Particle Breakage, Volume 12 (Handbook of Powder Technology)

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: An™Elementary 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