Particle Breakage, Volume 12 (Handbook of Powder Technology) (Handbook of Powder Technology)

Particle breakage is an important process within a wide range of solids processing industries, including pharmaceuticals, food, agricultural and mining. Breakage of particles can be defined as intentional and unintentional, depending on whether it is desired or not. Through understanding of the science and underlying mechanisms behind this phenomenon, particle breakage can be either minimised or encouraged within an efficient and effective process. Particle Breakage examines particle breakage at three different length scales, ranging from single particle studies through groups of particles and looking at solid processing steps as a whole. This book is the widest ranging book in the field and includes the most up-to-date techniques such as Distinct Element Method (DEM), Monte Carlo simulations and Population Balance Equations (PBE). This handbook provides an overview of the current state-of-the- art and particle breakage. From the small scale of a single particle, to the study of whole processes for breakage; both by experimental study and mathematical modelling. * Covering a wide range of subjects and industrial applications * Allows the reader an understanding of the science behind engineered breakage processes * Giving an unrestrictive and interdisciplinary approach FOREWORD......Page 1 CONTRIBUTORS......Page 2 Contents......Page 4 Introduction......Page 7 Single-particle Impact Testing......Page 11 Drop Weight Testing......Page 13 Pendulum Testing......Page 16 Compression Testing......Page 22 Description......Page 25 Principle of the measurements......Page 26 Signal deconvolution......Page 29 Comminution energy and coefficient of restitution......Page 32 Particle Breakage Characteristics......Page 35 Particle fracture energy and fracture probability distribution......Page 37 Particle strength, PLT strength and KIC......Page 40 Particle stiffness......Page 41 Energy-specific progeny size distribution......Page 44 Energy utilization......Page 48 Type of stressing......Page 49 Stressing intensity......Page 51 Stressing and deformation rate......Page 53 Particle size......Page 55 Particle shape......Page 61 Moisture content......Page 62 Application to Comminution......Page 63 Acknowledgements......Page 66 Appendix: Definition of Terms......Page 67 References......Page 70 Introduction......Page 73 Background and Literature Review......Page 74 Double Impact Tests......Page 75 Key Issues......Page 77 Summaries of Recent Development......Page 79 Theoretical solution......Page 80 Experimental study......Page 83 Development of DIFAR......Page 86 Acknowledgments......Page 87 References......Page 88 Industrial importance......Page 90 Mechanisms: bulk solids flow and attrition......Page 92 Shear cell test......Page 95 Other tests......Page 97 Comparison of materials......Page 98 Product size distribution......Page 101 Extent of attrition......Page 102 Equipment type......Page 103 Stress and strain......Page 104 Subject development......Page 105 Recent work......Page 107 Influence of particle strength and shape, extensive stress and shear strain......Page 108 Population balance modelling......Page 111 Breakage in narrow clearances......Page 113 What next?......Page 116 References......Page 118 The Principles of Single-Particle Crushing......Page 120 Terminology......Page 121 Definition......Page 122 Comminution effects......Page 123 Comminution phases......Page 125 Definition based on grain sizes......Page 126 Definition of the term crushing......Page 128 Physical formulation and mathematical methods......Page 129 Loading conditions......Page 134 Stress-strain behaviour......Page 135 Failure criteria......Page 138 Empirical models......Page 145 Assessment of concepts......Page 146 Crusher as a System......Page 148 Crushing Parameters......Page 151 Definition of related and equivalent features......Page 153 Crushing resistance......Page 156 Physical and mathematical formulation......Page 157 Impact......Page 160 Percussion......Page 163 Crushing force......Page 167 Physical and mathematical formulation......Page 168 Compression......Page 169 Percussion......Page 177 Loading time......Page 179 Impact......Page 180 Percussion......Page 181 Physical and mathematical formulation......Page 182 Impact......Page 183 Crushing product......Page 187 Physical and mathematical formulation......Page 188 Compression......Page 189 Impact......Page 193 Percussion......Page 201 Physical and mathematical formulation......Page 205 Percussion......Page 206 Conclusions......Page 209 Physical and mathematical formulation......Page 210 Percussion......Page 211 Mechanical design......Page 217 Process design......Page 219 Properties of particulate materials......Page 220 Acknowledgements......Page 221 References......Page 225 Rotor Impact Mills......Page 229 Model of the Milling Process in Rotor Impact Mills......Page 230 Impact processes in the rotor......Page 232 Impact processes in the milling gap......Page 235 Stress speed......Page 237 Influence of impact frequency (dwell time)......Page 238 Non-classifying processes......Page 239 Classifying processes......Page 240 Scale-up......Page 242 Designs......Page 244 References......Page 249 Wet Grinding in Stirred Media Mills......Page 250 Development......Page 252 Development of stirred media mills......Page 253 Principal arrangement......Page 254 Movement of the grinding media......Page 257 Introduction......Page 261 Description of production rate......Page 262 Determination of product quality as function of the grinding time and specific energy......Page 264 Mill related stress model......Page 268 Product related stress model......Page 269 Application of the stress models on stirred media mills......Page 273 Estimation of number of stress events and stress frequency......Page 275 Estimation of stress energy and stress intensity......Page 277 Specific energy and energy transfer factor......Page 280 Influence of Important Operating Parameters on the Grinding and Dispersing Result......Page 282 Relation between product fineness and stress number......Page 283 Stirrer tip speed and grinding media density......Page 286 Grinding media size......Page 287 Stress energy......Page 289 Grinding of crystalline materials with high modulus of elasticity......Page 293 Deagglomeration and cell disintegration......Page 295 Conclusions from the influence of stress number and stress energy......Page 300 Determination of optimum operating parameters......Page 302 Filling ratio of grinding media......Page 303 Solids concentration and flow behaviour of the suspension......Page 306 Construction and size of the stirred media mill......Page 310 Conditions of producing nano-particles with stirred media mills......Page 313 Experimental setup......Page 315 Experimental results......Page 316 Transport Behaviour and Operation Mode......Page 320 Basic considerations......Page 321 Modelling the axial transport in stirred media mills......Page 322 Effect of the operation mode on the residence time distribution......Page 326 Effect of residence time distribution on the particle size distribution......Page 331 Power draw......Page 334 Power-number diagram without grinding media......Page 335 Power-number diagram with grinding media......Page 336 Influence of important operating parameters......Page 338 Summary on power draw......Page 340 Experimental results on media packing......Page 341 Grinding media distribution model......Page 343 Wear of mills......Page 346 Wear of grinding media......Page 347 Influence of operating parameters......Page 348 Influence of structural constitution of ceramic media......Page 354 Influence of grinding media and product hardness......Page 355 Autogenous grinding......Page 357 Scale-up......Page 361 Stirred media mills with disc stirrer......Page 362 Stirred media mills with an annular gap......Page 363 Grinding behaviour of different mill sizes......Page 365 Calculation of stress energy distribution and mean stress energy......Page 369 Calculation of energy transfer factor......Page 371 Scale-up with Newton-Reynolds diagrams......Page 374 References......Page 379 Introduction......Page 382 The Structure of the Wheat Kernel......Page 384 The International Development of Modern Flour Milling......Page 386 Roller Milling of Wheat Kernels......Page 390 Grist to the mill......Page 393 Key Issues in Milling of Wheat......Page 394 Breakage of Wheat Kernels during First Break Roller Milling......Page 395 Pearling of Wheat Prior to Milling......Page 411 Acknowledgements......Page 414 References......Page 415 Introduction......Page 419 Fluid impact mills......Page 420 Spiral jet mills, pancake mills......Page 423 Oval chamber jet mills......Page 424 Modelling......Page 425 Parametric modelling......Page 427 Population balances......Page 428 Pharmaceutical industry......Page 429 Toner production......Page 431 References......Page 433 Breakage and Morphological Parameters Determined by Laboratory Tests......Page 434 Formulation of the problem for grinding circuits......Page 435 Cumulative progeny fragment distribution......Page 436 Size--mass rate balance modelling......Page 437 Slowing down phenomena in ball milling......Page 438 Morphological parameters......Page 439 Quartz......Page 441 Calcite......Page 444 Barite......Page 449 Zeolite......Page 451 Clinker......Page 452 Chromite......Page 453 Ceramic raw materials......Page 454 Simulation of ball milling products using the breakage parameters......Page 456 Materials and methods employed......Page 460 Quartz......Page 467 Calcite and barite......Page 469 Talc......Page 476 Summary......Page 479 Concluding Remarks......Page 480 References......Page 482 Introduction......Page 484 Classification of Fine Grinding Mills......Page 485 Impact mills......Page 486 Ball media mills......Page 488 Roller mills......Page 491 Other mill types......Page 493 Selection after the Particle Size of Feed and Product......Page 494 Selection after the Feed Properties......Page 495 Heat-sensitive materials......Page 496 Wet and dry milling......Page 497 Open- and closed-circuit grinding system......Page 498 Applications of Fine Grinding Mills to Particle Modification......Page 503 Conclusions......Page 504 References......Page 505 Introduction......Page 506 Fine Grinding Mills......Page 507 Rate Process of Grinding Phenomena......Page 508 Simulation of Media Motion during Milling......Page 509 Mechanochemical phenomena......Page 513 Phase change......Page 514 Solid-state reactions......Page 515 Material processing......Page 520 Formation of nano-particles......Page 523 References......Page 524 Introduction......Page 526 Kick’s law......Page 527 Holmes’s law......Page 528 Fracture of spheres......Page 529 Variation of fracture energy with particle size......Page 530 Bond’s Work index......Page 532 Grindability in fine grinding......Page 533 Ball Mill Grinding......Page 536 Variation of optimum grinding condition with rotational mill speed......Page 537 Rate constant of feed size reduction......Page 539 Expression of fine grindability......Page 543 References......Page 547 Enabling Nanomilling through Control of Particulate Interfaces......Page 548 Van der Waals interactions......Page 549 Electrostatic interactions......Page 551 The origin of surface charges in aqueous media......Page 552 The origin of surface charges in organic liquids......Page 553 The electrical double layer......Page 554 Born interactions......Page 557 Introduction......Page 558 The DLVO-theory......Page 559 Steric stabilization......Page 561 Summary of stabilization methods......Page 569 Coagulation in stirred media mills......Page 571 Influence of Particle Interactions on Suspension Rheology in Stirred Media Mills......Page 574 Suspension rheology......Page 575 Rheology of electrostatically stabilized suspensions......Page 578 Rheology of sterically stabilized suspensions......Page 580 Experiments in Nanomilling......Page 583 Mechano-chemical Effects during Nanomilling......Page 590 Summary......Page 595 References......Page 598 Introduction......Page 601 Energy Laws Revisited......Page 602 Evaluation of Milling Rate......Page 604 Population Balance Models......Page 606 Role of Feed Properties and Definition of Dimensionless Groups Describing the Breakage Propensity......Page 609 Flexure testing......Page 610 Indentation testing......Page 611 Yield stress (sigmay)......Page 612 Compaction studies......Page 613 Single-edge notched beam (SENB)......Page 614 Double-torsion testing......Page 615 Radial edge cracked tablets......Page 616 Indentation fracture test......Page 617 Discussion......Page 618 Derived parameters......Page 619 Analysis of Milling Rate based on the Input Power and Material Properties......Page 620 Conclusions......Page 625 References......Page 628 Introduction......Page 631 Random nature of breakage......Page 633 Batch grinding......Page 634 Conventional solution method......Page 636 Stochastic solution method......Page 637 Typical example of application......Page 638 Monte Carlo method......Page 639 Distribution functions......Page 641 Sampling......Page 642 The most useful sampling technique......Page 643 Monte Carlo approach to batch grinding......Page 644 Computational procedure......Page 645 Numerical results and discussion......Page 647 Summary......Page 652 References......Page 653 Numerical Investigation of Particle Breakage as Applied to Mechanical Crushing......Page 655 Background and literature review......Page 656 Methodology......Page 660 Brief introduction of RFPA2D......Page 661 Validation of RFPA2D by simulating Brazilian test......Page 663 Breakage of single particle under diametral loading without confinement......Page 670 Breakage of a single particle under diametral loading with confinement......Page 675 Discussions......Page 678 Confinement effect and energy release......Page 679 Failure modes......Page 681 Cracks and crack branching......Page 682 Brief description of RFPA2D-dynamics code and numerical models......Page 683 Influence of heterogeneity on stress wave propagation......Page 686 Influence of pressure stress wave amplitude on fracture process and failure pattern......Page 687 Single-Particle Breakage under Various Loading Conditions......Page 691 Point-to-point loading......Page 693 Plane-to-plane loading......Page 694 Point-to-plane loading......Page 699 Multi-point loading......Page 700 Failure modes and mechanisms under various loading conditions......Page 704 Effect of particle shape, size and loading conditions......Page 706 Numerical model......Page 710 Stress field......Page 713 Inter-particle breakage process......Page 714 Resultant force and displacement relationship......Page 718 Energy transformation......Page 719 Size distribution......Page 721 Discussions......Page 722 Influence of the particle shape on the inter-particle breakage......Page 723 Two kinds of fracture pattern in the inter-particle breakage process......Page 726 Summary......Page 728 References......Page 731 The Cohesion of Fractal Agglomerates: AnTMElementary Numerical Model......Page 734 Introduction......Page 735 Universality of the Fractal Structures......Page 737 Characteristics and synthesis of fractal aggregates......Page 738 Diffusion-limited cluster-cluster aggregation......Page 739 Reaction-limited cluster-cluster aggregation......Page 740 Aerosils......Page 741 Ceramics......Page 742 Fractal aggregates in food processing......Page 743 Fractal aggregates in agriculture and environment......Page 744 Aggregate cohesion and additives......Page 745 Aggregate assemblies: scaling approach......Page 746 Cohesion against break-up rate......Page 750 From experimental observation towards modelling......Page 753 Determination of the rate of aggregate breakage......Page 755 The model of Horwatt et al.......Page 756 Fragmentation controlled by the number v of intra-agglomerate connections......Page 757 The Cohesion of Fractal Agglomerates: An Elementary Model......Page 758 Agglomerate formation......Page 759 Number of configurations......Page 760 Connection frequency......Page 761 Agglomerate cohesion......Page 762 Fragmentation of DLA and RLA agglomerated systems confronted to the cohesion model......Page 764 Fragmentation of aggregates formed under conditions of diffusion-limited aggregation......Page 765 Fragmentation of aggregates formed under conditions of reaction-limited aggregation......Page 767 Forward Look......Page 770 Aggregate cohesion and aggregate growth......Page 771 Aggregate growth in the presence of connection constraints......Page 775 Conclusion......Page 779 Acknowledgements......Page 780 References......Page 781 The Linear Breakage Equation: From Fundamental Issues to Numerical Solution Techniques......Page 785 Introduction......Page 786 The breakage equation......Page 788 Overview......Page 789 Product and sum-type kernels......Page 791 Erosion kernels......Page 792 Discrete homogeneous kernels......Page 793 Iterative techniques......Page 794 Analytical solutions......Page 796 Formulation of the Self-Similarity Problem......Page 798 Continuous kernels......Page 800 Discrete kernels......Page 801 Some features of the self-similar PSD......Page 803 Is the self-similar PSD realizable?......Page 804 Formulation of the steady-state problem......Page 805 General behaviour - Asymptotic results......Page 807 Analysis for the sum of powers kernel......Page 810 Approach to the limiting steady state......Page 811 The erosion equation......Page 812 Decomposition to generations - Analytical solution......Page 814 Moments of the generations......Page 816 Case study......Page 817 Methods of Moments......Page 819 Sectional Methods......Page 821 Current and Future Research Topics on Breakage Equation......Page 823 References......Page 825 Introduction......Page 828 Models of Agglomerate Strength and Failure......Page 830 Theoretical models......Page 831 Weber number......Page 832 Mechanistic analysis of the breakage of interparticle contacts......Page 834 Chipping model......Page 836 Introduction......Page 837 Agglomerate behaviour using distinct element method......Page 838 Analysis of breakage of contacts......Page 840 Fragmentation and breakage......Page 842 Breakage patterns......Page 849 Effect of size ratio on the breakage of agglomerate......Page 853 Stress ratio......Page 854 Damage ratio......Page 856 Comparison with experiments......Page 857 Relevance to granulation process......Page 860 References......Page 861 Modelling of Mills and Milling Circuits......Page 864 Examples of Milling Circuits......Page 865 Modelling Levels for Milling Circuits......Page 868 The population balance model......Page 869 The non-linear grinding kinetics......Page 870 The perfect mixing grinding approach......Page 874 The N-mixers in series approach......Page 875 Modelling of milling circuits involving different mill types......Page 876 Vertical spindle mills......Page 877 Dry and wet ball mills......Page 878 Air jet mills......Page 880 Roller mills......Page 882 Determination of Model Parameters......Page 883 SolidSim - a new tool for flowsheeting of particulate processes......Page 884 Comminution......Page 887 Mill›classifier circuits within SolidSim......Page 889 The reference state method for modelling of mill-classifier circuits......Page 890 Classification......Page 891 Comminution......Page 892 Influence of the mill operation mode on the product size distribution......Page 893 How to produce narrow particle size distributions: the example of powder paint......Page 896 Design parameters......Page 897 References......Page 901 Introduction......Page 903 Particle Breakage and Wear......Page 904 Simulating Particle Strength by Numerical Modelling......Page 911 Fatigue by Repeated Loading......Page 912 Experimental Studies on Multi Particle Breakage......Page 914 Relation between Single- and Multi-Particle......Page 916 Prediction of breakage in pneumatic transport with repeated impact testing......Page 917 Differences between the repeated impact tester and pneumatic transport system......Page 920 References......Page 926 Introduction......Page 928 Tablet compaction......Page 930 Measurement of tablet strength......Page 932 Effect of process parameters on tablet strength......Page 935 Punch velocity and dwell time effects......Page 936 Compression position in die......Page 938 Compaction simulators......Page 939 Effect of punch velocity and dwell time......Page 941 Tablet formulation: discrimination of bonding and compression effects at the molecular level......Page 942 The effect of tablet structure on strength......Page 943 Effect of density distribution on the strength and friability of capsule-shaped tablets......Page 944 Effect of density distribution on the strength, friability and failure mode of round curved-faced tablets......Page 949 Summary and conclusions......Page 954 References......Page 956 Introduction......Page 958 Experimental Background......Page 961 Distribution Kinetics......Page 965 Results and Discussion......Page 969 Conclusions......Page 972 References......Page 973 Amount of Particle Compounds and Solid Waste......Page 976 Theoretical aspects of liberation of valuables......Page 978 Classification of Waste into Brittle, Rubber-Elastic and Ductile......Page 980 Stressing modes......Page 982 Size reduction by compaction......Page 983 Machines used for rubber-elastic and ductile materials......Page 984 Machines used for brittle materials......Page 990 Motivations for applying the discrete element method......Page 991 Description of the simulation method......Page 993 DEM model and its calibration......Page 994 Crack patterns, particle size distributions and liberation degrees......Page 997 Crushing chambers of machines......Page 1000 Conclusions......Page 1003 References......Page 1004 Introduction......Page 1006 Process-Dependent Attrition......Page 1007 Simple fluidised bed systems - elutriation and size distribution......Page 1012 Jet effects......Page 1016 Attrition in Wet Systems......Page 1019 Attrition in Reacting Systems......Page 1023 Standard Tests and Characterisations......Page 1028 Acknowledgements......Page 1036 References......Page 1038 A Mechanistic Description of Granule Deformation and Breakage......Page 1041 Introduction......Page 1042 Autoadhesion......Page 1046 Wettability and surface energy of solids......Page 1048 Adhesion models......Page 1049 Deformable solids......Page 1050 Hertz contact model......Page 1051 Johnson, Kendall and Roberts (JKR) adhesion model......Page 1052 Friction models......Page 1055 Static friction (adhesive peeling)......Page 1057 Sliding friction......Page 1058 Liquid bridges......Page 1059 Static capillary force......Page 1060 Viscous junctions......Page 1064 Solid bridges......Page 1066 Macroscopic Granule Strength......Page 1068 Ensemble elastic modulus......Page 1069 Rumpf’s theory of granule strength......Page 1072 Kendall’s theory of granule strength......Page 1073 Diametric compression experiments......Page 1076 Impact experiments......Page 1079 Multi-granule testing......Page 1082 Quantification of breakage propensity......Page 1083 Diametric compression simulations......Page 1085 Impact simulations......Page 1086 Understanding wet granulation mechanisms......Page 1088 Effect of impact velocity......Page 1091 Effect of primary particle size......Page 1092 Effect of binder content, binder viscosity and binder surface tension......Page 1093 Targeted performance......Page 1095 Concluding Remarks......Page 1099 References......Page 1102 Introduction......Page 1107 Compression tests......Page 1110 Experimental Setup......Page 1112 Glass......Page 1113 Aluminium oxide......Page 1116 Polymethylmethacrylate......Page 1119 Form (2)......Page 1120 Form (3)......Page 1121 Calcium carbonate granules......Page 1122 Primary particle size......Page 1124 Speed of compression......Page 1126 Wet granules......Page 1127 Binderless granules......Page 1130 Summary......Page 1132 References......Page 1133 A New Concept for Addressing Bulk Solids Attrition in Pneumatic Conveying......Page 1135 Fundamentals......Page 1136 Components of pneumatic conveying installations......Page 1137 A systematic definition of the term attrition......Page 1140 Process scale......Page 1142 Single-particle scale......Page 1144 Material scale......Page 1149 A New Concept for Addressing Attrition in Pneumatic Conveying......Page 1152 Approach by Euler-Lagrange......Page 1154 Determination of impact conditions from numerical simulations......Page 1156 Cumulative number distributions of the stress conditions......Page 1159 Dense phase conveying......Page 1163 Stress mode in plug flow conveying......Page 1164 Stress intensity from measurements of the pressure exerted by plugs......Page 1165 Stress intensity from analysis of Discrete Element Methods (DEM)......Page 1167 Conclusions from the determination of the process function......Page 1169 Test material......Page 1170 Sample preparation and determination of attrition rate......Page 1172 Experimental setup and parameters......Page 1173 Discussion of experimental results......Page 1174 Experimental validation of process function for dilute phase conveying......Page 1177 Application of existing attrition models on results obtained in single-particle experiments......Page 1179 Hardness and fracture mechanical properties......Page 1183 Thermo-mechanical properties......Page 1185 Experiments on the process scale......Page 1189 Qualitative model of attrition in pneumatic conveying......Page 1192 Bridging the Gap between Academic Research and Industrial Needs......Page 1196 Summary......Page 1198 References......Page 1202 index.pdf......Page 1205