotographs using a ruler and the magnification factor. Chapter* EXPERIMENTAL MATERIALS AND METHODS 122 Table 4-6-1 Average densities of the nylon fibres observed from the experimental measurements. Fibre Length (mm) Coarseness (mg/m) Mean Density (kg/m3) Std. Dev. Number of Repeats (n) 1 0.17 1145 5.3 4 1 0.68 1147 5.8 4 3 0.17 1143 4.2 4 Table 4-6-2 Fibre thickness values calculated from the coarseness definition and measured from the microphotographs. Fibre Length (mm) Coarseness (mg/m) Fibre Density (kg/m?) Fibre Thickness (Df) (/on) Calculated Value Measured Value 0.17 1X7 12.8 1 0.34 19.4 19.2 0.68 1145 27.5 27.6 0.17 13.7 12.8 3 0.34 19.4 19.2 0.68 27.5 27.6 The results are shown in Table 4-6-2. Note that the calculated results and the measured results show good agreement between the two methods of deterrnining fibre thickness. Chapter* EXPERIMENTAL MATERIALS AND METHODS 123 4.7 Experimental Reproducibility Table 4-7-1 surrirriarizes the reproducibility of the experimental data. Iri it, the ranges for the overall percentage errors ( = 100 x the standard deviation/the mean value) are reported for the various experimental data that were collected. These variations are acceptably low enough that our conclusions, based on analysis of these data, are not attributable to experimental errors. Table 4-7-1 Overall percentage errors of fibre fractionation experimental measurements. The Rejects The Accepts Flowrate Consistency Fibre Length Coarseness Flowrate Consistency Fibre Length Coarseness 0 -4% 0.4 -6% 0 -5% 0 -9% 0 -4% 0.3 -7% 0 -2% 0 -8% Chapter5. EXPERIMENTAL RESULTSANDDISCUSSION 124 Chapter 5 EXPERIMENTAL RESULTS AND DISCUSSION 5.1 Synthetic Fibres (Nylon) Fractionation Nylon fibres having known fibre lengths and fibre coarseness values were used in various suspensions as feed to a hydrocyclone. (See Chapter 4) The characteristics of the various feed suspensions are summarized in Table 4-4-1, and Table 4-5-1. In all of these experiments a variety of feed flowrates and suspension consistencies were used. The principal objective of these experiments was to see if the fibre fractionating behavior of a hydrocyclone working with nylon fibres was similar to what had been observed with wood pulp fibres [84, 85]. Also it was of interest to know if the theory of Chapter 3 could be verified experimentally. In the course of these experiments, in addition to measuring fibre length and coarseness, it was easy to collect data on various aspects of hydrocyclone performance such as feed, accepts and rejects stream flowrates and consistencies, thickening ratio, pressure drop, volumetric reject ratio and mass reject ratio. The results concerning pressure drop, feed, accepts and rejects consistency, thickening ratio and volumetric reject ratio can be found in Appendix E . It is one thing to show that the feed, rejects and accepts have different lengths and/or coarseness values but to make practical use of any significant differences between the fibre properties in the rejects and accepts there must be a sufficiently large mass of fibres in each Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 125 stream to do somediing with (e.g. make paper, send to refiner, etc.), hence the importance of mass reject ratio. 5.1.1 Coarseness Figure 5-1-1 is a plot of the feed, accepts and rejects coarseness for various feed flowrates at feed consistencies of 0.3, 0.5 and 0.9%. The feed slurry (Feed A) was a 50% : 50% (mass basis) mixture of 1 mm fibres having coarseness values of 0.17, and 0.68 mg/m. 0 c Coarseness (mg/m) 0.5 H 0.4 0.3 H 0.2 0.1 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 13 The Rejects (A) Feed {AX The Accepts (A) a o 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-1 Feed, accepts, and rejects coarseness value vs. feed flowrate at various feed consistencies for Feed A. It can be seen in Figure 5-1-1 that in all cases the rejects coarseness values were greater than those of the accepts. In all cases the rejects coarseness was greater than the feed coarseness and the accepts coarseness was less than the feed coarseness. Thus fibre fractionation on the Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 126 basis of coarseness differences was achieved. In addition, as the flowrate increased, the coarseness value of both the rejects and the accepts decreased. Note that at high flowrates the accepts stream contained only low coarseness fibres (C = 0.17 mg/m) while the rejects stream contained both low (C= 0.17 mg/m) and high (C = 0.68 mg/m) coarseness fibres. Figure 5-1-2 shows the difference between the rejects and accepts coarseness as a function of feed flowrate at the various consistencies. In this figure, it is clear that the difference between rejects and accepts coarseness was dependent on consistency. The greatest difference was observed at the lowest consistency. The difference was also dependent on flowrate. There was an optimum flowrate at which the difference was maximized. For consistencies of 0.9 and 0.5% this occurred at around 50 kg/min; at 0.3% consistency the maximum was less sharply defined but 50 kg/min was still the optimum flowrate. 0.35 Coarseness TRejects-AcceptsI (mg/m) 0.30 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 0.25 A 0.20 0.15 0.10 • V o • z V o • 8 0.05 -I 1 1 1 1 1 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-2 Differences in coarseness values between the rejects and the accepts for Feed A at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 127 Figure 5-1-3 is a plot of the feed, accepts and rejects coarseness for various feed flowrates at feed consistencies of 0.3, 0.5 and 0.9%. The feed slurry (Feed O) was a 1 1 1 33—%:33—%:33—% (mass basis) mixture of 1 mm fibres having coarseness values of 0.17, 0.34 and 0.68 mg/m. It can be seen that in all cases the rejects coarseness values were greater than those of the accepts. In all cases, but one (at the highest flowrate), the rejects coarseness was greater than the feed coarseness and the accepts coarseness was less than the feed coarseness. Thus again it was demonstrated that fibre fractionation based on coarseness was achieved. As the flowrate increased the coarseness values of both the rejects and the accepts decreased. Again at high flowrates the accepts stream contained only the lowest coarseness fibres whereas the rejects stream was a mixture of the three coarseness. 0.6 Coarseness (mg/m) 0.5 H O 0.9% consistency (Feed C)_Tip I v 0.5% consistency (Feed C)_Tip I • 0.3% consistency (Feed C)_Tip I 0.4 H T h e Rejec ts (C) 0.3 -] F e e d (CJ. 0.2 H 0.1 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-3 Feed, accepts, and rejects coarseness values vs. feed flowrate at various feed consistencies for Feed C. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 128 Figure 5-1-4 shows the difference between the rejects and accepts coarseness as a function of feed flowrate at the various consistencies. In this figure, it is clear that the difference between rejects and accepts coarseness was dependent on consistency. The greatest difference was again observed at the lowest consistency. The difference was also dependent on flowrate. There was an optimum flowrate at which the difference was maximized. In this case, the optimum flowrate for maximum coarseness difference was again at 50 kg/min for 0.3% consistency, and 60 kg/min for the other consistencies. 0 . 3 5 0 . 3 0 0 . 2 5 0 . 2 0 0 . 1 5 0 . 1 0 Coarseness [Rejects-Accepts] (mg/m) 0 . 0 5 D y V O O 0.9% consistency (Feed C)_Tip I V 0.5% consistency (Feed C)_Tip I • 0.3% consistency (Feed C)_Tip I — i — 5 0 O V o u o 3 0 4 0 6 0 Feed Flowrate (kg/min) 7 0 8 0 Figure 5-1-4 Differences in coarseness values between the rejects and the accepts for Feed C at various consistencies. Figure 5-1-5 shows the feed, accepts and rejects coarseness for various feed flowrates at feed consistencies of 0.3,0.5 and 0.9%. The feed slurry (Feed D) was a 25% : 75% (mass basis) mixture of 1 mm fibres having coarseness values of 0.17, and 0.68 mg/m. It can be seen that in all cases the rejects coarseness values were greater than those of the accepts. In all cases the Cbapter5. EXPERIMENTAL RESULTS AND DISCUSSION 129 rejects coarseness was greater than the feed coarseness and the accepts coarseness was less than the feed coarseness. Once more fibre fractionation based on coarseness differences was shown to have occurred. In addition, as the flowrate increased, the coarseness value of both the rejects and the accepts decreased. At 0.3% consistency and high flowrates the accepts stream contained only the low coarseness fibres. At high consistencies the accepts stream was a mixture of low and high coarseness fibres as was the ejects stream. 0 7 Coarseness (mg/m) 0.6 i 0.5 0.3 H 0.2 0.1 0.4 A Feed (D) 30 O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_Tip I —i 1 1 1— 40 50 60 70 Feed Flowrate (kg/min) 80 Figure 5-1-5 Feed, accepts, and rejects coarseness values vs. feed flowrate at various feed consistencies for Feed D. Figure 5-1-6 demonstrates the difference between the rejects and accepts coarseness as a function of feed flowrate at the various consistencies. In this figure, it is clear that the difference between rejects and accepts coarseness was dependent on consistency. The greatest difference was observed at the lowest consistency. The difference was also dependent on flowrate. There Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 130 was an optimum flowrate at which the difference was maximized. This time, the optimum again occurred at 50 kg/min for all three consistencies. 0.35 0.30 0.25 H 0.20 0.15 0.10 Coarseness fRejects-AcceptsI (mg/m) 0.05 o V V o • V O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I O 0.3% consistency (Feed D)_Tip I • v o V o 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-6 Differences in coarseness values between the rejects and the accepts for Feed D at various consistencies. For the various nylon fibre mixtures tested it was evident that the hydrocyclone used was able to achieve some degree of fibre fractionation in terms of coarseness. Coarser fibres were preferentially rejected, finer fibres were preferentially accepted. This result is in accord with what was observed in our group's work on wood pulp fibres [46, 47, 84, 85] and with what has been reported by other workers in fibre fractionation [63, 65, 81, 107]. The degree of fibre separation achieved depended on feed slurry consistency and feed flowrate. The lower the consistency the greater the difference between the rejects and accepts coarseness, which agrees with what others have found [58, 81, 98, 109]. It is interesting to note that while the greatest degree of fractionation occurred at the lowest consistency, a significant amount of fractionation Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 131 did also occur at the highest consistency (0.9%), contrary to the opinions of some [81] that a significant level of fractionation would not occur if the consistency was greater than 0.3%. This agrees with work done here on wood pulp fractionation [85] in which fractionation was observed at consistencies of up to 1%. The difference between rejects and accepts coarseness was maximized at an optimal flowrate in the range of 50 —60 kg/min. In comparing the results for Feeds A and D, it is seen that the differences between rejects and accepts coarseness were greater for Feed D than for Feed A. This no doubt occurred because there was more coarse fibre in Feed D. The coarseness differences between rejects and accepts for Feed C were less than those noted for Feed A at similar flowrates and consistencies, even though the mean coarseness of Feed C (0.29 mg/m) was almost the same as the mean coarseness of Feed A (0.27 mg/m). Thus the relative concentrations of the different kinds of fibre also plays a role in fibre fractionation. 0.190 Coarseness (mg/m) 0.185 -0.180 -0.175 -0.170 0.165 0.160 0.155 0.150 T 0.5% consistency (Feed B)_Tip \_Rejects V 0.5% consistency (Feed B)_Tip \_Accepts • 0.3% consistency (Feed B)_Tip Lfte/ecte • 0.3% consistency (Feed B)_Tip \_Accepts Feed (B) H 3 0 40 The Rejects (B) • T • T • • V • V • V • V • The Accepts (B) —i— 50 6 0 70 Feed Flowrate (kg/min) 80 Figure 5-1-7 Feed, accepts, and rejects coarseness vs. feed flowrate at various feed consistencies of Feed B. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 132 Figure 5-1-7 demonstrates the accepts, rejects and feed fibre mean fibre coarseness vs. feed flowrate for Feed B. Feed B nominally consisted of fibres all having a mean fibre coarseness of 0.17 mg/m However, Figure 4-2-2 indicates that there was a very narrow distribution of fibre lengths around the mean value of 1 mm, so there was probably (it was not measured) a narrow range of coarseness values around the mean value. Figure 5-1-7 shows that even for such a small variation in fibre coarseness, the rejects fibres were coarser than the accepts. Now let's consider these results in terms of separation efficiencies. For their definitions and methods of determination refer to Chapter 3, Section 3.4. Figure 5-1-8 is a plot of the hydrocyclone uncorrected separation efficiency (SEmC/R) vs. flowrate for Feed A at consistencies of 0.3, 0.5 and 0.9%. The separation efficiency plotted is S E m C / R which means separation efficiency (SE), mass basis (m) for getting coarse fibres into the rejects (C/R). This quantity is defined by Equation (3.4.53) in Chapter 3. It is the mass of coarse fibres in the rejects divided by the mass of coarse fibres in the feed. As explained in Section 3.4, Chapter 3, this definition of separation efficiency has some drawbacks. If one simply wants to know what is the ratio of the mass of coarse fibres in the rejects to the mass of coarse fibres in the feed S E m C / A is a useful number. If on the other hand one wanted to know how effective the hydrocyclone under study was in fractionating fibres, that is in separating coarse fibres from fine fibres, then SEn^C/R^ would be more appropriate. Since this thesis is primarily about fibre fractionation we will emphasize the centrifugally corrected separation efficiency over the corrected separation efficiency. However, to demonstrate the differences we will report all the various definitions of separation efficiency for the case of Feed A only below. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 133 In Figure 5-1-8, it is obvious that the uncorrected separation efficiency was highest at the lowest consistency used and also that there were maxima in the plots for all three consistencies at flowrates of around 60 kg/min. Figure 5-1-9 is a plot of the corrected separation efficiency SEnjC/R^n. for the same tests. This corrects for the thickening effects of the hydrocyclone. The values for S E , , ^ ] ^ . were much lower than the equivalent uncorrected values. This means that a large part of the uncorrected SE was attributable to large mass reject ratios. For Feed A, these mass reject ratios ranged from 20 ~ 55%, see below, Section 5.1.3. The effects of consistency on SE were climinished in SEmC/B^.on. compared to the uncorrected values and the maxima had moved to a lower flowrate close to 50 kg/min. S E C / R 1.0 0.8 A • • V o o 0.6 A V o V o o cr 0.4 A o 0.2 A O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 0.0 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-8 Separation efficiency for coarse fibres in the rejects for Feed A at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 134 1.0 0.8 0.6 0.4 0.2 4 SEmC/R r„„ m corr 0.0 30 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I • 40 50 60 Feed Flowrate (kg/min) • 70 80 Figure 5-1-9 Corrected separation efficiency for coarse fibres in the rejects for Feed A at various consistencies. 1.0 SE m C/R r f r m ctr 0.8 0.6 4 0.4 0.2 0.0 9 o V o O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I V O V O o7 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-10 Centrifugal separation efficiency for coarse fibres in the rejects for Feed A at various consistencies. Chapter^. EXPERIMENTAL RESULTS AND DISCUSSION 135 Figure 5-1-10 demonstrates the use of SEjyB^. Again the values of SE were reduced compared to the uncorrected values, but they were higher than the corrected values. The consistency effect was more pronounced with this value than with the corrected SE of the previous plot. Nevertheless the lowest consistency still always gave the highest SE. The maxima were then seen at a flowrate of around 50 kg/min. Figures 5-1-11 to 5-1-13 are plots of S E m F / A , SEJF/A^ and S E J V A ^ vs. flowrate. These values tended to be higher than the corresponding values for SE m C/R, implying that it was easier to get fine fibres into the accepts of this hydrocyclone than it was to get coarse fibres into the rejects. At low flowrates there was an obvious consistency effect, i.e. the lowest consistency gave the highest SE. But at higher flowrates, unlike the S E m C / R plots, this consistency effect tended to disappear. S E F / A 1.0 0.8 0.6 0.4 0.2 0.0 30 V O • S • O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 8 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-11 Separation efficiency for fine fibres in the accepts for Feed A at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 136 1.0 SE„F/A„. 0.8 H 0.6 0.4 0.2 A 0.0 V O • 8 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 9 9 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-12 Corrected separation efficiency for fine fibres in the accepts for Feed A at various consistencies. L O i m cb-0.8 0.6 0.4 0.2 0.0 • 8 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I n 0.3% consistency (Feed A)_Tip I O 30 40 50 60 Feed Flowrate (kg/min) 70 .80 Figure 5-1-D Centrifugal separation efficiency for fine fibres in the accepts for Feed A at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 137 It can be seen in Figure 5-1-13 that at 0.3% consistency, SEJ^/A^. continually decreased as flowrate increased; at 0.5% it also decreased, slowly at first and then more rapidly, at 0.9% there was an initial increase followed by a decrease at higher flowrates. As flowrate increases the centrifugal force on the fibres would tend to increase. Since these nylon fibres had a density greater than that of the water, in which they were suspended, they would tend to have higher outward radial velocities and thus as flowrate increased they would have a greater probability of being rejected. As a result S E m F / A would be reduced. Figure 5-1-14 is a plot of the combined, uncorrected separation efficiency S E m C / R F / A . Figure 5-1-15 shows the equivalent values of SEnjC/RF/A^ and Figure 5-1-16 the values for S E m C / R F / A ^ . All three plots indicate that the values for S E m C / R F / A were higher the lower the consistency (with one exception) and that there were maxima (again with one exception) at flowrates of 50 —60 kg/min. SE C/RF/A 1.0 - — — 0.8 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 0.6 0.4 0.2 H • V • V V o V o o V o 0.0 -I 1 1 1 1 1 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-14 Combined separation efficiency of Feed A at various consistencies. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 138 1.0 S E m C / R F / A c o r r 0.8 H 0.6 0.4 H 0.2 0.0 o O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 9 o -8-30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-15 Corrected combined separation efficiency for Feed A at various consistencies. 1.0 SE_C/RF/A r t p m ctr 0.8 H 0.6 0.4 0.2 0.0 O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I • o V • V • V • V o • 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-16 Centrifugal combined separation efficiency for Feed A at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 139 We were unable to determine separation efficiencies for the three component mixture of feed C because instead of solving 4 equations in 4 unknowns it would have been necessary to solve 6 equations in 6 unknowns. We were unable to write 6 independent equations for this situation. Figure 5-1-17 is a plot of S E m C / R vs. flowrate at various consistencies for Feed D. It shows that the uncorrected separation efficiency was highest at the lowest consistency used, which is similar to the results for Feed A. The effects of consistency and flowrate seemed less pronounced with Feed D compared to Feed A. There was a shallow optimum at a flowrate of 50 l^min . for the 0.9% consistency. For the other two consistencies the separation efficiency decreased as flowrate increased. The uncorrected separation efficiencies of Feed D were higher than those of Feed A at a given consistency and flowrate, probably because there was a greater proportion of coarser fibre in Feed D. 1.0 S E M C / R m • V 0.8 A • V o V o 8 0.6 A 0.4 A 0.2 A O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I o 0.3% consistency (Feed D)_Tip I 0.0 — I — 50 30 40 60 70 Feed Flowrate (kg/min) 80 Figure 5-1-17 Separation efficiency for coarse fibres in the rejects for Feed D at various consistencies. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 140 Figure 5-1-18 demonstrates the use of SEjnC/R^. for Feed D. Again the values of SE were reduced compared to the uncorrected values. The consistency effect was more notable with this value than with the uncorrected SE of the previous plot. Nevertheless the lowest consistency still always gave the highest SE. 1.0 m ctr 0.8 0.6 0.4 0.2 -\ 0.0 V O O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_Tip I V o V o • 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-18 Centrifugal separation efficiency for coarse fibres in the rejects for Feed D at various consistencies. Figures 5-1-19 and 5-1-20 show S E m F / A , and S E J V A ^ vs. flowrate for Feed D. It can be seen in Figure 5-1-20 that at 0.9% consistency, SE^/A^, . continually decreased as flowrate increased; at 0.5% it also decreased, slowly at first and then more rapidly, at 0.3% there was an initial increase followed by a decrease at higher flowrates. Comparing Figures 5-1-19 and 5-1-20 (Feed D) to Figures 5-1-11 and 5-1-13 (Feed A), it can be noted that the values for separation Chapters. EXPERIMENTAL RESULTS A ND DISCUSSION 141 efficiency were lower for Feed D, probably because there was a lesser proportion of fine fibre in FeedD. Figure 5-1-21 is a plot of the combined, uncorrected separation efficiency S E m C / R F / A for Feed D. Figure 5-1-22 shows the equivalent values for S E m C / R F / A c t r . These plots indicate that the values for S E m C / R F / A were higher the lower the consistency (with one exception) and that the combined separation efficiency decreased as the flowrate increased. Comparing these two figures to Figures 5-1-14 and 5-1-16 for Feed A, it can be observed that the uncorrected combined separation efficiencies were lower for Feed A than for Feed D at low flowrates. At higher flowrates the Feed D values were lower than those of Feed A A similar trend can be discerned in the centrifugal, combined separation efficiencies SEmF/A O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_Tip I • V • O V o B o • V o 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-19 Separation efficiency for the fine fibres in the accepts for Feed D at various consistencies. 0.8 0.6 0.4 0.2 8 Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 142 1.0 0.8 A 0.6 0.4 0.2 A SE F/A„ 0.0 30 Q O 40 D V O O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I a 0.3% consistency (Feed D)_Tip I • V a v o 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-20 Centrifugal separation efficiency for fine fibres in the accepts for Feed D at various consistencies. SE_C/RF/A 1.0 - — m -0.8 O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_Tip I 0.6 0.4 0.2 9 O • V o o V o 9 o • V o 0.0 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-21 Combined separation efficiency for Feed D at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 143 1.0 SEmC/RF/A r t r m ctr 0.8 O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_Tip I 0.6 H 0.4 0.2 0.0 30 • V o 40 V O 50 V O • V o 60 • JSZL 70 80 Feed Flowrate (kg/min) Figure 5-1-22 Centrifugal combined separation efficiency for Feed D at various consistencies. Figures 5-1-23, 5-1-24 and 5-1-25 show S E m C / R vs. feed flowrate for Feed A, D, SI, and S2 at 0.9, 0.5 and 0.3% consistency respectively. Data for Feeds SI and S2 are included in these figures as points of reference. Since the fibres in each of feeds Si and S2 all had the same coarseness no fractionation was possible. For such single component feeds the "separation efficiency" for getting fibres into the rejects is just the mass reject ratio. With the exception of the Feed D values, the S E m C / R values were higher the higher the mean coarseness of the fibres in the feed. The Feed D values also fit into this pattern at high flow rates, but did not at low flowrates. These figures again show that coarseness is an important factor in fibre fractionation. Chapter 5. EXPERIMENTA L RESULTS AND DISCUSSION 144 1.0 SEmC/R m 0.8 H 0.6 H 0.4 H 0.2 0.0 30 o o 40 V o o o O 0.9% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.9% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m • 0.9% consistency (Feed S1)_L = 1 mm, C = 0.17 mg/m O 0.9% consistency (Feed S2)_L = 1 mm, C = 0.68 mg/m 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-23 Separation efficiency for coarser fibres in the rejects for Feed A, D , Si, S2 at 0.9% consistency, L = number mean fibre length, C = number mean coarseness. 1.0 SE„C/R 0.8 V O o v 0.6 0.4 o o 0.2 0.0 O 0.5% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.5% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m • 0.5% consistency (Feed S1)_L = 1 mm, C = 0.17 mg/m 0 0.5% consistency (Feed S2)_L = 1 mm, C = 0.68 mg/m 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-24 Separation efficiency for coarser fibres in the rejects for Feed A, D, SI, S2 at 0.5% consistency, L = number mean fibre length, C = number mean coarseness. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 145 S E C / R 1.0 — m -0.8 0.6 4 0.4 0.2 0.0 V o o v O 0.3% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.3% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m • 0.3% consistency (Feed S1)_L = 1 mm, C = 0.17 mg/m O 0.3% consistency (Feed S2)_L = 1 mm, C = 0.68 mg/m 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-25 Separation efficiency for coarser fibres in the rejects for Feed A, D , Si, S2 at 0.3% consistency, L = number mean fibre length, C = number mean coarseness. Figures 5-1-26, 5-1-27 and 5-1-28 are plots of S E j ^ R ^ . that were derived from Figures 5-1-23 to 5-1-25. They show that the highest coarseness fibres (Feed D) tended to produce the highest SE m C/R c t r , particularly at low flowrates, for all three consistencies. Feed D produced SEjnC/Rj-u. values that tended to decrease with increased flowrate. SEnjC/R^. values for Feed A were much lower than those of Feed D at low flowrates but as flowrate increased they rose to a maximum then declined in about the same way as those of Feed D. Thus others things being equal, i.e. flowrate and consistency, higher coarseness fibres have higher separation efficiencies. This conclusion is supported by the mass reject ratio results discussed below where it is shown that with single component fibre slurries the higher the coarseness the greater the mass reject ratio. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 146 1.0 SE m C/R c t r 0.8 A 0.6 A 0.4 0.2 0.0 O 0.9% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.9% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m v 9 O V 30 40 50 60 Feed Flowate (kg/min) 70 80 Figure 5-1-26 Centrifugal separation efficiency for coarser fibres in the rejects for Feed A, D at 0.9% consistency, L = number mean fibre length, C = number mean coarseness. 1.0 SE m C/R c t r 0.8 A 0.6 0.4 0.2 0.0 30 O 0.5% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.5% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m 5 40 50 60 Feed Flowrate (kg/min) o v 70 80 Figure 5-1-27 Centrifugal separation efficiency for coarser fibres in the rejects for Feed A, D at 0.5% consistency, L = number mean fibre length, C = number mean coarseness. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 147 1.0 0.8 0.6 4 0.4 0.2 0.0 0 0.3% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.3% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m V o o V o V 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-28 Centrifugal separation efficiency for coarser fibres in the rejects for Feed A, D at 0.3% consistency, L = number mean fibre length, C = number mean coarseness. 1.0 S E m F / A c t r 0.8 0.6 0.4 0.2 0.0 30 O 0.9% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.9% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m O V 40 50 —i— 60 70 80 Feed Flowrate (kg/min) Figure 5-1-29 Centrifugal separation efficiency for fine fibres in the accepts for Feed A, D at 0.9% consistency, L = number mean fibre length, C = number mean coarseness. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 148 1.0 S E m F / A c t r 0.8 0.6 A 0.4 A 0.2 0.0 30 O 0.5% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.5% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m O V O V 40 50 60 70 Feed Flowrate (kg/min) 80 Figure 5-1-30 Centrifugal separation efficiency for fine fibres in the accepts for Feed A, D at 0.5% consistency, L = number mean fibre length, C = number mean coarseness. S E m F / A c t r 1.0 T O-0.8 0.6 0.4 0.2 0.0 o V o V O 0.3% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.3% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m 30 40 50 60 Feed Flowrate (mg/m) 70 80 Figure 5-1-31 Centrifugal separation efficiency for fine fibres in the accepts for Feed A, D at 0.3% consistency, L = number mean fibre length, C = number mean coarseness. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 149 Figures 5-1-29, 5-1-30 and 5-1-31 are plots of the centrifugal corrected separation efficiencies for fine fibres in the accepts vs. flowrate at feed consistencies of 0.9, 0.5 and 0.3% respectively for Feeds A and D. In these figures it can be seen that the values of SE m F/A^. were lower for the high coarseness fibres of Feed D at all three consistencies. Summary The results in regard to fibre coarseness have demonstrated that fibre fractionation based on coarseness was achieved. Coarser fibres were preferentially rejected, finer fibres were preferentially accepted. In this sense nylon fibres behaved in a qualitatively similar way to wood pulp fibres. We can conclude that as the flowrate increased the coarseness values of both the rejects and the accepts decreased. The degree of fibre separation depended on feed slurry consistency and feed flowrate. The lower the consistency the greater the difference between the rejects and accepts coarseness. There was an optimum flowrate that resulted in a maximum in the difference in coarseness value between the rejects and accepts. This occurred at flowrates between 50 ~ 60 l^min. The experimental results are in accord with the theory in as much as the theory suggested that higher coarseness fibres would have higher radial velocities and thus would be more likely to be rejected than would finer fibres. At low flowrates through the hydrocyclone, fine fibres tend to be readily accepted and coarse fibres rejected but not as readily as fine fibres are accepted. As flowrate increases the centrifugal force on all the fibres increases but for reasons outlined in Chapter 3, the coarse fibres move faster towards the wall than the fine ones do. Therefore, the S E m C / R tends to increase. As velocity further increases the centrifugal force on the fine fibres increases causing them to move more rapidly towards the wall. Thus, they too tend to exit via the rejects outlet which causes a reduction in S E m C / K This is believed to be the reason why there is a flowrate at Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 150 which separation efficiency for getting coarse fibres into the rejects is maximized. See for example Figures 5-1-8 and 5-1-10. Of course as flowrate increases and more fine fibres are rejected the value of S E m F / A would be expected to decrease and it does; see Figures 5-1-11 and 5-1-13 for example. Higher coarseness fibres tended to have higher separation efficiencies at a given consistency. Lower consistency resulted in higher SEs (Feeds SI, S2, A, D). The combined separation efficiencies were higher the lower the consistency, and decreased as the flowrate increased (Feeds SI, S2, A, D). 5.1.2 Fibre Length Figure 5-1-32 is a plot of the arithmetic average fibre length of the feed, accepts and rejects for various feed flowrates at feed consistencies of 0.3%, and 0.5%. Attempts to fractionate mixtures containing 3 mm fibres at consistencies of 0.9% failed due to plugging of the hydrocyclone reject outlet. The feed slurry (Feed B) was a 50% : 50% (mass basis) mixture of 1 and 3 mm fibres having a coarseness value of 0.17 mg/m It can be seen that in all cases the accepts fibre lengths were greater than those of the rejects. As the feed flowrate increased, the arithmetic average fibre lengths of the rejects and accepts increased. Figure 5-1-33 shows the difference between rejects and accepts fibre lengths as a function of feed flowrate at the two consistencies. In this figure, it is clear that the difference between rejects and accepts fibre length was dependent on consistency. The greatest difference was observed at the lowest consistency. Note that these differences were rather small, of the order of 0.25 ~ 0.3 mm Results from Rehmat [85] using wood pulp fibres and the same hydrocyclone, showed that the length differences between the accepts and the rejects were also Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 151 small ranging from 0 ~ 0.5 mm. Those differences were also dependent on flowrate. There was a flowrate at which the difference was minimized. This occurred at around 60 kg/min. 1 6 Arithmetic Av. Length (mm) 1.5 1.4 1.3 1.2 1.1 H 1.0 The Accepts (B) -JSZ-Feed (B) The Rejects (B) V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I 30 40 , 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-32 Feed, accepts, and rejects arithmetic average fibre lengths vs. feed flowrate at various feed consistencies for Feed B. 0.35 Arithmetic Av. Length [Accepts-Rejects] (mm) 0.30 4 0.25 0.20 4 0.15 0.10 0.05 • V • V • V V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-33 Differences in the arithmetic average fibre lengths between the rejects and the accepts for Feed B at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 152 Figure 5-1-34 is a plot of the arithmetic average fibre lengths of the feed, accepts and rejects for various feed flowrates at feed consistencies of 0.3% and 0.5%. The feed slurry (Feed E) was a 75% : 25% (mass basis) mixture of 1 and 3 mm fibres having a common coarseness value of 0.17 mg/m It can once more be seen that in all cases the accepts fibre lengths were greater than those of the rejects. As the feed flowrate increased, the arithmetic average fibre lengths of the rejects and accepts increased. Figure 5-1-35 shows the difference between rejects and accepts fibre lengths as a function of feed flowrate at the two consistencies. Again these differences were quite small in magnitude (0.08 —0.16 mm). In this figure, it is again clear that the difference between rejects and accepts fibre length was dependent on consistency. The greatest difference was observed at the lowest consistency. The difference was also dependent on flowrate. There was a flowrate at which the difference was minimized. For Feed E this occurred at around 50 kg/min. 1 .6 1.5 Arithmetic Av. Length (mm) 0.5% consistency (Feed E)_Tip I 0.3% consistency (Feed E)_Tip I 1.4 H 1.3 4 Feed Flowrate (kg/min) Figure 5-1-34 Feed, accepts, and rejects average arithmetic fibre lengths vs. feed flowrate at various feed consistencies for Feed E . Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 153 0 1 g Arithmetic Av. Length [Accepts-Rejectsl (mm) 0.16 0.14 H 0.12 0.10 0.08 V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I 0.06 -I 1 1 , 1 1 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-35 Differences in the average arithmetic fibre lengths between the rejects and the accepts for Feed E at various consistencies. Figure 5-1-36 demonstrates the accepts, rejects and feed fibre mean fibre length vs. feed flowrate for Feed A. Feed A nominally consisted of fibres all having a mean fibre length of 1 mm. However, Figure 4-2-2 indicates that there was a very narrow distribution of fibre lengths around the mean value of 1 mm. Figure 5-1-36 shows that even for such a small variation in fibre length, the rejects fibres were shorter than the accepts. For the various nylon fibre mixtures tested it was evident that the hydrocyclone used was able to achieve some degree of fibre fractionation in terms of fibre length. Longer fibres were preferentially accepted and shorter fibres preferentially rejected. This result is in agreement with what we have observed before in our wood pulp fibre work using the same hydrocyclone design [46, 47, 81, 84, 85]. It is the opposite to what other workers in fibre fractionation have noted [28, 63, 85, 93], and to the theory described in Chapter 3. Ffowever given the turbulent flow inside the hydrocyclone, it is quite possible that conclusions reached in Chapter 3, based on Cox' Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 154 drag coefficients, valid only for low Reynolds number flows, are not relevant. Those workers who have reported that their hydrocyclones rejected long fibres were using different hydrocyclones than the one used in this work for nylon fibres. The degree of fibre separation achieved depended on the feed slurry consistency and feed flowrate. The lower the consistency the greater the difference between the accepts and rejects fibre length. At flowrates of 50 ~ 60 kg/min, there were minima in the plots of the accepts - rejects fibres vs. flowrate plots. The greatest differences between rejects and accepts mean fibre length were achieved at the highest flowrates used. 1.20 Arithmetic Av. Length (mm) 1.15 1.10 1.05 1.00 0.95 0.90 • 0.9% consistency (Feed A)_Tip \_Rejects O 0.9% consistency (Feed A)_Tip \_Accepts • 0.5% consistency (Feed A)_Tip \_Rejects V 0.5% consistency (Feed A)_Tip \_Accepts • 0.3% consistency (Feed A)_Tip \_Rejects • 0.3% consistency (Feed A)_Tip \_Accepts a The Accepts (A) 9 The Rejects (A) Q Feed (A) 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-36 Feed, accepts, and rejects fibre length vs. feed flowrate at various feed consistencies of Feed A Figures 5-1-37 and 5-1-38 are plots of SE m S/R and S E m L / A vs. flowrate. They show that the consistency did not have any significant affect on the SE m S/R of Feed B. As the flowrate increased, SE m S/R increased slightly, and S E m L / A decreased slightly. S E J L / A was Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 155 affected by consistency, that separation efficiency was higher for the lower consistency. Figure 5-1-39 is a plot of the centrifugal separation efficiencies, S E ^ / R ^ . It can be observed clearly that the lower consistency resulted in higher SEctrs at a given flowrate. SE^/R^,. increased as the flowrate increased. Figure 5-1-40 shows the combined separation efficiency, S E m S / R L / A , for Feed B. Again the higher values were noted for the lower consistency. Flowrate had no significant effect at 0.5% consistency but as flowrate increased so did this separation efficiency at 0.3%. Plots of the corrected and centrifugal separation efficiencies for long fibres in the accepts are not presented because subtracting the correction factor resulted in negative values, which are of course, impossible. The negative values were probably a result of taking the difference between numbers that were close to one another and to variations in the measured quantities. SE S/R 1.0 0.8 V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I 0.6 0.4 0.2 A 0.0 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-37 Separation efficiency for short fibres in the rejects for Feed B at various consistencies. Chapter5. EXPERIMENTAL RESULTS A ND DISCUSSION 156 1.0 0.8 0.6 0 . 4 0.2 S E m L / A 0.0 D o V V V 0.5% consistency (Feed B)_Tip I O 0.3% consistency (Feed B)_Tip I v 3 0 4 0 50 6 0 7 0 8 0 Feed Flowrate (kg/min) Figure 5-1-38 Separation efficiency for long fibres in the accepts for Feed B at various consistencies. 1.0 S E m S / R , , , 0.8 0.6 H 0.4 0.2 H 0 . 0 • V V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I • v 3 0 4 0 5 0 6 0 7 0 Feed Flowrate (kg/min) 8 0 Figure 5-1-39 Centrifugal separation efficiency for short fibres in the rejects for Feed B at various consistencies. Cbapter5. EXPERIMENTAL RESULTS AND DISCUSSION 157 SE_S/RL/A V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I 0.8 -0.6 A 0.4 A 0.2 - ° • v v v V v 0.0 -I 1 1 1 1 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-40 Combined separation efficiency for short fibres in the rejects for Feed B at various consistencies. Figure 5-1-41 -5-1-44 are plots of SEmS/R, SEJL/A, S E ^ / R ^ , and S E m S / R L / A vs. feed flowrate for Feed E . Figure 5-1-41 (as does Figure 5-1-37 for Feed B) indicates that consistency did not play much of a role in the uncorrected SE for getting short fibres into the rejects, however, in contrast, Figure 5-1-42 shows that consistency did have an influence on the SE for getting long fibres into the accepts. The lower the consistency the higher was the S E m L / A As flowrate increased SE m S/R increased. As flowrate increased S E m L / A did not change at 0.3% consistency but declined at 0.5%. Figure 5-1-43 shows that consistency had little effect on the centrifugal separation efficiencies for Feed E . Figure 5-1-44 demonstrates the combined separation efficiency results for Feed E . Its value increased as flowrate increased but consistency did not have much influence. Again negative values appeared when trying to calculate the corrected and centrifugal separation efficiencies. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 158 1.0 0.8 A 0.6 0.4 4 0.2 A SE„S/R o.o V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I • v • V 9 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-41 Separation efficiency for the short fibres in the rejects for Feed E at various consistencies. 1.0 0.8 0.6 0.4 0.2 SEmL/A 0.0 • v V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I v 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-42 Separation efficiency for long fibres in the accepts for Feed E at various consistencies. Chapter^. EXPERIMENTAL RESULTS AND DISCUSSION 159 1.0 0.8 0.6 0.4 0.2 SEmS/FL,r m ctr 0.0 v 0.5% consistency (Feed E)_Tlp I • 0.3% consistency (Feed E)_Tip I • v • V 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure 5-1-43 Centrifugal separation efficiency for short fibres in the rejects for Feed E at various consistencies. SE S/RL/A 1.0 0.8 0.6 0.4 0.2 0.0 • V V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I 9 • v • V —I 1 1 1— 40 50 60 70 Feed Flowrate (kg/min) 30 80 Figure 5-1-44 Combined separation efficiency for short fibres in the rejects for Feed E at various consistencies. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 160 Figures 5-1-45 and 5-1-46 show the effects of feed flowrate and feed composition on SE m S/R. Data for Feeds SI and S3 are included for reference. These were single component feeds each having fibres of only one fibre length; 1 mm for Feed SI and 3 mm for Feed S3. Thus fractionation of these feeds was not possible. All the fibres in this plot had a common coarseness of 0.17 mg/m Considering only the single component feeds SI and S3 Figure 5-1-45, for which consistency equal to 0.5%, indicates that as the mean fibre length decreased SE m S/R increased, thus indicating that fibre length plays a part in fibre mass reject ratio and that long fibres had lower separation efficiencies than short fibres. In considering the mixed fibre length feeds B and E , it again appears that the shorter, on average, fibres of Feed E had higher separation efficiencies than Feed B. As flowrate increased the value of SE m S/R also increased. Figure 5-1-46 illustrates similar effects at consistency equals to 0.3%. 1.0 0.8 0.6 A 0.4 0.2 A SE„S/R 0.0 30 O 0.5% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.5% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm • 0.5% consistency (Feed S1)_C = 0.17 mg/m, L = 1.0 mm O 0.5% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm o V O 40 V o o — I — 50 V O 60 70 Feed Flowrate (kg/min) 80 Figure 5-1-45 Separation efficiency for short fibres in the rejects for Feed B, E , SI, and S3 at 0.5% consistencies, L = number mean fibre length, C = number mean coarseness. Chapter 5. EXPERIME NTA L RESULTS AND DISCUSSION 161 1.0 SEmS/R 0.8 0.6 0.4 0.2 0.0 O 0.3% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.3% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm • 0.3% consistency (Feed S1 )_C = 0.17 mg/m, L = 1.0 mm O 0.3% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm • s o a v o O • v o O • v o • V o o 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure 5-1-46 Separation efficiency for short fibres in the rejects for Feed B, E , SI, and S3 at 0.3% consistencies, L = number mean fibre length, C = number mean coarseness. Summary The results in regard to fibre length have demonstrated that fibre fractionation based on length was achieved. Longer fibres were preferentially accepted and shorter fibres preferentially rejected. In this sense nylon fibres behaved in a similar way to wood pulp fibres when passing through the hydrocyclone that was used. This result is in agreement with what we have observed before in our research on wood pulp fibres and with the results of some others [46, 47, 81, 84, 85], also working with wood pulp fibres. However it is the opposite to what still other workers in fibre fractionation have noted [28, 63, 85, 93], and to the theory described in Chapter 3. Given the turbulent flow conditions inside the hydrocyclone, it is quite possible that conclusions reached in Chapter 3, based on Cox' drag coefficients, valid only for low Reynolds number flows, are not relevant. Those workers Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 162 who have reported that their hydrocyclones rejected long fibres were using different hydrocyclones than the one used in this work for nylon fibres. It is clear that the difference between rejects and accepts fibre length was dependent on consistency. The greatest difference was observed at the lowest consistency. It was also dependent on flowrate. At flowrates of 50 ~ 60 kg/min, there were minima in the differences between fibre length in the accepts and in the rejects. For the mixed fibre length feeds B and E it appeared that the shorter, on average, fibres of Feed E had higher separation efficiencies than Feed B. As flowrate increased the value of SE m S/R also increased. The separation efficiencies observed when fractionating on the basis of differences in fibre length tended to be lower than those noted when fractionating on the basis of coarseness differences. Perhaps our results with respect to fibre length can be rationalized by invoking a "wall effect" similar to one proposed by Karnis [56]. If the rejects tip opening is small (ours was 5 mm in most of our experiments) relative to the fibre length (our fibres had lengths of 1 and 3 mm) long fibres could be moving toward the rejects outlet but experience a bottleneck or partial blockage near the outlet. Thus there would be more opportunity for them to be dragged out of the rejects-bound flow near the wall, into the accepts-bound flow near the core. Figures 5-1-58 and 5-1-59 show the long fibres (3 mm) had lower mass rejects rations than short ones (1 mm) at consistencies of 0.3 and 0.5%. When 3 mm fibres at 0.9% consistency were used the rejects tip opening plugged. When a rejects tip openings of 6 mm was used plugging did not occur at 0.9% consistency. Li [64] using a 6 mm rejects tip opening found that the rejects fibres had a higher mean length weighted fibre length than the accepts. Another hydrocyclone used for fibre fractionation and which tends to reject long fibres is believed to have a rejects tip opening much greater than 5 mm Thus, the ratio of rejects tip opening Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 163 diameter to fibre length would appear to be an important factor in determining whether a hydrocyclone will tend to reject long or short fibres. 5.1.3 Mass Reject Ratio Mass reject ratio is the ratio of the mass flowrate of fibres in the rejects, to the mass flow rate of fibres in the feed. It is also equal to the product of the thiclffining ratio and the volumetric reject ratio. It is an important factor in determining whether a hydrocyclone fractionation would be of economic importance. Thus if fractionation is possible, then there has to be a sufficient amount of fibres in the rejects and accepts, that are sufficiently different from each another, to support any downstream processing of either or both of these streams. The mass reject ratios measured in the following ranged from 20 to 80% when fractionating on the basis of coarseness differences (Feeds A, Q D) and from 10 to 25% when fractionating on the basis of fibre length differences (Feeds B, E). These values are fairly high indicating that there could be an adequate amount of fibres in the accepts and rejects to provide for effective downstream processing, particularly when considering coarseness. Figures 5-1-47-5-1-54 are plots of mass reject ratio (as a percentage) as a function of feed flowrate at various feed consistencies for all of the types of feeds used. In almost all cases the mass rejects ratio increased as the feed flowrate increased. Use of Feed D resulted in little change with flowrate as did use of Feed S3 (3 mm fibres). In all of the tests done using Tip I (5 mm) the highest mass reject ratio was observed at the lowest consistency. With the 6 mm opening the opposite was noted. Generally speaking the highest mass reject ratios were noted at the lowest feed consistencies. Figure 5-1-55 demonstrates mass reject ratio vs. flowrate for feeds A, C, D, SI and S2 at 0.9% consistency in an attempt to sort out the role of fibre coarseness on this ratio. Considering Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 164 the single component Feeds SI (C = 0.17 mg/m) and S2 (C = 0.68 mg/m) it can be noted that the reject ratio was higher for the coarser fibres. This was also the case in Figures 5-1-53, 5-1-54 for 0.5 and 0.3% consistency. Plowever, in studying the behaviour of Feeds A, C and D it can be observed that the Feed C fibres, which had almost the same mean coarseness as the feed A fibres, had higher reject ratios, at all three consistencies, than the Feed A fibres. At low flowrates in Figure 5-1-55 (0.9% consistency) Feed D (C = 0.40 mg/m) ranked above all of the others. At high flowrates it ranked between Feeds A and C. In Figure 5-1-56 (0.5% consistency), Feed D gave the highest reject ratio at the lowest flow but as flowrate increased gave values more or less the same as Feed C even though its mean coarseness (C = 0.40 mg/m) was significandy higher. In Figure 5-1-57 (0.3% consistency) Feed D had the highest reject ratio at the lowest flowrate but as flowrate increased it ranked above Feed C as one would expect based on the relative coarseness values. It would appear that something other than consistency and mean coarseness was also playing a role in determining mass reject ratio. 100 Reject Ratio % (mass basis) 80 A 60 A • V o • • 40 A o 20 A O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I 0 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-47 Mass reject ratio vs. feed flowrate at various consistencies of Feed A. Chapter 5. EXPERIMENTA L RESULTS AND DISCUSSION 165 1 0 0 Reject Ratio % (mass basis) 80 60 40 20 i * O 0.9% consistency (Feed C)_Tip I V 0.5% consistency (Feed C)_Tip I • 0.3% consistency (Feed C)_Tip I 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-48 Mass reject ratio vs. feed flowrate at various consistencies of Feed C. 1 0 Q Reject Ratio % (mass basis) 80 60 A 40 20 • V • • <Sf a O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D) Tip I • 0.3% consistency (Feed D)_Tip I 30 40 50 60 Feed flowrate (kg/min) 70 80 Figure 5-1-49 Mass reject ratio vs. feed flowrate at various consistencies of Feed D. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 166 1 0 0 Reject Ratio % (mass basis) 80 H 60 40 H 20 <5> V V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I •v • V • V 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-50 Mass reject ratio vs. feed flowrate at various consistencies of Feed B. 1 0 0 Reject Ratio % (mass basis) 80 60 A 40 H 20 • V • V V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I • V • V • V 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-51 Mass reject ratio vs. feed flowrate at various consistencies of Feed E . Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 167 1 0 0 Reject Ratio % (mass basis) 80 60 A 40 20 O O 0.9% consistency (Feed S1 )_Tip I V 0.5% consistency (Feed S1 )_Tip I • 0.3% consistency (Feed S1 )_Tip I v o o —I 1 1 1— 40 50 60 70 Feed Flowrate (kg/min) 30 80 Figure 5-1-52 Mass reject ratio vs. feed flowrate at various consistencies of Feed SI. 1 0 0 Reject Ratio % (mass basis) 80 60 40 A 20 A V o • V o • V o • o7 O 0.9% consistency (Feed S2)_Tip I V 0.5% consistency (Feed S2)_Tip I • 0.3% consistency (Feed S2)_Tip I 30 40 50 60 Feed flowrate (kg/min) 70 80 Figure 5-1-53 Mass reject ratio vs. feed flowrate at various consistencies of Feed S2. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 168 100 Reject Ratio % (mass basis) 80 A V 0.5% consistency (Feed S3)_Tip I • 0.3% consistency (Feed S3)_Tip I 60 A 40 A 20 A * * * 30 40 50 60 70 80 Feed Flowrate (kg/min) Figure 5-1-54 Mass reject ratio vs. feed flowrate at various consistencies of Feed S3. 100 80 60 40 Reject Ratio % (mass basis) 20 A 0 0 o o o o o V O o O o O O o 0 -I 1 1 1 • 1 30 40 50 60 70 80 Feed Flowrate (kg/min) O 0.9% consistency (Feed A)_L = 1 mm, C = 0.27 mg/m V 0.9% consistency (Feed C)_L = 1 mm, C = 0.29 mg/m • 0.9% consistency (Feed D)_L = 1 mm, C = 0.40 mg/m 0 0.9% consistency (Feed S1)_L = 1 mm, C = 0.17 mg/m 0 0.9% consistency (Feed S2)_L = 1 mm, C - 0.68 mg/m Figure 5-1-55 Mass reject ratio vs. feed flowrate at 0.9% consistency of Feed A, Q D, S1.S2. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 169 100 Reject Ratio % (mass basis) 80 A 60 A 40 A 20 A o O O • 0 • • o o o o o 30 40 50 60 Feed Flowrate (kg/min) 70 80 O 0.5% consistency (Feed A)J_ = 1.0 mm, C = 0.27 mg/m V 0.5% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.5% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m O 0.5% consistency (Feed S1)_L = 1.0 mm, C = 0.17 mg/m 0 0.5% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m Figure 5-1-56 Mass reject ratio vs. feed flowrate at 0.5% consistency of Feed A, Q D, S1,S2. 1 Q 0 Reject Ratio % (mass basis) 80 60 40 20 • 0 O o • V • V o o o 0 -I 1 1 1 1 1 30 40 50 60 70 80 Feed Flowrate (kg/min) O 0.3% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.3% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.3% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m O 0.3% consistency (Feed S1)_L = 1.0 mm, C = 0.17 mg/m 0 0.3% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m Figure 5-1-57 Mass reject ratio vs. feed flowrate at 0.3% consistency of Feed A, C, D, SI, S2. Chapter5. EXPERIMENTAL RESULTS AND DISCUSSION 170 Figures 5-1-58 and 5-1-59 present mass reject ratio vs. feed flowrate for Feeds B, E , Si and S3 at 0.5% and 0.3% consistency in an attempt to isolate the effects of fibre length on mass reject ratio. Considering the single component feeds Si (L = 1 mm) and S3 (L = 3 mm) clearly the lowest fibre length gave rise to the highest reject ratio at both consistencies. The association of lower fibre length with higher reject ratio was also observed when Feeds B and E were compared at 0.5% and 0.3% consistencies. Figure 5-1-60 presents data on the reject ratio in terms of feed flowrate and consistency for Feed S3 using Tip II. As already noted use of Tip II resulted in inverting the effects of consistency on mass reject ratio when compared to the use of Tip I. As would be expected because of the wider diameter of Tip II, the mass reject ratios obtained with it were higher than those obtained with Tip I (compare Figures 5-1-60 and 5-1-54). 100 Reject Ratio % (mass basis) 80 60 40 20 O 0.5% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.5% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm • 0.5% consistency (Feed S1)_C = 0.17 mg/m, L = 1.0 mm O 0.5% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm z o v o o o v o 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-58 Mass reject ratio vs. feed flowrate at 0.5% consistencies of Feed B, E , SI and S3. Chapter5. EXPERIMENTAL RESULTS AND DISCUSSION 171 100 Reject Ratio % (mass basis) 80 60 40 4 20 30 O 0.3% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.3% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm • 0.3% consistency (Feed S1)„C = 0.17 mg/m, L = 1.0 mm O 0.3% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm V O O v o O V o V o V o 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-59 Mass reject ratio vs. feed flowrate at 0.3% consistencies of Feed B, E , SI, S3. 100 80 60 40 20 Reject Ratio % (mass basis) 30 O S o V O 0.9% consistency (Feed S3)_Tip II V 0.5% consistency (Feed S3)_Tip II o 0.3% consistency (Feed S3)_Tip II O V • V • v o 40 50 60 Feed Flowrate (kg/min) 70 80 Figure 5-1-60 Mass reject ratio vs. feed flowrate at various consistencies of Feed S3 with Tip II. Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 172 The crowding factor is a measure of the number of fibres inside a sphere having a diameter equals to the fibre length. It was hoped that perhaps this measure of fibre concentration would consolidate the effects of consistency, fibre length and fibre coarseness into one parameter. Perhaps that parameter would be an indicator of how fibres pack together as they concentrate when moving into the wall region flow, which moves towards the rejects outlet. It was also thought that the mass reject ratio might be a function solely of this parameter. Thus an attempt was made to correlate the mass reject ratio results by using the crowding factor (see Chapter 4, Section 4.4) as a correlating parameter. Figures 5-1-61 and 5-1-62 are plots of mass reject ratio and mass accept ratio vs. crowding factor. In these figures, data for the single component fibre feeds SI, S2 and S3 were used. The crowding factors were calculated from Equation (4.4.1) using values for the mean fibre length and mean coarseness and the consistency of either the rejects stream or the accepts stream Figure 5-1-61 shows that mass reject ratios when plotted against crowding factor gave straight lines such that as crowding factor increased so did mass rejects ratio, but each consistency, coarseness and fibre length gave rise to a distinctly different straight line. Figure 5-1-62 shows the mass accepts ratio vs. crowding factor. Here it can be seen at low values (close to 0) of the crowding factor with Feed S2, that the crowding factor had no effect on mass accepts ratio, nor did consistency. At higher values with Feed SI mass accepts ratio increased as the crowding factor increased, more or less linearly and there was a consistency effect. For Feed S3 the mass accepts ratio approached 100% and there was no obvious consistency effect other than the influence of consistency on the crowding factor itself. 5. EXPERIMENTAL RESULTS AND DISCUSSION 100 80 Mass Reject Ratio (%) 60 H 40 20 H • V • v o V D o V o V a v o D • v o • V o o -I 1 1 1 1 1 r 20 40 60 80 100 120 140 160 Rejects Crowding Factor (N) O 0.9% consistency (Feed S1)_CmR = 1.62% - 4.54%, C = 0.17 mg/m, L = 1.0 mm V 0.5% consistency (Feed S1)_CmR= 1.02%- 2.84%, C = 0.17 mg/m, L = 1.0 mm • 0.3% consistency (Feed S1)_CmR = 0.58% - 1.51%, C = 0.17 mg/m, L = 1.0 mm O 0.9% consistency (Feed S2) CmR = 3.49% - 8.22%, C = 0.68 mg/m, L = 1.0 mm V 0.5% consistency (Feed S2)_CmR = 2.01% - 4.45%, C = 0.68 mg/m, L = 1.0 mm • 0.3% consistency (Feed S2) Cm R = 1.45% - 2.69%, C = 0.68 mg/m, L = 1.0 mm V 0.5% consistency (Feed S3)_CmR = 0.12% - 0.35%, C = 0.17 mg/m, L = 3.0 mm • 0.3% consistency (Feed S3)_CmR = 0.09% - 0.25%, C = 0.17 mg/m, L = 3.0 mm Figure 5-1-61 Mass reject ratio vs. rejects crowding factor of Feed SI, S2, S3. Chapters. EXPERIMENTAL RESULTS AND DISCUSSION 174 1 0 0 Mass Accept Ratio (%) 40 60 80 100 120 140 Accepts Crowding Factor (N) O 0.9% consistency (Feed S1)_Cm A= 0.782% - 0.470%, C = 0.17 mg/m, L = 1.0 mm V 0.5% consistency (Feed S1 )_Cm A = 0.458% - 0.281 %, C = 0.17 mg/m, L = 1.0 mm O 0.3% consistency (Feed S1)_Cm A = 0.293% - 0.198%, C = 0.17 mg/m, L = 1.0 mm O 0.9% consistency (Feed S2)_Cm A = 0.576% - 0.007%, C = 0.68 mg/m, L = 1.0 mm V 0.5% consistency (Feed S2)_Cm A = 0.302% - 0.006%, C = 0.68 mg/m, L = 1.0 mm • 0.3% consistency (Feed S2)_Cm A= 0.191% - 0.001%, C = 0.68 mg/m, L = 1.0 mm V 0.5% consistency (Feed S3)_Cm A = 0.482% - 0.455%, C = 0.17 mg/m, L = 3.0 mm • 0.3% consistency (Feed S3) C m A = 0.341% - 0.318%, C = 0.17 mg/m, L = 3.0 mm Figure 5-1-62 Mass accepts ratio vs. rejects crowding factor of Feed S i , S2, S3. Thus it would appear that the crowding factor as the sole correlating parameter is not very useful in determining hydrocyclone mass reject or accept ratios. In considering these effects one should keep in mind that the rejects tip opening was 5 or 6 mm while the accepts outlet diameter was 16 mm. Mass reject ratio was particularly low and mass accepts ratio was particularly high for the 3 mm long fibres of Feed S3. No further work was done attempting to relate crowding factor to reject ratio. Flowever, it is interesting to note that Kerekes and Schell Chapter 5. EXPERIMENTAL RESULTS AND DISCUSSION 175 [60] have suggested that if N is less than 65 coherent floes are unlikely to be found. In this study the Crowding Factor (N) values ranged from almost 0 to almost 140. In the accepts flow the N values were less than 65 for all Feeds but Feed S3, which contained only 3 mm long fibres. In the rejects flows there were also several cases in which N was less than 65. Thus, in computing fibre trajectories in a hydrocyclone perhaps ignoring flocculation and consistency effects could be justified in some cases on the grounds of low crowding factor, however more research is necessary before such factors justifiably are ignored. Summary As feed flowrate increased mass reject ratio tended to increase. The highest mass reject ratios were noted at the lowest consistencies when the rejects tip diameter was 5 mm for all types of feeds. With a 6 mm rejects tip opening the highest mass reject ratio was observed at the highest consistency. For the single component feeds Si and S2, the higher the coarseness the higher was the mass reject ratio. This relationship between coarseness and reject ratio did not apply well to the mixed fibre coarseness Feeds A C and D. For the single fibre component Feeds SI and S3 the longer the fibre length was the lower the mass reject ratio. With the mixed fibre component Feeds B and E the mean fibre lengths were close to one another (1.3 mm and 1.1 mm). At 0.5% consistency there was no significant difference in the mass reject ratios for these two feeds, although the fibres with the longer mean length gave rise to the lower mass reject ratio. There was more difference at 0.3% consistency and again the longer fibres gave the lower reject ratio. Thus the pattern for the single component and the mixed component feeds was the same but the reject ratios for the 1.1 mm fibres (Feed E) were significantly lower than those of the 1 mm fibres (Feed SI). Chapter 6. COMPUTATIONAL FLUID DYNAMICS 176 Chapter 6 C O M P U T A T I O N A L F L U I D D Y N A M I C S 6.1 Introduction Significant experimental work has been done to investigate velocity profiles within a hydrocyclone [27, 58, 59, 62, 80, 89]. Thus, equations to estimate particle separation efficiency have usually relied on empirical formulas, which were derived from experimental results. There is a complex flow of three phases, solids, liquid, and air in a hydrocyclone. Because the pressure at the center of a cyclone can be lower than atmospheric pressure and the apex is usually open to the atmosphere, an air core may be formed inside. But there is very little literature that deals with the shape, size, and effects of the air core. Computational Fluid Dynamics (CFD) can be used to predict flow and pressure patterns in flows where measurements of velocity and pressure may be difficult or impossible. For example C F D has been used to measure the hydraulic resistance of a pulp screen slot [38,112]. Complete modeling of the flow in a hydrocyclone would involve predicting the liquid phase velocities, slurry concentration profiles, the turbulent viscosities, and the slip velocities of particles with respect to the liquid; from these, particle trajectories could be plotted and separation efficiencies could be calculated. Thus the prediction of hydrocyclone behavior could be sought by applying the fundamentals of fluid mechanics to obtain a mathematical model which could then be used to predict the separation efficiency of a hydrocyclone. Some relevant investigations have already been done in this direction [51, 52, 66, 67, 68,87]. Chapter 6. CQMPUTA TIONA L FL UID DYNAMICS 177 A computational procedure has been used in our research group to predict the fluid velocity fields, etc. in hydrocyclones of different geometry operating under a wide range of conditions. The CFD turbulence model we have used is the k-£ model. Malhotra et al. [66, 67, 68] proposed a modified k-e turbulence model to predict the fluid flow field in hydrocyclone operated without an air core. The modifications included an equation for the tangential velocity and modified transport of turbulent dissipation equation. Reasonable agreement between some of the experimental data of Dabir and Malhotra's model predictions was observed [27, 66, 67, 68]. The modeling can be separated into two parts: calculating the liquid phase flow field to predict the liquid phase velocities, and then calculating particle motion with respect to the fluid. From the trajectories of the particles of each size starting from various entry points it can be determined whether a particle will be rejected or accepted and hence a separation efficiency can be calculated. For dilute slurries, where the variations of local density and viscosity are small and the particle/particle interactions can be reasonably neglected the computation of the liquid-phase velocities and particle motion can be executed. 6.1.1 The Mathematical Model The mathematical model used to describe the fluid motion is based on a standard k-e model, which involves conservation equations for mass, momentum, kinetic energy of turbulence and its dissipation [106]. Cylindrical coordinates were used and constant fluid density was assumed. It was also convenient to adopt an axi-symmetric approach to model the flows inside a hydrocyclone, because it appears that a hydrocyclone rapidly approaches an axially symmetric condition away from the inlet. Hsieh [51, 52] observed that velocity profiles in the main body of a hydrocyclone which determine particle classification were axi-symmetric. Under Chapter 6. COMPUTA TIONAL FLUIDDYNAMICS 178 the assumption of axi-symmetry, the relevant number of significant coordinates can be reduced so that we have a two-dimensional problem. Malhotra et al.'s [66, 67, 68] equation for the dissipation of turbulent kinetic energy was employed. The standard constants for the k-e model, together with the constants proposed by Malhotra et al. for the modified dissipation equation, were used. However, this axi-symmetric assumption is not accurate in the region near the feed inlet, and the use of the step-wise rectangular grid to approximate the inclined side wall might result in inaccurate representation of the wall boundary. A fully three-dimensional model was studied by He et al. [43]. Their computational mesh was constructed using a union of cylindrical grids for the radial-circumferential planes with curvilinear grids for the radial-axial plans. Their 3D modelling shows extra detail for the structure of the flow field near the inlet pipe. 6.1.1.1 Turbulence Model In addition to the usual continuity equation and the Navier-Stokes equations, the k-e model includes equations for the transport of turbulent kinetic energy (k) and its dissipation (e). These equations are shown as following: Standard k- e Model 3k 3k a U h V = dx dr 3x rvjk} i a ( v .ak^ +-a r ov3r + (P-e) (6.1.1) a e + v a e _ _ a / ax ar ax v,ae ^ i a ar v t 3e V ^ 7 +(p.-o (6.1.2) where v, =C„ The Dissipation Equations: Chapter 6. COMPUTATIONAL FLUID DYNAMICS 179 The Conventional Model is: P £ - e E = C e ^ P - C £ ^ -k k The Modified Model (Malhotra [67]) is: l 5 E 2 k 4 For the high Reynolds number region: CLk< where C L = 0.18 + 0.1851 For the low Reynolds number region: L = y w The constants of the Modified Model are: ok = 1.0, ce = 1.3, Q , = 1.44, Q 2 = 1.92 (6.1.3) (6.1.4) (6.1.5) (6.1.6) and Qt= 0.09, = 0.76, Q = 2.7 6.1.1.2 Boundary Conditions (B.C.) and Assumptions • No slip (all velocities are 2ero) on all solid boundaries. • Impermeable, no flow through solid boundaries. • Uniform velocity boundary conditions were used at the exits and inlet, the velocity being calculated from the specified mass flow rates at inlet and exits. The radial velocity (V), is regarded as positive in an outward direction from the centerline. The axial velocity (U), is regarded as positive in a downward direction towards the conical part. Chapter6. COMPUTATIONAL FLUE)DYNAMICS 180 • At the inlet: the specified velocities were the radial (V) and swirl (tangential) (W) velocities. • At the exits (both underflow and overflow): the specified velocities were the axial velocity (U), and both the radial velocity (V) and the axial gradient swirl velocity (3W/3X) were set equal to zero. • The assigned inlet radial velocity (V) was computed from V ; n l e t = M i n / p p D D 1 5 the assigned inlet swirl velocity (W) was calculated from W i n l e t = 4 M i n / pnD\, where = mass feed flowrate (kg/s), D = diameter of the widest section of a hydrocyclone (m), ~DX = inlet diameter (m). Similarly, the assigned uniform exit velocities were computed from the specified mass flow rates at the exits. • Uniform kinetic energy and dissipation were specified at the inlet with zero axial gradients at the exit. • The inlet kinetic energy was calculated from K I N =a t Uf n , with = 10"3, the turbulence dissipation at the inlet was calculated from e in = (2K<^)/A,r , where XK (a length scale) was set equal to 0.005 times the radius of the base of the hydrocyclone [68]. • As the flow was considered to be axi- symmetric, the radial velocity (V) and the tangential velocity gradient in the radial direction (9W/9r) can be considered to be zero on the axis of symmetry. 6.1.1.3 Air Core When there is a lower than atmospheric pressure region in the center of a hydrocyclone, and if the cyclone is open to the atmosphere, then air flows into this low pressure, center region. Sevilla [95] assumed that the air liquid boundary was impermeable and that the radial and Chapter 6. COMPUTA TIONAL FLUID DYNAMICS 181 3U~ tangential velocities were equal to zero at the air/water interface (— 3r = 0). She chose an interface air core diameter arbitrarily as some specified fraction of the diameter of the reject tip. She found that there was no clear evidence that the air core influenced the axial and radial velocity profiles, but it was evident that the magnitude of the tangential velocity decreased as the diameter of the air core increased. The pressure profile showed no significant difference as a result of different diameters of the core. The presence of the air core slightly increased the pressure drop. The kinetic energy of the turbulence and its dissipation increased with the air core diameter increased. 6.1.2 Computational Code The computer program used in this work was the T E A C H code, which was originally developed at Imperial College, London, UK, but it was modified by Malhotra et al. [68] to conform for fitting the geometry of a hydrocyclone. This code is able to accommodate non-uniform grids. Indeed, it applied a staggered grid so that the grid locations for the axial velocity are different in the axial direction from the other variables. Similarly, the radial locations of radial velocity are different from the other variables [82]. Finite difference methods were used to solve the continuity equation, the Navier-Stokes equations and the modified turbulent transport equations. A grid was designed to fit our hydrocyclone geometry, see Figure 6-1-1. The radial space was divided into three uniformly spaced zones with the grid spacing different for each zone. In the axial direction, four uniformly spaced zones with the grid spacing different for each zone were also employed. Chapter 6. CQMPUTA TIONAL FLUIDDYNAMICS 182 Y ( m ) 0.04 0.02 0.00 0.2 0.4 0.6 X ( m ) 0.8 Figure 6-1-1 Diagram of a non-uniform F D (finite difference) grid with a 42x32 control volume (CV) grid, X: axial position, Y: radial position. Y scale is expanded (X/Y = 1/5) to give a clearer illustration of the grid pattern. In the conical section, the axial grid spacing was dependent on the cone angle and the radial spacing in order to account for the conical shape. These were arranged so that the number of radial nodes reduced by one node at each consecutive step in the conical section, see Figure 6-1-2. The grid cells were small enough to guarantee that the results were independent of the grid size. As currently set up we use a 42x32 grid for the calculations [66, 67, 68]. Figure 6-1-2 Grid divisions for computations. Chapter6. COMPUTA TIONAL FLUID DYNAMICS 183 6.1.2.1 The Particle Separation Efficiency To determine the particle separation efficiency, the first stage was to estimate the trajectory of each particle from the time it entered the hydrocyclone to the time it exited from one of the outlets. The relative velocity between the particle and the fluid must be determined before the particle trajectory can be calculated. 6.1.2.1.1 Particle Trajectory In order to trace the particle trajectory, the particle velocity has to be determined. The particle velocity is obtained from both the fluid velocities, which are computed by using C F D methods, and the particle slip velocities, which are calculated by a dynamic force balance on the particle. Once the particle velocity was determined, the particle trajectory can be traced throughout the hydrocyclone by a numerical integration. The path of each particle entering the hydrocyclone at various inlet positions was calculated. Thus, it was determined, for each particle, whether it would leave the hydrocyclone via the rejects or accepts outlet. After a sufficiently large number of particles trajectories have been calculated, then the particle separation efficiency can be calculated. A subroutine was developed by Sevilla, which calculated the trajectories of particles having different sizes and different entry positions. It determines the separation efficiency for each particle size. These computational programs also have been modified by author to make them more suitable and efficient to solve our problems, but we were not used to calculate the fibre trajectories. Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 184 6.2 Computational Results 6.2.1 The Velocity and Pressure Profiles In this current work regarding the velocities, pressure, turbulent kinetic energy and dissipation of turbulent kinetic energy, calculations were carried out for water in hydrocyclones, with the configurations and flowrates tabulated in Table 6-2-1. These computational works were done for the Bauer 3" cleaner detailed in Chapter 4. Note that at the time the computations were done an error was made in measuring the dimensions of the hydrocyclone. The correct dimensions and the ones used in the computations are shown in Figure 4-2-1. The simulation results, which were obtained from the CFD methods described, are presented below to show the flow profiles inside a hydrocyclone. Table 6-2-1 Dimensions, feed flowrates (kg/s), and overflow/underflow ratio used in CFD, see Figure 4-2-1, page 111. Bauer Cleaner D(m) 0.0762 D,(m) 0.0127 D2(m) 0.0508 Ds(m) 0 . D4(m) 0.8954 D5(m) 0.0258 D6(m) 0.0032 Min (kg/s) Mass Flowrate of Feed 0.67,0.83,1.0 Min/Mun Mass Flowrate of Feed/Mass Flowrate of Underflow 8 Chapter 6. COMPUTATIONAL FLUID DYNAMICS 185 Figures 6-2-1 to 6-2-9 demonstrate what can be done using our existing CFD model for flows in a hydrocyclone. Three flowrates were chosen to cover the range in which optima were noted in terms of coarseness and fibre length differences as described in Chapter 5. In addition, the same reject ratio used in the CFD calculation. Our objective here was to see if there was anything obvious in the velocity distributions inside the hydrocyclone which could suggest why these optima occurred. The output files generated by the CFD model were converted to various graphical outputs using TECPLOT-v.8.0 software. The radial dimension (R) has been magnified relative to the axial dimension in the contour diagrams and vector plots for clarity. For the axial velocities, a positive value indicates a velocity directed towards the apex of the conical section. For the radial velocities, a positive value indicates a velocity directed towards the wall of the hydrocyclone. Figure 6-2-1 is a pressure contour diagram illustrating the pressure prevailing inside the Bauer 3" hydrocyclone and Figure 6-2-2 shows profiles of the pressure at various locations inside the Bauer 3" hydrocyclone. The x dimension on these plots is the distance from the top (vortex finder end) of the hydrocyclone. x = 0.0267 m is between the top of the hydrocyclone and the bottom of the vortex finder, x = 0.0589 m is just below the bottom of the vortex finder. The other x values are progressively further away from the bottom of the vortex finder. The vortex finder is located at R = 0.013 m. The zero pressure values at the hydrocyclone wall are an artifact of the computational code. It can be seen that as the feed flowrate increased from 40 l^min. to 60 kg/min. the magnitude of the pressure inside tended to increase. Since pressure drop is a function of flowrate (see Figure Fl-1, Appendix F) this is what would be expected. The highest pressures are at the inlet and the lowest at the oudets. The rejects outlet was open to the surroundings so, Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 186 as expected, the pressure in the region of that outlet was 0. Thus the pressure contours tend to conform 'with expectations lending some support to the validity of the CFD modelling process. Figure 6-2-3 is an axial velocity contour diagram depicting the axial fluid velocities prevailing inside the Bauer 3" hydrocyclone. Figure 6-2-4 presents profiles of axial fluid velocity drawn at various distances from the top of the hydrocyclone. It can be observed that as the flowrate increased, the axial fluid velocity increased both in the upward and downward directions. Note that near the inlet at the top of the hydrocyclone there are axial velocities directed towards the rejects opening. Near the wall but closer to the hydrocyclone core the velocities are directed upward towards the accepts opening. For x = 0.673 m the whole flow is reject bound. Short circuit flows near the vortex finder can be seen. Figure 6-2-5 is a radial velocity contour diagram illustrating the radial fluid velocities prevailing inside the Bauer 3" hydrocyclone and Figure 6-2-6 shows profiles of these radial velocities at various locations inside the hydrocyclone. Note that the radial fluid velocities are much smaller than the axial (Figures 6-2-3 and 6-2-4) and tangential fluid velocities (Figures 6-2-7 and 6-2-8). Figure 6-2-7 is a tangential fluid velocity contour diagram which shows the tangential velocities prevailing inside the Bauer 3" hydrocyclone. Figure 6-2-8 shows profiles of these tangential velocities at various locations inside the hydrocyclone. As feed flowrate increased the tangential velocities increased. For the uppermost two profiles the tangential velocities were 0 at the wall, rose to their highest values near the wall, then dropped, reaching 0 again at the vortex finder. They then rose to a maximum inside the vortex finder and went down to 0 at the centre of the vortex finder. Below the vortex finder the tangential velocities went from 0 at the wall to a maximum value and then back down to 0 at the centre of the hydrocyclone. These velocity Chapter 6. COMPUTATIONAL FLUID DYNAMICS 187 profiles displayed reasonable agreement both in overall trend and in magnitude with the experimental results of Kelsall (see Figure 3-1-1) and Efcieh [51]. Figure 6-2-9 is a vector plot of radial/axial fluid velocity patterns for this 3" Bauer cleaner under the same conditions used in plotting the velocity and pressure contour diagrams. The expected pattern of the downward axial flow near the wall and the upward flow near the core can be clearly observed. Several short-circuit flows also appeared near the inlet, and at the middle of the conical section. These short-circuit flows (eddy) could effect the residence time that a particle is in the hydrocyclone and its separation efficiency. Consideration of Figures 6-2-1 — 6-2-9 does not point to any immediately obvious reason, such as for example, the formation and disappearance of an eddy, as to why optima occurred in the differences between accepts and rejects coarseness and fibre length at feed flowrates between 40 and 60 kg/min. The vector diagrams of Figures 6-2-9, when superimposed, do show that the higher the flowrate the greater were the fluid velocities heading towards the vortex finder (accepts) outlet. They also indicate that more of the flow is moving towards the accepts as flowrate increases, thus less flow would go to the rejects. These results are consistent with the trends in volumetric reject ratio as indicated in Figure E4-1 to E4-13. Thus, the next step in a CFD analysis should be the calculation of fibre trajectories. Chapter 6. COMPUTA TIONAL FL UID DYNAMICS 188 Reynolds Number = 8.38E+4 Feed Flowrate = 40 kg/mln Overflow/Underflow = 8 R(m) 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96 E+2 kg/m3 P(Pa) 14000.0 12250.0 10500.0 8750.0 7000.0 5250.0 3500.0 1750.0 500.0 50.0 0.0 0.0 X(m) Reynolds Number = 1.04E+5 Feed Flowrate = 50 kg/min Overflow/Underflow = 8 R(m) 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96 E+2 kg/m3 P(Pa) •14000.0 12250.0 10500.0 '—| 8750.0 I 7000.0 5250.0 3500.0 1750.0 500.0 50.0 00 = 0.0 X(m) Reynolds N umber = 1.25E+5 Feed Flowrate = 60kg/min Overflow/Underflow = 8 R(m) 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density • 9.96 E+2 kg/m3 P(Pa) 14D00.0 12250.0 10500.0 8750.0 7000.0 5250.0 3500.0 1750.0 500.0 500 00 0.0 X(m) Figure 6-2-1 Pressure contour plots of Bauer 3" Cleaner at various feed flowrates. Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 189 Feed Flowrate = 40 kg/min Ratio (Overflow/Underflow) = 8 Feed Flowrate = 50 kg/min Ratio (Overflow/Underflow) = 8 S a . x = 0.0267 m x = 0.0589 m x = 0.124 m x = 0.382 m x = 0.673 m -Z? 20000 CO Q. a. x = 0.0267 m x = 0.0589 m x = 0.124 m x = 0.382 m x = 0.673 m 0.01 0.02 0.03 Radial Position (m) 0.02 0.03 Radial Position (m) Feed Flowrate = 60 kg/s Ratio (Overflow/Underflow) = 8 e a . x = 0.0267 m X = 0.0589 m x = 0.124 m x = 0.382 m x = 0.673 m 0.02 0.03 Radial Position (m) Figure 6-2-2 Bauer 3" Cleaner: computed pressure profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Chapter 6. COMPUTA TIONAL FLUID DYNAMICS 190 U (m/s) X(m) U (m/s) Reynolds Number = 1.04E+5 Feed Flowrate = 50 kg/min Overflow/Underflow = 8 R(m) 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96E+2 kg/m3 2.00 1.50 1.00 0.50 0.00 •0.00 -0.50 -1.00 -1.50 -2.00 X(m) U (m/s) Reynolds Number = 1.25E+5 Feed Flowrate = 60 kg/min Overflow/Underflow = 8 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96E+2 kg/m X(m) Figure 6-2-3 Axial fluid velocity contour plots of Bauer 3" Qeaner at various feed flowrates. Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 191 Feed Flowrate = 60 kg/min Ratio (Overflow/Underflow) = 8 " 2 0 0 0.01 0.02 0.03 Radial Position (m) Figure 6-2-4 Bauer 3" Cleaner computed axial fluid velocity profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Chapter 6. COMPUTA TIONAL FLUID DYNAMICS Reynold Number = 8.38E+4 Feed Flowrate = 40 kg/min Overflow/Underflow = 8 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density • 9.96 E+2 kg/m R(m) 0.04 H V (m/s) 0.200 0.165 0.130 0.095 0.060 0.025 0000 -0.000 -0.010 -0.045 -0.080 -0.115 -0.150 X(m) V(m/s) Reynold Number = 1.04E+5 Feed Flowrate = 50 kg/min Overflow/Underflow = 8 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96 E+2 kg/m3 0200 0.165 0130 0.095 0.060 0025 0.000 -0 000 -0010 -0 045 -0.080 -0.115 -0150 X(m) V (m/s) Figure 6-2-5 Radial fluid velocity contour plots of Bauer 3 " Cleaner at various flowrates. Chapter 6. CQMPUTA TIONA L FL UID DYNAMICS 193 Feed Flowrate = 40 kg/min Ratio (Overflow/Underflow) = 8 0 0.01 0.02 0.03 Radial Position (m) Feed Flowrate = 60 kg/min Ratio (Overflow/Underflow) = 8 [ 1 1 1 0 0.01 0.02 0.03 Radial Position (m) Feed Flowrate = 50 kg/min Ratio (Overflow/Underflow) = 8 «r o.io E f £ 0.05 > 1 •o IS 0.00 oc -0.05 x = 0.0267 m x = 0.0589 m x = 0.124 m X = 0.382 m X = 0.673 m I I 0 0.01 0.02 0.03 Radial Position (m) Figure 6-2-6 Bauer 3" Cleaner: computed radial fluid velocity profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 194 Reynold Number = 8.38E+4 Feed Flowrate = 40 kg/min Overflow/Underflow = 8 R(m) 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96 E+2 kg/m W (m/s) W 700 6.13 HH 5.25 ™ 4.38 — 3.50 • 2.63 • 1.75 • 0.88 • O.OO 0.00 X(m) Reynold Number = 1.25E+5 Feed Flowrate = 60 kg/min Overflow/Underflow = 8 R(m) 0.04 H 30°C Fluid Viscosity = 8.00E-4 Pa s Fluid Density = 9.96 E+2 kg/m3 W(m/s) 7.00 6.13 5.25 4.38 3.50 2.63 1.75 0.38 0DO 0.00 X(m) Figure 6-2-7 Tangential fluid velocity contour plots of Bauer 3" Geaner at various feed flowrates. Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 195 Feed Flowrate = 40 kg/min Feed Flowrate = 50 kg/min Ratio (Overflow/Underflow) = 8 Ratio (Overflow/Underflow) = 8 ^8 .oo F 5 8 0 0 r Feed Flowrate = 60 kg/min Ratio (Overflow/Underflow) = 8 Radial Position (m) Figure 6-2-8 Bauer 3" Qeanen computed tangential fluid velocity profiles at various positions of different values of feed flowrate and same overflow/underflow ratio. Chapter 6. COMPUTA TIONA L FL UID DYNAMICS 196 Reynolds Number = 8.38E+4 30°C Feed Flowrate = 40 kg/min Fluid Visciosity = 8.00E-4 Pa s Overflow/Underflow = 8 Fluid Density = 9.96 E+2 kg/m R(m) Reynolds Number = 1.04E+5 30°C Feed Flowrate = 50 kg/min Fluid Visciosity = 8.00E-4 Pa s Overflow/Underflow = 8 Fluid Density = 9.96 E+2 kg/m3 R(m) Reynolds Number = 1.25E+5 30°C Feed Flowrate = 60 kg/min Fluid Visciosity = 8.00E-4Pa s Overflow/Underflow = 8 Fluid Density = 9.96 E+2 kg/m R(m) Figure 6-2-9 Vector plots of radial and axial fluid velocity patterns of Bauer 3" Cleaner at various feed flowrates. Chapter7. CONCLUSIONS 197 Chapter 7 CONCLUSIONS 7.1 Theory A theoretical, fluid dynamical analysis was used to develop the equations of motion for fibres, both swollen and unswollen, moving in a centrifugal field. According to the theory, a fibre of larger diameter, or lower specific surface, or higher specific volume/specific surface ratio (if swollen) or higher coarseness value or bigger L / D value, would have a higher radial velocity which means that it would move faster towards the wall, in a given residence time in a hydrocyclone, and would be more likely to be dragged along with the downward flow to the rejects outlet. The theory is in agreement with the experimental work of the author in terms of fibre diameter, specific surface and coarseness using nylon fibres. It is also in agreement with the experimental work of others using wood pulp fibres (e.g. Wood and Karnis [110], Rehmat [85]) with respect to specific surface and coarseness. In terms of fibre length, assuming Cox' drag coefficients are correct, the theory predicts that long fibres would be preferentially rejected whereas the author's and some other's [81, 85] experiments, using a Bauer hydrocyclone, showed that short fibres tended to be rejected. On the other hand the theory's predictions are in agreement with the experimental works of [28,63,85,93] in terms of fibre length. The model used in deriving the equations of motion requires determining a and a using Robertson and Mason's water permeability technique, and a measurement of p f w or pf. Chapter7. CONCLUSIONS 198 Calculated Reynolds numbers for fibres moving in a hydrocyclone were sufficiently low that experimentally measured drag coefficients were applicable in some situations. However in others they were too high. They were also affected significantly by the fibre's swellability. Equations for calculating separation efficiencies (SEJ have been derived mathematically. These equations for calculating the separation efficiencies should be useful in accounting for how successful a hydrocyclone would be in directing coarse (short) fibres to the rejects and fine (long) fibre to the accepts. 7.2 Nylon Fibre Fractionation: Nylon fibres behaved in a qualitatively similar way to wood pulp fibres when passing through the hydrocyclone used in the experiments. That is the hydrocyclone tended to reject coarse, short fibres. • Coarseness The results presented in Chapter 5 have demonstrated that fibre fractionation based on coarseness was achieved. Coarser fibres were preferentially rejected, and finer fibres were preferentially accepted. As the flowrate increased, the coarseness values of both the rejects and the accepts decreased. The degree of fibre separation depended on feed slurry consistency and feed flowrate. The lower the consistency the greater the difference between the rejects and accepts coarseness. There was an optimum flowrate, which occurred between 50 ~ 60 kg/min, that resulted in a maximum in the difference in coarseness value between the rejects and accepts. Chapter7. CONCLUSIONS 199 The experimental results were found to agree qualitatively with those predicted of the theory. The theory indicated that higher coarseness fibres would have higher radial velocities and thus would be more likely to be rejected than would finer fibres. Higher coarseness fibres tended to have higher separation efficiencies at a given consistency. Lower consistency resulted in higher SEs (Feeds SI, S2, A, D). The combined separation efficiencies were higher at lower consistency, and decreased as the flowrate increased (Feeds SI, S2, A, D). • Fibre Length The results have demonstrated that fibre fractionation based on length was achieved. Longer fibres were preferentially accepted and shorter fibres preferentially rejected. The difference between rejects and accepts fibre length was dependent on consistency. The greatest difference was observed at the lowest consistency. It was also dependent on flowrate. At flowrates of 50 ~ 60 kg/min, there were minima in the differences between fibre length in the accepts and in the rejects. For the mixed fibre length feeds B and E it appeared that the longer fibres (on average) of Feed E had higher separation efficiencies than Feed B. As flowrate increased the value of SEmS/R also increased. This result agrees with some other researchers' results, and with what our group has observed before in our wood pulp fibre work [46, 47, 81, 84, 85]. It is the opposite to what some workers in fibre fractionation have noted [28, 63, 85, 93], and to the theory described in Chapter 3. Those workers who have reported that their hydrocyclones rejected long fibres were using different hydrocyclones than the one used in this work for nylon fibres, thus hydrocyclone design (geometry) affects fibre fractionation. Chapter7. CONCLUSIONS 200 The separation efficiencies observed when fractionating on the basis of differences in fibre length are lower than those noted when fractionating on the basis of coarseness differences. Thus it would appear that fibre fractionation based on coarseness differences, at least in the hydrocyclone used, is easier than fibre fractionation based on differences in fibre length. Reject tip opening diameter appeared to play an important role in fractionation on the basis of fibre length. • Mass Reject Ratio As feed flowrate increased mass reject ratio increased. The highest mass reject ratios were noted at the lowest consistencies when the rejects tip diameter was 5 mm for all types of feeds. With a 6 mm rejects tip opening, the highest mass reject ratio was observed at the highest consistency. For the single component feeds SI and S2, the higher the coarseness the higher was the mass reject ratio. This relationship between coarseness and reject ratio did not apply well to the mixed fibre coarseness Feeds A, C and D. For the single fibre component Feeds SI and S3 the longer the fibre length was the lower the mass reject ratio. With the mixed fibre component Feeds B and E , the mean fibre lengths were close to one another (1.3 mm and 1.1 mm). At 0.5% consistency there was no significant difference in the mass reject ratios for these two feeds, although the fibres with the longer mean length gave rise to the lower mass reject ratio. There was more difference at 0.3% consistency and the longer fibres gave the lower reject ratio. Thus the pattern for the single component (SI, S3) and the mixed component feeds (B, E) was the same but the reject ratios for the 1.1 mm fibres (Feed E) were lower than those of the 1 mm fibres (Feed SI). Chapter7. CONCLUSIONS 201 7.3 Computational Fluid E)ynamics The results of the CFD simulations agree with what would be expected based on prior knowledge of hydrocyclone behaviour. The trends and relative magnitudes of the pressure (P), and the velocities (U, V, W) are as expected thus providing some support for the validity of the CFD modelling process. These pressure and velocity profiles displayed reasonable agreement both in overall trend and in magnitude with experimental observations of Bradley, Kelsall, and Hsieh [17,51,59]. Chapter 8. RECOMMENDATIONS FOR FUTURE WORK 202 Chapter 8 RECOMMENDATIONS FOR FUTURE WORK 1) Using a transparent hydrocyclone and a high speed motion picture or video camera, images of fibres moving in a hydrocyclone should be obtained to see if fibres rotate or remain in a fixed orientation. The results could be used in deciding whether or not the models of Chapter 3 need to consider fibre rotation. These images could also be used in comparing the imaged fibre trajectories with those predicted using CFD. 2) The kinds of nylon fibre studies done in this thesis should be repeated using a hydrocyclone that is known to reject long fibres. 3) More detailed studies of the effects of hydrocyclone design on fibre fractionation should be made. Thus the effects of several different reject tip openings, vortex finder diameters, cone angles, overall diameters etc. on separation efficiency should be measured. 4) The effects of an air core and its size in predicting fibre trajectories, using CFD, should be investigated. 5) Attempts should be made to measure drag coefficients for swollen fibres at fibre diameter based Reynolds numbers greater than 2. 6) Mass reject ratios should be measured over a range of flowrates at several consistencies, up to 1.5%, using fibres having several values of coarseness but the same fibre length, and several values of fibre length but the same coarseness. Chapter 8. RECOMMENDATIONS FOR FUTURE WORK 203 7) Use CFD to calculate fibre trajectories and then calculate separation efficiencies. 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Chem Eng., 51, June 1973. 63. Kure, K-A., Dahlqvist, G., Ekstrom, J., Helle, T . , "Hydrocyclone Separation, and Reject Refining, of Thick-Walled Mechanical Pulp Fibres", Nordic Pulp and Paper Research Journal, 14(2), 100,1999. 64. Li, M., "Fractionation of Pulp suspension and Characterization of the Fibre Fractions", Thesis of Master of Engineering Science, Department of Chemical Engineering, Monash University, Melbourne, Australia, Oct. 1997. BIBLIOGRAPHY 210 65. Li, M., Johnston, R., Xu, L., Filonenko, Y., Parker, I., "Characterization of Hydrocyclone-Separated Eucalypt Fibre Fractions', Journal of Pulp and Paper Science, 25(8), 299,1999. 66. Malhotra, A., Branion, R.M.R., Hauptmann, E . G . , "Near Wall Modeling of Turbulence", PGRL 505, Pulp and Paper Research Institute of Canada, 1992. 67. Malhotra, A., Branion, R.M.R., Hauptmann, E . G . , "A New Model of Turbulence Dissipation Equation", PGRL 543, Pulp and Paper Research Institute of Canada, 1993. 68. Malhotra, A., Branion, R.M.R., Hauptmann, E . G . , "Modeling the Flow in a Hydrocyclone'', PGRL 557, Pulp and Paper Research Institute of Canada, 1994, see also Canadian Journal of Chemical Engineering 72,953,1994. 69. Marton, R., Robie, J.D., "Characterization of Mechanical Pulps by a Settling Technique", Tappi, 52 (12), 2400,1969. 70. McCulloch, CD., "Cleaning Groundwood with Vorjects at Port Alfred", Pulp & Paper Magazine of Canada, 60(1), T22,1959. 71. Mickley, H.S., Sherwood T .K, Reed C.E., "Applies Mathematics in Chemical Engineering", Second Edition, McGraw-Hill Series in Chemical Engineering, McGraw-Hill Book Company, Inc., 1957. 72. Mohlin, U-B., "Fibre Bonding Ability - A Key Pulp Quality Parameter for Mechanical Pulps to Be Used in Printing Papers", Proceedings of the International Mechanical Pulping Conference, pp. 49, Helsinki, 1989. 73. Mukoyoshi, S., Ohsawa, J., "Mechanism of Vessel Separation with Hydrocyclone I. Vessel Separation with Qntri-Cleaner" (in Japanese), Japan TAPPI, 40(11), 55,1986. BIBLIOGRAPHY 211 74. Mukoyoshi, S., Ohsawa, J., "Mechanism of Vessel Separation with Hydrocyclone II. Settling Velocity of Pulp And Model Particles" (in Japanese, translation available), Japan TAPPI, 40(12), 71,1986. 75. Muvundamina, M., Li, M., "Fractionation of Recycled Pulp Obtained From Mixed Paper", Tappi, 80(2), 149,1997. 76. Noss, A.B., "Improved Mechanical Pulp for Wood Containing Printing Paper with Radiclone Fractionation Systems", brochure. 77. Ohtake, T. , Usuda, M., Kadoya, T. , "A Fundamental Study of Hydrocyclones Part 1. Flow Pattern in The Hydrocyclone", (in Japanese, translation available) Japan TAPPI, 41(2), 60,1987. 78. Olgard, G., "Fractionation of Fibre Suspensions by Liquid Column Flow", Tappi, 53(7), 1240,1970. 79. Olson, J.A., "The Effect of Fibre Length on Passage through Narrow Apertures", Ph.D. thesis, Department of Mechanical Engineering, University of British Columbia, Vancouver, B .G, 1996. 80. Ohasi, H . , Maeda, S., "Motion of Water in an Hydraulic Cyclone", Chml. Eng. Japan 22:200,1958. 81. Paavilainen, L., "The Possibility of Fractionating Softwood Sulfate Pulp According to Cell Wall Thickness", Appita, 45(5), 319,1992. 82. Patankar, S.V., "Numerical Heat Transfer and Fluid Flow", Hemisphere Publishing Corp., Washington, D.C., 1980. 83. Pesch, A.W., US patent 3,083,927, April 16,1963. 84. Rehmat, T . , Branion, R.M.R., "Fibre Fractionation in Hydrocyclones", preprints 81st Annual Meeting Technical Section Canada Pulp and Paper Association, Montreal, 1995. BIBLIOGRAPHY 212 85. Rehmat, T., "Fibre Fractionation in Hydrocyclones'', M.Sc Thesis, University of British Columbia, Vancouver, B.C., 2001. 86. Rewatakar, V.B., Masliyah, J.H., "Woodpulp Fibre Fractionation", in 'Mixed-flow hydrodynamics', Advances in Engineering Series, Gulf Publishing, Houston, 1996. 87. Rhodes, N., Pericleous, K A , Drake, S.N., "The Prediction of Hydrocyclone Performance with a Mathematical Model", 3rd Int. Conf. on hydrocyclones, Oxford, England, Paper B3,1987. 88. Ricker, N.L., House, K.L., "Thickening of Pulp Suspensions In A Hydrocyclone", AIChE Symposium Series Vol. 80, No.232, pp. 8,1984. 89. Rietema, K., "Performance and Design of Hydrocyclones- I, II, III, IV", Chemical Engineering Science, Vol. 15, pp.298-325,1961. 90. Robertson, A.A, Mason, S.G., "Specific Surface of Cellulose Fibres By The Liquid Permeability Method", Pulp & Paper Magazine of Canada, 50(13) 1,1949. 91. Rodes, N., Pericleous, K.A., Drake, S.N., "The Prediction of Hydrocyclone Performance with a Mathematical Model", 3rd Int. Conf. on Hydrocyclones, Oxford, England, Paper B3, 1987. 92. Sandberg, C , Nilsson, L., Nikko, A , "Fibre Fractionation - A Way to Improve Paper Quality", Proceedings, 1997 International Mechanical Pulping Conference, 1997. 93. Seifert, P., Long, K.J., "Fibre Fractionation - Methods and Applications", Tappi, 57(10), 69,1974. 94. Sevilla, E.M., Branion, R.M.R., "Simulation of the Flow in Hydrocyclones Operating without an Air Core", unpublished report, UBC Pulp and Paper Centre, 1995. BIBLIOGRAPHY 213 95. Sevilla, E.M., Branion, R.M.R., "Prediction of low Density Contaminants Removal in Dilute pulp Suspensions", internal report of University of British Columbia, Pulp and Paper Centre, 1997. 96. Smook, G.A., "Handbook of Pulp and Paper Terminology - A Guide to Industrial and Technology Usage", Angus Wilde Publications, Vancouver, B.C., 1990. 97. So, R.M.C., Zhang, H.S., Speziale, C.G. , "Near Wall Modelling of the Dissipation Rate Equation", AIAA Journal, 29(12), 2069-2076,1991. 98. Soszynski, R.M., Kerekes, R.J., "Elastic Interlocking of Nylon fibres Suspended in Liquid", Part 1, Nature of Cohesion among Fibres, Nordic Pulp and Paper Research Journal, No 4, pp. 172 - 179,1988. 99. Stephens, J.R., Pearson, AJ., "The Cleaning Of Eucalypt Groundwood by the Use of The 623 Bauer Hydrocyclone", Appita 21(3), 79,1967. 100. Strelis, I., Kennedy, R.W., "Identification of North American Commercial Pulp Woods and Pulp Fibres", pp. 97, Published in association with the Pulp and Paper Research Institute of Canada by University of Toronto Press, 1967. 101. Svarovsky, L., "Hydrocyclone", Technomic Publishing Co., Inc., 1984. 102. TAPPI, "Fibre Length of Pulp By Classification", TAPPI Test Method T233 cm-82,1982. 103. TAPPI, "Consistency of Stocks", TAPPI Test Method D16,1984. 104. Thode E.F., Ingmanson W.L., "Factors Contributing to the Strength of a Sheet of Paper I. External Specific Surface and Swollen Specific Volume ", Tappi, Vol. 42, No.l , pp. 74-83, Jan. 1959. 105. Vollmer, H . , "Fibre Fractionation for Quality Improvement of Multiply Paper", Paper 3, PIRA 5th International Paper and Board Industry Conference Scientific and Technical Advances in Refining, Vienna, 1999. BIBLIOGRAPHY 214 106. White, F.M., "Viscous Fluid Flow, 2nd Edition", McGraw Hill, New York, 1991, pp. 182. 107. Wong, B.T. , "The Hydrodynamics of Individual Pulp Fibres", M.Sc Thesis, University of British Columbia, Vancouver, B.C., 2000. 108. Wood, J.R., Grondin, M., Karnis, A., "Characterization of Mechanical Pulp Fines with a Small Hydrocyclone. Part I: The Principle And Nature Of The Separation", J. Pulp & Paper Science, 17(1), J l , 1991. See also Preprints 76th Annual Meeting, Technical Section, Canadian Pulp & Paper Association, Montreal, pp. B137,1990. 109. Wood, J.R., Karnis, A., "Towards A Lint-Free Newsprint Sheet", Paperi ja Puu 59(10), 660,1977. 110. Wood, J.R., Karnis, A., "Distribution of Fibre Specific Surface of Paperrnaking Pulps", Pulp & Paper Canada, 80(4), T116,1979. 111. Wood, J.R., Karnis, A., "Linting Propensity of Mechanical Pulps", Pulp & Paper Canada, 93(7), T191,1992. 112. Yu, CJ., Defoe R.J., "Fundamental Study of Screening Hydraulics. Part 1: Flow Pattern at the Feed-Side Surface of Screen Basket; Mechanism of Fibre-Mat and Remixing." TAPPI, 77(8): 219-226,1994. Appendix A. SUMMARY OF LITERATURE REVIEW ON FIBRE FRA CTIONATION IN HYDROCYCL ONES 215 Appendix A SUMMARY OF LITERATURE REVIEW ON FIBRE FRACTIONATION IN HYDROCYCLONES What follows is an abbreviation of the literature survey (Chapter 2) in the form of a list of effects of various parameters on hydrocyclone fibre fractionation as reported by various researchers. Effects of Equipment Configuration on Fibre Fractionation • Hydrocyclone DiameterBcackmy(1962)[14J, Jones etal. (1966)[53], Stephens etd (1967)[99] The smaller the diameter of the hydrocyclone, the higher the separation efficiency. • Hydrocyclone Cone Angle Karnis (1997)[56] A smaller cone angle hydrocyclone had a better separation efficiency than one with a larger cone angle. • Hydrocyclone Tip Size Jones et al (1966p3J, Stephens et al (1967)[99], Ho et al (1999, 2000)[46, 47] As the tip opening size increased, the amount of the rejects increased, and the amount of the accepts decreased. A larger tip produced a greater reject rate, consumed less power, provided the best separation of shives, specks and dirt, but it rejected an uneconomical amount of usable fibre. • Hydrocyclone Inlet/Outlet Diameter Bliss (1984)[6] Appendix A. SUMMARY OF LITERATURE REVIEW ON FIBRE FRACTIONATIONIN HYDROCYCLONES 216 A larger inlet than standard caused less fractionation. A smaller inlet than standard, showed no difference in fractionation compared to the standard but had lower capacity at equal pressure drop. With a smaller outlet, the capacity was reduced but fractionation had not improved. Effects of Fibre Properties on Fibre Fractionation in a Hydrocyclone • Summerwood/Springwood Pesch (1963)[83], Jones et al (1966)153], Mohlin (1989)[72], Paaukmen(1992)[81] The accepts contained the thin-walled springwood fibres, with low coarseness, the rejects consisted of coarse, thick-walled, summerwood fibres. There were some contradicting viewpoints which related to whether bleaching affected the springwood and summerwood fibre separation. • Freeness Jones et al (1966)[53J, Bliss (1984)[6], Gavdin et al(1991)[37], Wood etal (1977)fl09J, Rehrmtetal (1995)[84J, Kure etal (1999)[63], Ho etal (1999, 2000)[46, 47], Rehrmt(2001)[85] In generally, the rejects had higher freeness value than the accepts or the feed. The accepts had the lowest freeness. But the rejects having higher freeness values than the accepts might not always be true. • Specific Surface Jones et al (1966)[53], Wood et al (1977, 1979)[109, 110], Bliss (1983, 1984)[5, 6], Kure etal (1999)[63], Ho etal. (1999, 2000)[46, 47], Rebrmt (2001)[85] The rejects contained heavy contaminants, stiffer, less refined, lower specific surface fibres, and summerwood. The accepts contained light contaminants, flexible fibres, most of the extremely fine, well refined, higher specific surface fibres, and springwood. For unbeaten, mechanical pulp separation, the specific surface of the rejects remained unchanged Appendix A. SUMMARY OF LITE RA TURE RE VIE WON FIBRE FRA CTIONA TION IN HYDROCYCLONES 217 compared to the feed. For beaten chemical and mechanical pulps, the rejects had lower specific surface than the feed. • Coarseness Wood et al (1979)[107], Paaiilainen (1992)[81], Robrmt et al (1995)[84], Kure et al (1999)[63], Li etal (1999)[65], Ho etal (1999, 2000)[46, 47], Rehmt (2001)[85] The accepts consisted mostly of springwood/earlywood fibres, with lower coarseness. The rejects consisted mostiy of coarse, thick-walled, summerwood/late wood fibres. The accepts had lower coarseness than the feed and the rejects. • Fibre Length Paavkirm (1992)[81], Sandhrg et al (1997)[93]y Dernuner (1999)[28], Kure et al (1999)[63], Ho etal (1999, 2000)[46, 47], Rebmzt(2001)[85] The rejects mean fibre length was greater than the accepts mean fibre length (typical observation using Noss Radiclone fractionating hydrocyclones. And the opposite results were observed using Bauer 3" hydrocyclone. • Fibre Wall Thickness Paavkinen (1992)[81], Karros (1997)[56], Hoydahl et al (1997)[50], Kure etal (1999)[63], Li etal (1999)[65], Rehrmt(2001)[85] The accepts consisted most of thin-walled springwood/earlywood fibres and the rejects consisted of thick-walled, summerwood/latewood fibres. • Fibre Width Mukoyoshi et al (1986)[73], Paazilainen (1992)[81] The accepts had greater values of fibre width than the rejects. The settling velocities of cylindrical, non-swollen fibres were affected by fibre diameter. • Thickening Ratio Richer et al (1984)[88], Woodet al (1991)[108] Fibre specific surface area dominated the thickening of fibres. The tMcfening ratio could be used as a criterion to rank pulps regarding their low specific surface material contents. • Fibre Bonding Index Mohlin (1989)[72] Appendix A. SUMMARY OF LITERATURE REVIEW ON FIBRE FRA CTIONA HON IN HYDROCYCLONES 218 Fibres that were only loosely bonded to the sheet surface tended to be thicker (coarser). Thus the rejects which consisted mostly of summerwood fibres had a lower value of bonding index then the accepts, which consisted springwood fibres. • Pulp Linting Propensity (PLPI) Wood et al (1977,1992)[109, 111] The rejects had higher value of PLPI than the accepts. • Appearance (by Confocal Microscope, Microphotographs) Bliss (1983,1984)[5, 6], Wood et al (1992)[110]y Sandberg et al (1997)[93], Kure etal (1999)[63], Li et al (1999)[65], Ho etal (1999, 2000)[46, 47], Rehrmt (2001)[85] The rejects appeared coarser than the accepts. The accepts contained more collapsed fibres compared to the rejects. The flexibility plays a role in fibre fractionation. Operating Conditions • Reject Ratio Jones et al. (1966)[53], Bliss (1983,1984)[5, 6, 7, 8], Paadkinen (1992)[81], Rehrmt et al (1995)[84J, Karnis (1997p6], Ho etal (1999, 2000)[46, 47] As the reject ratio increased, the fibre length difference between the rejects and the feed decreased. The maximum difference in fibre length between the accepts and the rejects was at the lowest reject ratio. The maximum difference in fibre coarseness between the accepts and the rejects was at the highest reject ratio. As the rejects tip opening increased in diameter, the reject ratio also increased. It was noted that there were some contradictions regarding of the reject ratio in regard to getting summerwood-rich rejects and the springwood-rich accepts. • Temperature Jones et al (1966)[53], Richer et al (1984)[88J, Bliss (1983,1984)[5, 6] As the temperature increased, the mass amount of pulp from the accepts decreased, the mass amount of pulp from the rejects increased. The mass amount of springwood in the Appendix A. SUMMARY Cf LITERATURE RE VIE WON FIBRE FRA CTIONA TION IN HYDROCYCLONES 219 accepts increased, the mass amount of summerwood in the rejects showed no significant difference. A temperature increase causing the viscosity to decrease, might result in a significant increase in the separation efficiency. • Feed Pressure / Pressure Drop Jones etaL (1966)[53J, Stephens etal (1967)[99J, GaudinetaL (1991X37] The pressure drop was affected mainly by the feed flowrate. As the feed pressure, or pressure drop increased, both the reject rate and the separation efficiency would be increased. Some experimental results showed that hydrocyclone rejected more low specific surface fibre at a higher pressure drop. • Consistency Pesoh (1963X83], Jones et al (1966X53], Stephens et al (1967X99], Wood et al (1979X109], Bliss (1984X6], Ho etal (1999, 2000X46, 47] As the feed pulp consistency increased, the separation efficiency decreased. Consistency had less effect on the fibre length distributions, but did affect the specific surface distributions. If the consistency was too high, fibre interactions appeared, which may have resulted in lower separation efficiency. • Reject Rate Stephens et al (1967X99], Wood etal (1991X108] Increased feed pressure, and pressure drop, increased levels of both reject rate, and separation efficiency. • Multistage Fractionations Paavlainen (1992X81], Karnis (1997X56], Sandberg et al (1997X93], Ho etal (1999, 2000X46, 47], Rehrmt (2001X85] The summerwood content in the rejects increased after each stage, but the re-fractionation of the accepts didn't affect its summerwood content. The cell wall thickness of the rejects was greater than the feed and the accepts, and that of the accepts was less than the feed. After each stage, the cell wall thickness of the accepts decreased, and that of the Appendix A. SUMMARY OF LITERATURE RE VIE WON FIBRE FRA CTIONA TION IN HYDROCYCLONES 220 rejects increased. The accepts contained fine and long fibre, the rejects contained coarser material and a lesser amount of fines. The rejects were coarser than either the accepts or the feed, and the accepts were less coarse than the feed. Sheet Strength • Burst Factor Bliss (1983, 1984)[5, 6] Sheets which were made from the rejects were lower in burst index than those that were made from the accepts or the feed. • Breaking Length/Tensile Index Bliss (1983, 1984)[5} 6], Paavkinen (1992)[81], Sandberg et al (1997)[93], Li etal (1999)[65] Sheets which were made from the rejects were lower in breaking length than those that were made from the accepts or the feed. Sheets which were made from the accepts had the highest tensile index value compared to those that were made from the feed and the rejects. Those made from the rejects had the lowest tensile index value. • Tear Factor Bliss (1983,1984)[5, 6], Sandberg et al (1997)[93J Sheets which were made from the rejects were lower in tear index than those that were made from the accepts or the feed. • Opacity Jones et al (1966)[53] It was not affected by the hydrocyclone fractionation. • Air Resistance Paavkinen (1992)[81], Dennner(1999)[28] Sheets which were made from the accepts had higher air resistance then the feed and the rejects. Fold Index Bliss (1984)[6] Appendix A. SUMMARY OF LITERATURE RE VIE WON FIBRE FRA CTIONA TION IN HYDROCYCLONES 221 Sheets which were made from the rejects were lower in fold index than those that were made from the accepts or the feed. • Porosity Paavkinen (1992)f81] Sheets which were made from the rejects had higher porosity than those were made from the accepts or the feed. • Apparent Sheet Density Demuner (1999)[28] Apparent sheet density of the accepts pulp was greater than that of the feed pulp. • Light Scatting Sandberg et al (1997)[93], Demuner (1999)[28], Kure etal (1999)[63] Sheets which were made from the accepts had the greatest values of light scattering, and those which made from the rejects had the lowest values of light scattering. • BvHkLietal(1999)f65] Sheets which were made from the rejects had higher bulk values than those were made from the accepts. • Bendsten Roughness Demuner (1999)[28] The accepts Bendsten roughness was lower than the feed pulp roughness. • Refining Bliss (1983, 1984)[5, 6], Paavkinen (1992)[81], Hoydahl et al (1997)[50], Demuner (1999)[28], Kure etal (1999)[63]y Rehmat (200l)f8 5] After refining, sheets which were made from the rejects were significantly higher in burst index, tear index, breaking length, and fold index than those were made from the accepts. Sheets which were made from the unrefined accepts had higher tear index values than those that made from the unrefined rejects. Refining the thick-wall fibres reduced their fibre wall thickness. Refining of the rejects resulted in a slightly lower tensile index than that observed for the feed pulp. • Surface Smoothness (Multi-layer sheets) Vollmer (1999)[ 105] Appendix A. SUMMARY OF LITERATURE REVIEW ON FIBRE FRACTIONATION IN HYDROCYCLONES 222 The surface smoothness was improved compared to a sheet made from the same pulp but not fractionate. (Fractionated the pulp then sent the accepts to the surface layer, and the rejects to the core to form a three-ply sheet). Relationship of Drag Coefficients and Reynolds Number on Motion of Fibres • Free, Gravitational Setting A idun (1956)[IJ Experimental relationships between drag coefficients and Reynolds number for fibres having a ratio of fibre length to diameter greater than 90 were proposed. C D = 10.48N^e68 for 0.1 <N R e <2.0 Long Slender Solid Bodies Move in Viscous Fluid GK (1970)[26J Expression of the drag describing the force per unit length acting the slender cylinders by the fluid which included the ratio of the cylinder's length to its cross-section was proposed. Hydrodynamic Behaviour of Individual Pulp Fibre Wong(2000)[107] Experimental relationships between the drag coefficients to Reynolds numbers for Kraft pulp and TMP by using a rotating cylindrical tank, which was built to measure the velocity of various fibres in water under the influence of various centrifugal fields, were proposed. C o=77N; •-0.813 Re for 0.007 <N R p <0.1 Kraft: Q , =113N° R f 1 for 0.007 <N R e <1.0 TMP: Co =74N° R f 3 for 0.007 <N R e <1.0 Appendix B. CONSISTENCY MEASUREMENT 223 Appendix B C O N S I S T E N C Y M E A S U R E M E N T 1) Measure the weight of an empty, dry beaker (WB) 2) Sample from the feed using the dry beaker, weigh the suspension Weight of the Feed + Weight of Dry Beaker = W r a = W F + W B Weight of the Feed Suspension (WF) = Wpg - W B 3) Weight of the oven dried filter paper (WP) 4) Filter the feed suspension through the oven dried filter paper in a funnel and apply suction. Remove the filter paper with its pad. Then dry them in an oven at 105°C to constant weight, and weigh immediately Weight of the Oven-Dry Filter Paper + Weight of the Oven-Dry Feed Solid = W P + W F S 5) The consistency will then be Consistency = W F Appendix C MICROPHOTOGRAPHS OF NYLON FIBRES 224 Appendix C M I C R O P H O T O G R A P H S OF N Y L O N F IBRES 1 mm, 0.68 mg/m Appendix C MICROPHOTOGRAPHS OF NYLON FIBRES 225 2 mm, 1.7 mg/ m 8 mm, 1.7 mg/m Appendix D. DENSITYMEASUREMENT 227 Appendix D D E N S I T Y M E A S U R E M E N T S 1) Measure the weight of the empty dry volumetric flask (W^ 2) Calibrate the flask by adding water at 20°C to the mark on the flask Weight of Dry Flask + Added Water = W G + W w = W G W Weight of Water Added = W w = W G W - W G Density of Water at 20 °C (pw) =998 kg/m3 Total Volume = Volume of Water Added = V X O T A L 3) Add nylon fibres to the flask not to exceed the calibration mark Weight of Dry Flask + Weight of Nylon Fibres = W G + W F = W G F Weight of Nylon Fibres = W G F - W G = W F 4) Add water to fill the total volume up the calibration mark , M £ w , A i t , „ Mass of Water Addd W w Volume of Water Added = V W A D D = ; = Densityof Water p w Volume of Nylon Fibres = Total Volume - Volume of Water Added = V T O T A L - V W A D D = v F 5) Densityof Nylon Fibres = Mass of NylonFibres W F Volumeof NylonFibres V F AppendixE. HYDROCYCLONE OPERATIONS 228 Appendix E H Y D R O C Y C L O N E OPERAT IONS Additional data collected in regard to hydrocyclone performance, such as pressure drop, consistencies, thickening ratio and volumetric reject ratio are reported as follows: E l Pressure Drop Figure El-1 plots pressure drop across the Bauer hydrocyclone as a function of feed flowrate at various consistencies using two different reject tip openings (Tip I, Tip II). It shows that the direct relationship between the pressure drop (feed pressure - accept pressure) and the feed flowrate (all types of feeds) was not affected by the feed consistency. In addition, there was no significant effect on the relationship between pressure drop and the feed flowrate of the two sizes of the reject tip openings (5 mm and 6 mm). Therefore, it can be concluded that the consistency and the size of the reject tip openings have negligible effect on the mass flowrate for a given pressure drop. There is a lot of data plotted in Figure El-1 so the effects of consistency and reject opening may be obscured. However our conclusion as to no effect of either is supported by comparing plots (not shown) of the individual runs rather than by just using the combined data as in Figure El-1. AppendixE. HYDROCYCLONE OPERATIONS 229 Pressure Drop (psi) 50 60 Feed Flowrate (kg/min) 80 0.9% 0.5% 0.3% 0.9% 0.5% 0.3% 0.9% 0.5% 0.3% 0.5% 0.3% 0.5% 0.3% consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency consistency (Feed A)_Tlp I (Feed A)_Tlp I (Feed A)_Tlp I (Feed C)_Tlp I (Feed C)_Tlp I (Feed C)_Tlp I (Feed D)_Tlp I (Feed D)_Tlp I (Feed D)_Tlp I (Feed B)_T1p I (Feed B)_Tlp I (Feed E)_Tip I (Feed E)_Tlp I O V • O A O O V • O A 0.9% consistency (Feed 0.5% consistency (Feed 0.3% consistency (Feed 0.9% consistency (Feed 0.5% consistency (Feed 0.3% consistency (Feed 0.5% consistency (Feed 0.3% consistency (Feed 0.9% consistency (Feed 0.5% consistency (Feed 0.3% consistency (Feed 0% consistencyJTip I 0% conslstency_Tlp II S1)_Tlpl S1)_TIp I 51) _Tip I 52) _Tip I S2)_Tlp I 52) _Tlp I 53) _Tlp I S3)_Tlp I S3)_Tlp II S3)_Tlp II S3)_Tlp II Figure El-1 Pressure drop vs. feed flowrate at various feed consistencies using Feed A, G D, B, E , SI, S2, and S3 with two different sizes of the rejects tip opening. E2 Consistency The effects on the consistency of the accepts and rejects streams for various feed flowrates and various feeds (Feed A, B, Q D, E , SI, S2 and S3) of using the same reject tip opening = 5 mm (Tip I) are shown in Figures E2-1 —E2-8 respectively. Since the nylon fibres used in these studies had density > than water one would expect that the centrifugal forces generated by the swirling flow in the hydrocyclone would move fibres towards the outer wall. This would put them into a flow region that was directed towards the rejects opening. Thus one would expect the rejects consistencies to be higher than the accepts consistencies and they were. AppendixE. HYDROCYCLONE OPERATIONS 230 The rejects consistency was higher than the accepts consistency at all given feed flowrates, except when the feed contained only 3 mm long fibres of coarseness = 0.17 mg/m. As the feed flowrate increased, the rejects consistency increased while the accepts consistency decreased. There were substantial differences in the rejects consistencies at a particular flowrate that were dependent on the feed consistency in the cases of feeds A, Q D SI and S2. See Figures E2-1, E2-2, E2-3, E2-6 and E2-7. While there were consistency dependent differences in the accepts consistencies, these were rather small. All of these feeds contained only 1 mm long fibres of various coarseness. Feeds B, E and S3 contained fibres having fibre length = 3 mm. In these cases, see Figure E2-4, E2-5, E2-8, the differences between rejects and accepts consistencies were much smaller. In the case of Feed S3, Figure E2-8, which contained only 3 mm fibres with coarseness = 0.17 mg/m, the accepts consistencies were higher than those of the rejects. These fibres had a tendency to plug the rejects opening (diameter = 5 mm) of the hydrocyclone, particularly at high consistencies. Thus if the reject opening was to some extent blocked, it would force more fibres to exit via the accepts stream. At consistencies of 0.9% there were no rejects as a result of this plugging. To further investigate this Figure E2-9 plots the consistency of the rejects and the accepts of Feed S3 by using a larger reject tip (Tip II diameter = 6 mm) at various feed flowrate. As the feed flowrate increased, the rejects consistency increased while the accepts consistency decreased, which behaviour was similar to that observed when using the smaller reject tip (Tip I), see Figure E2-8. However, using the larger reject tip (Tip II), see Figure E2-9, still resulted in the rejects consistency being lower than the accepts consistency. Appendix E. HYDROCYCLONE OPERATIONS 10 Consistency (%) 6H • 0.9% consistency (Feed A)_Tip \_Rejects O 0.9% consistency (Feed A)_Tip \_Accepts T 0.5% consistency (Feed A)_Tip \_Rejects V 0.5% consistency (Feed A)_Tip l_>*ccepfs • 0.3% consistency (Feed A)_Tip \_ReJects • 0.3% consistency (Feed A)_Tip \_Accepts O _fl_ 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E2-1 Accepts, and rejects consistencies vs. feed flowrate at various f< consistencies for Feed A. 1 0 Consistency (%) 4H 30 • 0.9% consistency (Feed C)_Tip \_Relects O 0.9% consistency (Feed C)_Tip \_Accepts • 0.5% consistency (Feed C)_T1p l_ffe/ec(s V 0.5% consistency (Feed C)_Tlp \_Accepts • 0.3% consistency (Feed C)_Tip l_ffe/ecfs • 0.3% consistency (Feed C)_Tlp \_Accepts s - Q -40 50 i— 60 70 80 Feed Flowrate (kg/min) Figure E2 -2 Accepts, and rejects consistencies vs. feed flowrate at various consistencies for Feed C. AppendixE. HYDROCYCLONE OPERATIONS 10 Consistency (%) 30 • 0.9% consistency (Feed D)_Tip ^Rejects O 0.9% consistency (Feed D)_Tlp l_Accepts ^ 0.5% consistency (Feed D)_Tlp \_ReJects V 0.5% consistency (Feed D)_Tlp \_Accepts • 0.3% consistency (Feed D)_T1p \_ReJects • 0.3% consistency (Feed D)_Tip \_Accepts A. 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E2-3 Accepts, and rejects consistencies vs. feed flowrate at various f< consistencies for Feed D. 10 Consistency (%) 2H • 0.5% consistency (Feed B)_Tip \_ReJects V 0.5% consistency (Feed B)_Tip \_Accepts u 0.3% consistency (Feed B)_Tip \_Rejects • 0.3% consistency (Feed B)_Tip l_4ccepfs T E T w 40 50 60 Feed Flowrate (kg/min) A 30 70 80 Figure E2-4 Accepts, and rejects consistencies vs. feed flowrate at various consistencies of Feed B. AppendixE. HYDROCYCLONE OPERATIONS 1 0 Consistency (%) 6H 0.5% consistency (Feed E)_Tip \_Rejects 0.5% consistency (Feed E)_Tip LAccepfs 0.3% consistency (Feed E)_Tip \_Rejects 0.3% consistency (Feed E)_Tip I .Accepts 1 — r 70 3 0 4 0 5 0 6 0 Feed Flowrate (kg/min) 8 0 Figure E2-5 Accepts, and rejects consistencies vs. feed flowrate at various f< consistencies of Feed E . 10 Consistency (%) • 0.9% consistency (Feed S1)_Tip \_Rejects O 0.9% consistency (Feed S1 )_Tip \_Accepts T 0.5% consistency (Feed S1)_Tip \_Rejects V 0.5% consistency (Feed S1 )_Tip \_Accepts • 0.3% consistency (Feed S1 )_Tip \_Rejects • 0.3% consistency (Feed S1 )_Tip \_Accepts 9 B T O 3 a 3 0 4 0 5 0 6 0 Feed Flowrate (kg/min) 7 0 8 0 Figure E2-6 Accepts, and rejects consistencies vs. feed flowrate at various consistencies of Feed SI. AppendixE. HYDROCYCLONE OPERATIONS 10 Consistency (%) 2H 30 • 0.9% consistency (Feed S2)_Tip \_Hejects O 0.9% consistency (Feed S2)_Tip \_Accepts • 0.5% consistency (Feed S2)_Tip \_Rejects V 0.5% consistency (Feed S2)_TIp \_Accepls • 0.3% consistency (Feed S2)_TIp i_Re/ects • 0.3% consistency (Feed S2)_Tip \_Accepts 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E2-7 Accepts, and rejects consistencies vs. feed flowrate at various f< consistencies of Feed S2. 2.0 15-11 • 0.3% consistency (Feed S3)_Tip \_Accepts 1.0 0.5 0.0 V • V a v • •T • T V a 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E2-8 Accepts, and rejects consistencies vs. feed flowrate at various consistencies of Feed S3, Tip I. Appendix E. HYDROCYCLONE OPERA HONS 235 2.0 Consistency (%) 1.5 1.0 0.5 0.0 • 0.9% consistency (Feed S3)_Tip ILRe/ecfs O 0.9% consistency (Feed S3)_Tip \l_Accepls • 0.5% consistency (Feed S3)_Tip \\_Rejects V 0.5% consistency (Feed S3)_Tlp \\_Accepts • 0.3% consistency (Feed S3)_Tlp ll_He/ecfs • 0.3% consistency (Feed S3)_Tip \\_Accepts 0 V V T y o V • o T V 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E2-9 Accepts, and rejects consistencies vs. feed flowrate at various feed consistencies of Feed S3, Tip II. D3 Truckening Ratio Thickening ratio = rejects consistency/feed consistency was plotted against feed flowrate for various feed consistencies as shown in Figures E3-1 to E3-20. A thickening ratio = 1.0 indicates that the hydrocyclone is simply acting as a flow splitting device with no separating power. Thus thickening ratios > 1 would be expected for fibres having density > that of water since the centrifugal forces generated in the hydrocyclone would tend to move such fibres into the flow near the wall that is directed towards the reject opening. A thickening ratio < 1 implies that the accepts are more concentrated than the feed. With increasing flowrate, the data of these figures show that the thickening ratio increased at a given consistency. This was to be expected, since there would have been greater centrifugal forces acting on the fibres as the fluid velocity increases. AppendixE. HYDROCYCLONE OPERATIONS 236 The data also show that the ductaning ratio was affected by the feed consistency. For Feeds A, Q D, SI, S2 and S3 (with Tip I), the thickening ratio increased as the feed consistency decreased (see Figures E3-1, E3-2, E3-3, E3-6, E3-7). However, for Feed B, E (Figures E3-4 and E3-5) and S3 (with Tip II) (Figures E3-8 and E3-9), the trend was the opposite in that the thickening ratio was higher the higher the consistency. Again this might be attributed to the presence of long fibres which tended to block the rejects outlet. From Figures E3-8 and E3-9, it can be seen that increasing the reject tip opening caused the thickening ratio to increase at a given consistency. Figures E3-10 to E3-12 plot thickening ratio vs. feed flowrate for Feeds SI and S2 at consistencies of 0.9, 0.5 and 0.3% respectively. The thickening ratios for Feed S2 were higher than those of Feed SI in all three plots. Since the coarseness of Feed SI is 0.17 mg/m and that of S2 is 0.68 mg/m, this implies that higher coarseness was associated with higher thickening ratios. The fibre lengths in SI and S2 were equal at 1 mm. However when we consider Figures E3-13 to E3-15 which plot thickening ratio vs. feed flowrate for Feeds A, C and D at consistencies of 0.9, 0.5 and 0.3 % respectively we do not see a consistent pattern associating high coarseness with high thickening ratio. In Figure E3-13 (at 0.9% consistency) the highest thickening ratio was associated with Feed D which had the highest coarseness (0.41 mg/m) and the lowest ratio was found with Feed A which had the lowest coarseness (0.27 mg/m) but the plot for Feed C, which had a mean coarseness of 0.28, almost the same as Feed A, lies much closer to the Feed D plot. The same pattern can be detected in Figure E3-14 but all 3 curves are closer together. The curves become even closer together in Figure E3-15 at 0.3% consistency. The conclusion is that coarseness has more effect on thickening ratio at high consistencies than it does at low consistencies. Appendix E. HYDROCYCLONE OPERA HONS 237 Figures E3-16 to E3-19 illustrate the effects of mean fibre length on thickening ratio. Figure E3-16 for Feeds Si and S3 shows that at 0.5% consistency for a particular flowrate the thickening ratio was higher for the shorter fibres of Feed SI. The same behaviour can also be noted at 0.3% consistency in Figure E3-17. In considering the mixed fibre length feeds B and E (Figures E3-18 and E3-19) it can again be seen that the shorter fibres of Feed E give rise to higher thickening ratios at both 0.5 and 0.3% consistency. Thus we can conclude that short fibres are more readily concentrated than long fibres hence they lead to higher thickening ratios. Figure E3-20 plots thickening ratio vs. feed flowrates at two different reject tip opening diameters 5 mm (tip I) and 6 mm (tip II). The wider tip opening resulted in higher reject ratios. However the reject ratios with these S3 fibres were rather low compared to the others reported in this section. Tip I plugged if the hydrocyclone was run at 0.9% consistency with Feed S3 (mean fibre length = 3 mm). Under the same conditions tip II did not plug. 1 0 Thickening Ratio 8H O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I — i — 50 — i — 60 30 40 70 80 Feed Flowrae (kg/min) Figure e3-1 Thickening ratio vs. feed flowrate at various consistencies for Feed A. AppendixE. HYDROCYCLONE OPERATIONS 238 1 Q Thickening Ratio 8H • V • V • V O 0.9% consistency (Feed C)_Tip I V 0.5% consistency (Feed C)_Tip I • 0.3% consistency (Feed C)_Tip I —i— 70 30 40 50 60 Feed Flowrate (kg/min) 80 Figure E3-2 Thiclrening ratio vs. feed flowrate at various consistencies for Feed G 1 0 Thickening Ratio v o • O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_TIp I —i— 70 30 40 50 60 Feed Flowrate (kg/min) 80 Figure E3-3 Thickening ratio vs. feed flowrate at various consistencies for Feed D. AppendixE. HYDROCYCLONE OPERATIONS 239 n Thickening Ratio 10 -i S V 0.5% consistency (Feed B)_Tip I • 0.3% consistency (Feed B)_Tip I V • V • —I 1 1 1— 4 0 5 0 6 0 7 0 Feed Flowrate (kg/min) 3 0 8 0 Figure E3-4 Thickening ratio vs. feed flowrate at various consistencies for Feed B. 10 Thickening Ratio 8H V • V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I V • 3 0 4 0 5 0 6 0 7 0 Feed Flowrate (kg/min) 8 0 Figure E3-5 Thickening ratio vs. feed flowrate at various consistencies for Feed E . AppendixE. HYDROCYCLONE OPERATIONS 240 Thickening Ratio 10 -i 8H 8 V o O 0.9% consistency (Feed S1 )_Tip I V 0.5% consistency (Feed S1 )_Tip I • 0.3% consistency (Feed S1 )_Tip I o o o 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-6 TTuckeriing ratio vs. feed flowrate at various consistencies for Feed Si. 1 0 Thickening Ratio • v • • V • 8 O 0.9% consistency (Feed S2)_Tip I V 0.5% consistency (Feed S2)JTip I • 0.3% consistency (Feed S2) Tip I 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-7 Thickening ratio vs. feed flowrate at various consistencies for Feed S2. Appendix E. HYDROCYCLONE OPERA HONS 241 3.0 Thickening Ratio 2.5 A 2.0 A 1-5 H 1 0 A 0.5 0.0 V 0.5% consistency (Feed S3)_Tip I • 0.3% consistency (Feed S3)_Tlp I • v • V a v • V 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E3-8 Tmckening ratio vs. feed flowrate at various consistencies for Feed S3, with Tip I. 3 Q Thickening Ratio 2.5 2.0 1.5 1.0 0.5 0.0 O 0.9% consistency (Feed S3)_Tip II V 0.5% consistency (Feed S3)_Tip II • 0.3% consistency (Feed S3)_Tip II V • O V 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E3-9 Tmckening ratio vs. feed flowrate at various consistencies for Feed S3, with Tip II. Appendix E. HYDROCYCLONE OPERA TIONS 242 . Thickening Ratio 10 i O 0.9% consistency (Feed S1)_L = 1.0 mm, C = 0.17 mg/m V 0.9% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-10 Thiclffining ratio vs. feed flowrate at 0.9% consistency of Feed Si, S2 (Tip I), L = number mean fibre length, C = number mean coarseness. 10 Thickening Ratio O 0.5% consistency (Feed S1)_L = 1.0 mm, C = 0.17 mg/m V 0.5% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m — i — 50 30 40 60 70 80 Feed Flowrate (kg/min) Figure E3-11 Thickening ratio vs. feed flowrate at 0.5% consistency of Feed SI, S2 (Tip I), L = number mean fibre length, C = number mean coarseness. Appendix E. HYDROCYCLONE OPERA HONS 243 , n Thickening Ratio 10 -i 8H 2H O 0.3% consistency (Feed S1)_L = 1.0 mm, C = 0.17 mg/m V 0.3% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-12 Tmckening ratio vs. feed flowrate at 0.3% consistency of Feed SI, S2 (Tip I), L = number mean fibre length, C = number mean coarseness. 1 0 Thickening Ratio 8H 4 H • v V • V O 0.9% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.9% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.9% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-13 Thickening ratio vs. feed flowrate at 0.9% consistency of Feed A, C, D (Tip I), L = number mean fibre length, C = number mean coarseness. Appendix E. HYDROCYCLONE OPERA HONS 244 ,„ Thickening Ratio 10 -\ 30 • V V • • o O 0.5% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.5% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.5% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-14 TJiickening ratio vs. feed flowrate at 0.5% consistency of Feed A, C, D (Tip I), L = number mean fibre length, C = number mean coarseness. 1 0 Thickening Ratio • v o O 0.3% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.3% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.3% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E3-15 Thickening ratio vs. feed flowrate at 0.3% consistency of Feed A, C, D (Tip I), L = number mean fibre length, C = number mean coarseness. AppendixE. HYDROCYCLONE OPERATIONS 245 1 0 Thickening Ratio O 0.5% consistency (Feed S1)_C = 0.17 mg/m, L = 1.0 mm • 0.5% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E3-16 Tmckening ratio vs. feed flowrate at 0.5% consistency of Feed SI, S3 (Tip I), L = number mean fibre length, C = number mean coarseness. 1 0 Thickening Ratio O 0.3% consistency (Feed S1)_C = 0.17 mg/m, L = 1.0 mm • 0.3% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E3-17 Thickening ratio vs. feed flowrate at 0.3% consistency of Feed SI, S3 (Tip I), L = number mean fibre length, C = number mean coarseness. AppendixE. HYDROCYCLONE OPERATIONS 246 1 0 Thickening Ratio v o O 0.5% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.5% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm V O V O v O 3 0 4 0 50 60 70 Feed Flowrate (kg/min) 8 0 Figure E3-18 TJiickening ratio vs. feed flowrate at 0.5% consistency of Feed B , E (Tip I), L = number mean fibre length, C = number mean coarseness. 10 Thickening Ratio 84 O 0.3% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.3% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm 3 V o V o V o V o — I — 60 30 4 0 50 70 8 0 Feed Flowrate (kg/min) Figure E3-19 Thickening ratio vs. feed flowrate at 0.3% consistencies of Feed B , E (Tip I), L = number mean fibre length, C = number mean coarseness. AppendixE. HYDROCYCLONE OPERATIONS 247 3.0 Thickening Ratio 2.5 2.0 1.5 1.0 0.5 0.0 V 0.5% consistency (Feed S3)_Tip I • 0.3% consistency (Feed S3)_Tlp I ® 0.9% consistency (Feed S3)_Tip II • 0.5% consistency (Feed S3)_Tip II El 0.3% consistency (Feed S3) Tip II ® V i f V o V • V — I 1 1 1— 40 50 60 70 Feed Flowrate (kg/min) 30 80 Figure E3-20 Tmckening ratio vs. feed flowrate at various consistencies of Feed S3, with Tip I and II. E4 Volumetric Reject Ratio Figures E4-1 ~E4-15 plot the volumetric reject ratio (reject flowrate/feed flowrate, expressed as a %) as a function of the feed flowrate for different feeds at various consistencies. In all cases the volumetric reject ratio tended to go down as the feed flowrate went up. First, let's consider those feeds that contained only fibres that all had the same properties, such as Feeds SI, S2 and S3, using the same reject tip (Tip I); see Figures E4-1, and E4-3, in which data for water only (0% consistency) are included. The highest volumetric reject ratios were observed at the lowest consistencies, with the exception of the inexplicable 0% results of Figure E4-2. The same sort of behaviour was observed for the various coarseness mixture feeds (Feeds A, C, and D), in which the fibre length was 1 mm; see Figures E4-4, E4-5 and E4-6. The effects of differences in consistency on volumetric reject ratio were not large being of the order of a few %. AppendixE. HYDROCYCLONE OPERATIONS 248 In comparing Figures E4-1 and E4-2 for feeds Si (fibre coarseness = 0.17 mg/m, fibre length = 1 mm) and S2 (fibre coarseness = 0.68 mg/m, fibre length = 1mm) it can be seen that coarser fibres led to higher volumetric reject ratios. Comparing Figures E4-1 and E4-3 for Feeds SI (fibre coarseness = 0.17 mg/m, fibre length = 1mm) and S3 (fibre coarseness = 0.17 mg/m, fibre length = 3 mm) it can be noted that the volumetric reject ratios were higher with the longer fibres. Figures E4-7 —E4-9 plot volumetric reject ratio vs. feed flowrate for Feeds A, Q D, SI and S2 all of which had the same fibre length but differed in coarseness. As already observed consideration of the single component feeds suggests that the higher the coarseness the higher the reject ratio, but this is not so for the mixed component Feeds A, C and D. Figure E4-7 (consistency = 0.9%) shows that Feed A (C = 0.27 mg/m) had the highest reject ratio, Feed C (C = 0.29 mg/m) was next highest and Feed D (C = 0.40 mg/m) was the lowest of these three. Feeds C, D and SI produced volumetric reject ratios that were very close to one another. Figure E4-8 (consistency = 0.5%) shows pretty much the same pattern. In Figure E4-9 (consistency = 0.3%) there are some slight differences. Feed A was closer to Feed S2, both having relatively high values of volumetric reject ratio. The ranking order of the other feeds was, in decreasing order of reject ratio, Si, Q then D. Thus no consistent effect of coarseness on volumetric reject ratio was observed. With Feeds B, and E (see Figures E4-10 and E4-11), where some 3 mm long fibres were present, the same behaviour with respect to consistency was noted, i.e. low consistency was associated with higher reject ratio. This was particularly evident in Figure E4-10 for Feed B which had more of the longer fibres than Feed E (Figure E4-11). Figures E4-12 and E4-13 are plots of volumetric reject ratio vs. feed flowrate for Feeds B, E , SI and S3 in which the fibres all had a common coarseness value of 0.17 mg/m but AppendixE. HYDROCYCLONE OPERATIONS 249 various fibre lengths. From the results presented in these figures for the single component feeds one might conclude that longer fibres led to higher volumetric reject ratios at both 0.5 and 0.3% consistency. The same conclusion can be drawn in comparing Feed B to Feed E at 0.3% consistency but the opposite occurred at 0.5% consistency. Thus any effects of fibre length on volumetric reject ratio are confounded with other factors. Figures E4-3 and E4-14 plot the volumetric reject ratio of Feed S3 at various feed flowrates using two different diameters of the rejects tip opening (5 mm and 6 mm respectively). With the larger opening, as might be expected, the volumetric reject ratios were larger at a given flowrate and consistency. Figure E4-15 shows the effects of feed flow rate and reject tip opening diameter on the volumetric reject ratio with only water flowing through the hydrocyclone. As would be expected the wider tip opening gave rise to higher volumetric reject ratios 1 g Volumetric Reject Ratio (%) 16 4 14 12 10 + • 5 v o O 0.9% consistency (Feed S1)_Tip I V 0.5% consistency (Feed S1)_Tip I • 0.3% consistency (Feed S1 )_Tip I + 0% consistency _Tip I V O • V o • V 3 0 40 5 0 60 Feed Flowrate (kg/min) 70 80 Figure E4-1 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed SI with Tip I. AppendixE. HYDROCYCLONE OPERATIONS 250 1 8 Volumetric Reject Ratio (%) 1 6 H 1 4 12 H 10 H D O O 0.9% consistency (Feed S2)_Tip I V 0.5% consistency (Feed S2)_Tip I • 0.3% consistency (Feed S2)_Tip I + 0% consistency_Tip I 3 0 4 0 5 0 6 0 Feed Flowrate (kg/min) 7 0 8 0 Figure E4-2 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed S2 with Tip I. 1 8 Volumetric Reject Ratio (%) 1 6 1 4 1 2 1 0 + • V • V V 0.5% consistency (Feed S3)_Tip I • 0.3% consistency (Feed S3) Tip I + 0% consistency_Tip I • V • V • V 3 0 4 0 5 0 6 0 Feed Flowrate (kg/min) 7 0 8 0 Figure E4-3 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed S3 with Tip I. AppendixE. HYDROCYCLONE OPERATIONS 251 18 16 14 12 10 A Volumetric Reject Ratio (%) v o + o V o O 0.9% consistency (Feed A)_Tip I V 0.5% consistency (Feed A)_Tip I • 0.3% consistency (Feed A)_Tip I + 0% consistency_Tip I v o rf * a 8 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E4-4 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed A. 18 16 14 12 10 Volumetric Reject Ratio (%) + • v o • E O 0.9% consistency (Feed C)_Tip I V 0.5% consistency (Feed C)_Tip I • 0.3% consistency (Feed C)_Tip I + 0% consistency_Tip I 8 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E4-5 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed C AppendixE. HYDROCYCLONE OPERATIONS 252 1 8 Volumetric Reject Ratio (%) 16 14 12 10 • V O 0.9% consistency (Feed D)_Tip I V 0.5% consistency (Feed D)_Tip I • 0.3% consistency (Feed D)_Tip I + 0% consistency_Tip I • 8 • V o 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E4-6 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed D. 18 16 14 12 10 Volumetric Reject Ratio (%) O 0.9% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.9% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.9% consistency (Feed D) L = 1.0 mm, C = 0.40 mg/m •0 0.9% consistency (Feed S1 )_L = 1.0 mm, C = 0.17 mg/m 0 0.9% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m 0 O 0 o o 0 o o o 0 o 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E4 -7 Volumetric reject ratio vs. feed flowrate at 0.9% consistencies for Feed A, D , SI, S2, L = number mean fibre length, C = number mean coarseness. AppendixE. HYDROCYCLONE OPERATIONS 253 18 16 14 12 4 10 Volumetric Reject Ratio (%) o o O 0.5% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.5% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.5% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m O 0.5% consistency (Feed S1)_L = 1.0 mm, C = 0.17 mg/m 0 0.5% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m 0 o • 0 o 0 o V 0 o 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E 4 - 8 Volumetric reject ratio vs. feed flowrate at 0.5% consistencies for Feed A, D, SI, S2, L = number mean fibre length, C = number mean coarseness. 18 16 14 12 10 Volumetric Reject Ratio (%) • O 0.3% consistency (Feed A)_L = 1.0 mm, C = 0.27 mg/m V 0.3% consistency (Feed C)_L = 1.0 mm, C = 0.29 mg/m • 0.3% consistency (Feed D)_L = 1.0 mm, C = 0.40 mg/m O 0.3% consistency (Feed S1 )_L = 1.0 mm, C = 0.17 mg/m 0 0.3% consistency (Feed S2)_L = 1.0 mm, C = 0.68 mg/m 8 8 o 0 o 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E 4 - 9 Volumetric reject ratio vs. feed flowrate at 0.3% consistencies for Feed A, D, SI, S2, L = number mean fibre length, C = number mean coarseness. Appendix E. HYDROCYCLONE OPERATIONS 254 1 8 Volumetric Reject Ratio (%) 16 14 12 10 H + • V 0.5% consistency (Feed B) Tip I • 0.3% consistency (Feed B)_Tip I + 0% consistency_Tip I • + V 30 40 50 60 Fedd Flowrate (kg/min) 70 80 Figure E4-10 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed B with Tip I. 1 8 Volumetric Reject Ratio (%) 16 14 A 12 10 9 9 V V 0.5% consistency (Feed E)_Tip I • 0.3% consistency (Feed E)_Tip I + 0% consistencyJTip I 1 V — I — 70 30 40 50 60 Feed Flowrate (kg/min) 80 Figure E4-11 Volumetric reject ratio vs. feed flowrate at various consistencies for Feed E with Tip I. AppendixE. HYDROCYCLONE OPERATIONS 255 18 Volumetric Reject Ratio (%) 16 14 12 10 O 0.5% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.5% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm • 0.5% consistency (Feed S1 )_C = 0.17 mg/m, L = 1.0 mm O 6.5% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm • o V O O o a o O • o O • o 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E4-12 Volumetric reject ratio vs. feed flowrate at 0.5% consistency for Feed B, SI, S3, L = number mean fibre length, C = number mean coarseness. 18 16 14 H 12 10 Volumetric Reject Ratio (%) O 0.3% consistency (Feed B)_C = 0.17 mg/m, L = 1.3 mm V 0.3% consistency (Feed E)_C = 0.17 mg/m, L = 1.1 mm • 0.3% consistency (Feed S1 )_C = 0.17 mg/m, L = 1.0 mm O 0.3% consistency (Feed S3)_C = 0.17 mg/m, L = 3.0 mm O V O • o V o • V o • V 30 40 50 60 70 Feed Flowrate (kg/min) 80 Figure E4-13 Volumetric reject ratio vs. feed flowrate at 0.3% consistency for Feed B, SI, S3, L = number mean fibre length, C = number mean coarseness. AppendixE. HYDROCYCLONE OPERATIONS 256 1 8 Volumetric Reject Ratio (%) 16 14 12 10 V O V O O o V o O 0.9% consistency (Feed S3)_Tip II v 0.5% consistency (Feed S3)_Tip II • 0.3% consistency (Feed S3)_Tip II O 0% consistency_Tip II O a v o V o 30 40 50 60 Feed Flowrate (kg/min) 70 80 Figure E4-14 Volumetric reject ratio vs. feed flowrate at various consistencies of Feed S3 with Tip II. 1 8 Volumetric Reject Ratio (%) 16 A 14 A 12 10 + 0% consistency_Tip I O 0% consistency_Tip II — i 1 1 40 50 60 Feed Flowrate (kg/min) 30 70 80 Figure E4-15 Volumetric reject ratio vs. feed flowrate at 0 consistency with Tip I, and Tip II. 

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