Preface ...................................................... xiii
Acknowledgments .............................................. xvii
1 Introduction ............................................... 1
1.1 Adhesive Particle Flow ..................................... 1
1.2 Dimensionless Parameters and Related Simplifications ....... 5
1.2.1 Stokes Number ....................................... 5
1.2.2 Density Ratio ....................................... 7
1.2.3 Length Scale Ratios ................................. 8
1.2.4 Particle Reynolds Number ........................... 10
1.2.5 Particle Concentration and Mass Loading ............ 11
1.2.6 Bagnold Number ..................................... 14
1.2.7 Adhesion Parameter ................................. 15
1.3 Applications .............................................. 15
1.3.1 Fibrous Filtration Processes ....................... 15
1.3.2 Extraterrestrial Dust Fouling ...................... 18
1.3.3 Wet Granular Material .............................. 21
1.3.4 Blood Flow ......................................... 23
1.3.5 Aerosol Reaction Engineering ....................... 25
2 Modeling Viewpoints and Approaches ........................ 29
2.1 A Question of Scale ....................................... 29
2.2 Macroscale Particle Methods ............................... 30
2.2.1 Discrete Parcel Method ............................. 30
2.2.2 Population Balance Method .......................... 32
2.3 Mesoscale Particle Methods ................................ 34
2.3.1 Molecular Dynamics ................................. 36
2.3.2 Brownian Dynamics .................................. 37
2.3.3 Dissipative Particle Dynamics ...................... 38
2.3.4 Discrete Element Method ............................ 40
2.4 Microscale Dynamics of Elastohydrodynamic Particle
Collisions ................................................ 41
2.4.1 Microscale Simulations of Elastohydrodynamic
Interactions ....................................... 42
2.4.2 Experimental Results for Two-Particle Collisions ... 44
2.4.3 Simplified Models for Restitution Coefficient in
a Viscous Fluid .................................... 46
3 Contact Mechanics without Adhesion ........................ 51
3.1 Basic Concepts ............................................ 51
3.2 Hertz Theory: Normal Elastic Force ........................ 54
3.2.1 Derivation ......................................... 55
3.2.2 Two-Particle Collision ............................. 56
3.3 Normal Dissipation Force .................................. 58
3.3.1 Physical Mechanisms ................................ 58
3.3.2 Models for Solid-Phase Dissipation Force ........... 61
3.4 Hysteretic Models for Normal Contact with Plastic
Deformation ............................................... 66
3.5 Sliding and Twisting Resistance ........................... 69
3.5.1 Physical Mechanisms of Sliding and Twisting
Resistance ......................................... 69
3.5.2 Sliding Resistance Model ........................... 72
3.5.3 Twisting Resistance Model .......................... 73
3.6 Rolling Resistance ........................................ 74
3.6.1 Rolling Velocity ................................... 74
3.6.2 Physical Mechanism of Rolling Resistance ........... 77
3.6.3 Model for Rolling Resistance ....................... 78
4 Contact Mechanics with Adhesion Forces .................... 81
4.1 Basic Concepts and the Surface Energy Density ............. 82
4.2 Contact Mechanics with van der Waals Force ................ 86
4.2.1. Models for Normal Contact Force .................... 86
4.2.2 Normal Dissipation Force and Its Validation ......... 96
4.2.3 Effect of Adhesion on Sliding and Twisting
Resistance ......................................... 98
4.2.4 Effect of Adhesion on Rolling Resistance ........... 99
4.3 Electrical Double-Layer Force ............................ 100
4.3.1 Stern and Diffuse Layers .......................... 101
4.3.2 Ionic Shielding of Charged Particles .............. 102
4.3.3 DLVO Theory ....................................... 103
4.4 Protein Binding .......................................... 107
4.5 Liquid Bridging Adhesion ................................. 111
4.5.1 Capillary Force ................................... 111
4.5.2 Effect of Roughness on Capillary Cohesion ......... 116
4.5.3 Viscous Force ..................................... 117
4.5.4 Rupture Distance .................................. 118
4.5.5 Capillary Torque on a Rolling Particle ............ 118
4.6 Sintering Force .......................................... 120
4.6.1 Sintering Regime Map .............................. 121
4.6.2 Approximate Sintering Models ...................... 123
4.6.3 Hysteretic Sintering Contact Model ................ 124
5 Fluid Forces on Particles ................................ 130
5.1 Drag Force and Viscous Torque ............................ 131
5.1.1 Effect of Flow Nonuniformity ...................... 131
5.1.2 Effect of Fluid Inertia ........................... 132
5.1.3 Effect of Surface Slip ............................ 135
5.2 Lift Force ............................................... 138
5.2.1 Saffman Lift Force ................................ 138
5.2.2 Magnus Lift Force ................................. 140
5.3 Forces in Unsteady Flows ................................. 141
5.3.1 Pressure-Gradient (Buoyancy) Force ................ 141
5.3.2 Added Mass Force .................................. 142
5.3.3 History Force ..................................... 143
5.4 Brownian Motion .......................................... 145
5.5 Scaling Analysis ......................................... 147
5.6 Near-Wall Effects ........................................ 151
5.6.1 Drag Force ........................................ 151
5.6.2 Lift Force ........................................ 154
5.7 Effect of Surrounding Particles .......................... 156
5.7.1 Flow through Packed Beds .......................... 159
5.7.2 Flow through Fluidized Beds ....................... 159
5.7.3 Simulations ....................................... 161
5.7.4 Effect of Particle Polydispersity ................. 164
5.8 Stokesian Dynamics ....................................... 165
5.8.1 Example for Falling Cluster of Particles .......... 165
5.8.2 General Theory .................................... 169
5.9 Particle Interactions with Acoustic Fields ............... 170
5.9.1 Orthokinetic Motion ............................... 172
5.9.2 Acoustic Wake Effect .............................. 173
6 Particle Dispersion in Turbulent Flows ................... 182
6.1 Particle Motion in Turbulent Flows ....................... 182
6.2 Particle Drift Measure ................................... 185
6.3 Particle Collision Models ................................ 188
6.3.1 Collision Mechanisms .............................. 188
6.3.2 Orthokinetic Collisions (Small Stokes Numbers) .... 190
6.3.3 Accelerative-Independent Collisions (Large
Stokes Numbers) ................................... 192
6.3.4 Accelerative-Correlative Collisions
(Intermediate Stokes Numbers) ..................... 192
6.4 Dynamic Models for Particle Dispersion ................... 195
6.5 Dynamic Models for Particle Clustering ................... 199
7 Ellipsoidal Particles .................................... 206
7.1 Particle Dynamics ........................................ 207
7.2 Fluid Forces ............................................. 209
7.3 Collision Detection and Contact Point Identification ..... 211
7.3.1 Two-Dimensional Algorithms ........................ 212
7.3.2 Algorithms Based on a Common Normal Vector ........ 213
7.3.3 Algorithms Based on Geometric Level Surfaces ...... 214
7.4 Contact Forces ........................................... 217
7.4.1 Geometry of Colliding Particles ................... 217
7.4.2 Hertz Theory for Ellipsoidal Particles ............ 218
8 Particle Interactions with Electric and Magnetic Fields .. 223
8.1 Electric Field Forces and Torques ........................ 224
8.1.1 Coulomb Force and Dielectrophoresis ............... 224
8.1.2 Dielectrophoresis in an AC Electric Field ......... 227
8.1.3 Application to Particle Separation and Focusing ... 229
8.2 Mechanisms of Particle Charging .......................... 231
8.2.1 Field Charging .................................... 232
8.2.2 Diffusion Charging ................................ 233
8.2.3 Contact Electrification ........................... 235
8.2.4 Contact De-electrification ........................ 237
8.3 Magnetic Field Forces .................................... 237
8.4 Boundary Element Method .................................. 239
8.4.1 General Boundary Element Method ................... 239
8.4.2 Pseudoimage Method for Particles Near an
Electrode Surface ................................. 242
8.4.3 Problems with DEP Force Near Panel Edges .......... 243
8.5 Fast Multipole Method for Long-Range Forces .............. 245
8.6 Electrostatic Agglomeration Processes .................... 249
8.6.1 Relative Importance of Electrostatic and van der
Waals Adhesion Forces ............................. 249
8.6.2 Particle Chain Formation .......................... 250
9 Nanoscale Particle Dynamics .............................. 256
9.1 Continuum and Free-Molecular Regimes ..................... 257
9.1.1 Drag Force ........................................ 258
9.1.2 Brownian Force .................................... 260
9.1.3 Mean-Free-Path of Nanoparticles ................... 261
9.1.4 Thermophoretic Force .............................. 262
9.1.5 Competition between Diffusion and Thermophoresis
during Deposition ................................. 265
9.2 Nanoparticle Interactions ................................ 266
9.2.1 Collision of Large Nanoparticles .................. 266
9.2.2 Collision of Small Nanoparticles .................. 269
9.2.3 Long-Range Interparticle Electrostatic Forces ..... 271
9.3 Time Scales of Nanoparticle Collision-Coalescence
Mechanism ................................................ 274
9.3.1 Time Scale of Particle Collisions ................. 275
9.3.2 Time Scale of Nanoparticle Sintering .............. 278
10 Computer Implementation and Data Analysis ................ 286
10.1 Particle Time Stepping ................................... 286
10.1.1 Numerical Stability .............................. 287
10.1.2 Multiscale Time-Stepping Approaches .............. 288
10.2 Flow in Complex Domains .................................. 289
10.2.1 Particle Search Algorithm ........................ 290
10.2.2 Level Set Distance Function ...................... 293
10.3 Measures of Local Concentration .......................... 294
10.4 Measures of Particle Agglomerates ........................ 297
10.4.1 Particle Count and Orientation Measures ........... 297
10.4.2 Agglomerate Orientation Measures .................. 298
10.4.3 Equivalent Agglomerate Ellipse .................... 298
10.4.4 Agglomerate Fractal Dimension ..................... 300
10.4.5 Particle Packing Measures ......................... 302
11 Applications ............................................. 305
11.1 Particle Migration in Tube and Channel Flows ............. 305
11.1.1 Inertial Particle Migration in Straight Tubes...... 306
11.1.2 Collision-Induced Particle Migration .............. 307
11.1.3 Particle Migration in the Presence of Wavy Tube
Walls ............................................. 309
11.2 Particle Filtration ...................................... 311
11.2.1 Fiber Filtration .................................. 312
11.2.2 Enhancement of Filtration Rate by Particle
Mixtures .......................................... 316
11.2.3 Enhancement of Filtration Rate by Electric
Fields ............................................ 318
11.3 Rotating Drum Mixing Processes ........................... 320
11.3.1 Flow Regimes ...................................... 320
11.3.2 Mixing and Segregation ............................ 322
11.3.3 Cohesive Mixing and Segregation ................... 326
11.4 Dust Removal Processes ................................... 328
11.4.1 Hydrodynamic Dust Mitigation ...................... 328
11.4.2 Electric Curtain Mitigation for Charged
Particles ......................................... 331
11.5 Final Comments ........................................... 332
Index ......................................................... 339
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