Particle deposition and aggregation: measurement, modelling, and simulation

M. Elimelech, Xiadong Jia, John Gregory, Richard Williams9780750670241, 075067024X

Deposition and aggregation of small solid particles are encountered in many natural and industrial environments. Whether it be deposition of particles onto a surface immersed in a liquid suspension or aggregateion of individual particles, these processes are of enotmous significance. They are vital to the manufacture of magnetic tape, purification of water using packed bed filters, selective capture of solids, cells and macromolecular species, and many other applications. This book presents a unified approach to the measurement, modelling and simulation of these processes, bringing together the disciplines of colliod and surface chemistry, hydrodynamics, and experimental and computational methods. It will be required reading for graduates working in process and environmental engineering, postgraduates involved in industrial R & D and for all scientists wishing to gain a more detailed and realistic understanding of process conditions in these areas.

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Table of contents :
Front Matter……Page 1
Author Index……Page 0
Preface……Page 4
1. Introduction……Page 14
2. Electrical Properties of Interfaces……Page 20
2.1 Introduction……Page 21
2.2.1 Origin of Surface Charge……Page 22
2.2.2 The Gouy-Chapman Double Layer Model……Page 24
2.2.3 The Stern Model……Page 27
2.2.4 The Stern-Grahame Model……Page 32
2.2.5 Further Refinements to the Model……Page 33
2.3.1 General……Page 34
2.3.2 Electro-Osmosis……Page 36
2.3.3 Streaming Potential……Page 37
2.3.4 Particle Electrophoresis……Page 38
2.3.5 Interpretation of Zeta Potentials……Page 40
References……Page 42
3. Surface Interaction Potentials……Page 44
3.2 Double Layer Interaction Between Macroscopic Bodies……Page 45
3.2.1 Plate-Plate Interactions……Page 46
3.2.2 Sphere-Sphere Interactions……Page 49
3.3.1 Overview……Page 53
3.3.2 Hamaker Expressions for Interacting Spheres……Page 54
3.3.3 Calculation of Hamaker Constants……Page 57
3.3.4 Retardation……Page 59
3.4 Non-DLVO Forces……Page 61
3.4.1 Born Repulsion……Page 62
3.4.2 Hydration Effects……Page 63
3.4.3 Hydrophobic Interaction……Page 64
3.4.4 Steric Interaction……Page 65
3.4.5 Polymer Bridging……Page 66
3.5.1 Basis of the DLVO Theory……Page 69
3.5.2 Stability Criteria……Page 70
References……Page 74
4. Colloidal Hydrodynamics and Transport……Page 79
4.1.1 Navier-Stokes Equation……Page 82
4.1.2 Flow Field in Simple Geometries……Page 84
4.2.1 Brownian Motion……Page 88
4.2.2 Diffusion……Page 89
4.3.1 Motion of a Single Hard Sphere……Page 90
4.3.2 Motion of a Single Soft Sphere……Page 92
4.4.1 In Quiescent Fluid……Page 94
4.4.2 In Shear Flow……Page 100
4.5 Concentration Dependence of Diffusion Coefficients……Page 104
4.6.1 Overview……Page 107
4.6.2 Basic Equations and Boundary Conditions……Page 109
4.6.3 Perfect-Sink Model……Page 110
4.6.4 Non-Penetration Model……Page 115
Bibliography……Page 117
References……Page 118
5. Modelling of Particle Deposition Onto Ideal Collectors……Page 121
5.1.1 Hydrodynamics……Page 124
5.1.2 Particle Transport Equation……Page 125
5.2 Stagnation-point Flow……Page 128
5.2.1 Hydrodynamics……Page 129
5.2.2 Particle Transport Equation……Page 130
5.3.1 Hydrodynamics……Page 131
5.3.2 Particle Transport Equation……Page 132
5.4.1 Hydrodynamics……Page 134
5.4.2 Particle Transport Equation……Page 137
5.5 Interaction-force Boundary-layer Approximation……Page 140
5.5.2 Quantitative Formulation……Page 141
5.5.3 Available Analytical Solution……Page 143
5.5.4 Evaluation of KF……Page 145
5.6 Trajectory Analysis……Page 146
5.6.1 Collector and Flow Model……Page 147
5.6.2 Force Balance and Basic Formulations……Page 148
5.6.3 The Trajectory Equation……Page 150
5.7 Representatives Simulation of Particle Deposition……Page 151
5.7.1 Deposition in the Presence of Repulsive Double Layer Interactions……Page 152
5.7.2 Deposition in the Presence of Attractive Double Layer Interactions……Page 157
References……Page 162
6. Modelling of Aggregation Processes……Page 165
6.1 Collisions and Aggregation: the Smoluchowski Approach……Page 166
6.2.1 Perikinetic Aggregation……Page 168
6.2.2 Orthokinetic Aggregation……Page 173
6.2.4 Comparison of Rates……Page 177
6.3.1 Stability Ratio – the Fuchs Approach……Page 179
6.3.3 Hydrodynamic Interaction……Page 182
6.4 Form of Aggregates……Page 188
6.4.1 Model Studies: Fractal Clusters……Page 189
6.4.2 Aggregate Density……Page 192
6.4.3 Collision Rates of Fractal Aggregates……Page 193
6.5 Aggregate Strength and Break Up……Page 194
6.6.1 Analytical Approaches……Page 196
6.6.2 ‘Self-Preserving’ Distributions……Page 198
6.6.3 The ‘Maximum Entropy’ Approach……Page 200
6.7.1 Introduction……Page 202
6.7.2 Mixing……Page 203
6.7.3 Adsorption……Page 204
6.7.4 Reconformation……Page 205
6.7.5 Flocculation……Page 206
Bibliography……Page 207
References……Page 208
7. Selection of a Simulation Method……Page 211
7.1 Overview Of Simulation Protocol……Page 213
7.2 Useful Concepts In Statistical Mechanics……Page 217
7.3 Monte Carlo Methods……Page 221
7.3.1 Metropolis Monte Carlo Method……Page 222
7.3.2 Monte Carlo Methods for Various Ensembles……Page 223
7.3.3 Advanced Monte Carlo Methods……Page 224
7.4 Molecular Dynamics Methods……Page 226
7.4.1 Equations of Motion and Finite Difference Methods……Page 227
7.4.2 Application of Molecular Dynamics to Particulate Systems……Page 230
7.5.1 Brownian Dynamics for Hydrodynamically Independent Particles……Page 232
7.5.2 Brownian Dynamics for Hydrodynamically Interacting Particles……Page 234
7.5.3 Constraint Brownian Dynamics……Page 237
References……Page 238
8. Implementation of Computer Simulations……Page 242
8.1 Pair Potential Models……Page 243
8.2 Periodic Boundary Conditions……Page 245
8.3.1 Uniform Distribution……Page 247
8.3.2 Gaussian Distribution……Page 248
8.3.4 Exponential Distribution……Page 249
8.4 Example: Implementation of Metropolis MC Simulation……Page 250
8.5 Computer Hardware……Page 252
8.5.1 Classification of Computers……Page 254
8.5.2 Amdahl’s Law……Page 256
8.5.3 Registers and Memories……Page 259
8.6 Visualization of Simulation Results……Page 261
8.7.1 Hardware Specifications Relevant to Computer Simulations……Page 262
8.7.2 Guidelines for Efficient Programming……Page 264
8.7.3 Example of Visualization Tools……Page 267
References……Page 268
9. Experimental Techniques for Aggregation Studies……Page 269
9.1 General: Choice of Technique……Page 270
9.2.1 Microscopic Methods……Page 271
9.2.2 Sensing Zone Techniques……Page 272
9.3.1 Turbidity……Page 274
9.3.2 Static Light Scattering……Page 278
9.3.3 Dynamic Light Scattering……Page 283
9.4.1 Electro-Optic Techniques……Page 285
9.4.2 Turbidity Fluctuations……Page 286
9.5.1 Sedimentation Methods……Page 289
9.5.2 Permeability Methods……Page 291
References……Page 293
10. Experimental Techniques in Particle Deposition Kinetics……Page 296
10.1.1 Hydrodynamic Conditions……Page 297
10.1.3 Colloidal Suspensions……Page 298
10.1.5 Non-Aggregated Suspension……Page 299
10.2.1 Microscopic Means……Page 300
10.2.2 Particle Counters……Page 301
10.3.1 Stagnation-point Flow……Page 302
10.3.2 Rotating Disc……Page 306
10.3.3 Parallel-Plate Channel……Page 307
10.3.4 Packed-Bed Technique……Page 309
10.4 Determination of Experimental Collision Efficiencies……Page 311
References……Page 313
11. Theoretical Predictions Compared to Experimental Observations in Particle Deposition Kinetics……Page 316
11.1 Deposition with Repulsive Double Layers……Page 317
11.2 Deposition in the Presence of Attractive Double Layers……Page 323
11.2.1 Mechanisms of Paricle Deposition with Attractive Double Layers……Page 326
11.3 Possible Explanations for Observed Discrepancies in Unfavourable Deposition……Page 328
11.3.1 Distribution of Surface Properties……Page 329
11.3.2 Heterogeneity of Surface Charge……Page 331
11.3.3 Surface Roughness of Particles and Collectors……Page 334
11.3.4 Dynamics of Interaction……Page 337
11.3.5 Deposition in Secondary Minima……Page 339
11.3.6 Possibility of Additional Forces……Page 341
11.4.1 Theoretical Formulation of a Correlation Equation……Page 342
11.4.2 Testing the Correlation Equation……Page 344
References……Page 346
12. Performance of Packed Bed-filters……Page 350
12.1 Particle Removal Mechanisms……Page 351
12.2 Modelling of Particle Removal in Granular Filtration……Page 352
12.2.1 Phenomenological Theories……Page 353
12.2.2 Fundamental Theories……Page 354
12.3.1 Effect of Particle Size on the Single Collector Removal Efficiency……Page 357
12.3.2 Effect of Particle Size on Clean-Bed Removal Efficiency……Page 358
12.3.3 Effect of Filtration Rate on the Clean-Bed Removal……Page 360
12.3.4 Effect of Filter Grain Size on Clean-Bed Removal……Page 361
Bibliography……Page 362
References……Page 363
13. Transport of Colloidal Materials in Ground Water……Page 364
13.1.2 Colloidal Properties of Viruses……Page 365
13.1.3 Studies on Virus Transport in Soils and Ground Water……Page 367
13.2.2 Particle-Pollutant Interactions……Page 368
13.2.3 Previous Work on Colloid Transport……Page 369
13.3.1 Calculation of Colloid Travel Distance……Page 371
13.3.2 Simulations of Particle Travel Distance……Page 372
References……Page 376
14.1.1 Classification of Filtration Processes……Page 379
14.1.2 Classification of Filtration Models……Page 381
14.2.1 Generation of Model Structure……Page 382
14.2.2 Simulation of Coalescence of Liquid Droplets……Page 384
14.3.1 Generation of Model Structure……Page 385
14.3.2 Simulation of Particle Penetration……Page 389
14.4 Tessellation Models……Page 391
14.4.2 Prediction of Solvent Flux, Pore Blockage and Blinding……Page 392
14.5.1 Generation of Random Packing of Spheres……Page 396
14.5.2 Network Model of Granular Porous Media……Page 399
14.5.3 Simulation of Filtration Processes……Page 402
References……Page 403
15. Application of Simulation Techniques to Colloidal Dispersion Systems……Page 405
15.1 MC Simulation of Triplet Formation……Page 406
15.2 MC Simulation of Magnetic Flocculation……Page 407
15.3 BD Simulation of Colloidal Aggregation……Page 412
15.4 BD Simulation of Colloidal Deposition……Page 413
15.5 Simulation of Colloids Under Shear……Page 417
15.6 Stokesian Dynamics Simulations……Page 423
15.7 Conclusions……Page 426
References……Page 427
Author Index……Page 429
Subject Index……Page 435