Introduction to Dynamics of Colloids (eBook)

Front Cover 1
An Introduction to Dynamics of Colloids 4
Copyright Page 5
CONTENTS 10
CHAPTER 1. INTRODUCTION 20
1.1 An Introduction to Colloidal Systems 21
1.2 Mathematical Preliminaries 32
1.3 Statistical Mechanics 50
Appendix 68
Exercises 70
Further Reading and References 83
CHAPTER 2. BROWNIAN MOTION OF NON-INTERACTING PARTICLES 88
2.1 Introduction 89
2.2 The Langevin Equation 89
2.3 Time Scales 93
2.4 Chandrasekhar's Theorem 98
2.5 The pdf on the Diffusive Time Scale 99
2.6 The Langevin Equation on the Diffusive Time Scale 100
2.7 Diffusion in Simple Shear Flow 102
2.8 Rotational Brownian Motion 107
Exercises 121
Further Reading and References 124
CHAPTER 3. LIGHT SCATTERING 126
3.1 Introduction 127
3.2 A Heuristic Derivation 128
3.3 The Maxwell Equation Derivation 132
3.4 Relation to Density Fluctuations 141
3.5 Static Light Scattering (SLS) 144
3.6 Dynamic Light Scattering (DLS) 151
3.7 Some Experimental Considerations 154
3.8 Light Scattering by Dilute Suspensions of Spherical Particles 160
3.9 Effects of Polydispersity 163
3.10 Scattering by Rigid Rods 172
Exercises 179
Further Reading and References 188
CHAPTER 4. FUNDAMENTAL EQUATIONS OF MOTION 190
4.1 Introduction 191
4.2 A Primer on Hydrodynamic Interaction 196
4.3 The Fokker-Planck Equation 198
4.4 The Smoluchowski Equation 202
4.5 Diffusion of non-Interacting Particles 205
4.6 The Smoluchowski Equation with Simple Shear Flow 214
4.7 The Smoluchowski Equation with Sedimentation 223
4.8 The Smoluchowski Equation for Rigid Rods 227
Exercises 239
Further Reading and References 244
CHAPTER 5. HYDRODYNAMICS 246
5.1 Introduction 247
5.2 The Continuity Equation 248
5.3 The Navier-Stokes Equation 250
5.4 The Hydrodynamic Time Scale 253
5.5 The Creeping Flow Equations 257
5.6 The Oseen Matrix 260
5.7 Flow past a Sphere 263
5.8 Leading Order Hydrodynamic Interaction 269
5.9 Faxen's Theorems 272
5.10 One step further : the Rodne-Prager Matrix 274
5.11 Rotational Relaxation of Spheres 276
5.12 The Method of Reflections 277
5.13 Hydrodynamic Interaction in Shear Flow 295
5.14 Hydrodynamic Interaction in Sedimenting Suspensions 300
5.15 Friction of Long and Thin Rods 301
Appendix A 307
Appendix B 313
Appendix C 314
Appendix D 315
Appendix E 319
Exercises 321
Further Reading and References 330
CHAPTER 6. DIFFUSION 334
6.1 Introduction 335
6.2 Collective Diffusion 336
6.3 Self Diffusion 343
6.4 Diffusion in Stationary Shear Flow 348
6.5 Short-time Diffusion 350
6.6 Gradient Diffusion 370
6.7 Long-time Self Diffusion 375
6.8 Diffusion in Stationary Shear Flow 382
6.9 Memory Equations 391
6.10 Diffusion of Rigid Rods 411
Appendix A 434
Appendix B 435
Appendix C 437
Appendix D 439
Appendix E 440
Exercises 443
Further Reading and References 456
CHAPTER 7. SEDIMENTATION 462
7.1 Introduction 463
7.2 Sedimentation Velocity of Interacting Spheres 465
7.3 Non-uniform Backflow 480
7.4 The Sedimentation-Diffusion Equilibrium 487
7.5 The Dynamics of Sediment Formation 492
Exercises 500
Further Reading and References 509
CHAPTER 8. CRITICAL PHENOMENA 514
8.1 Introduction 515
8.2 Long Ranged Interactions 520
8.3 The Ornstein-Zernike Static Structure Factor with Shear Flow 534
8.4 The Temperature and Shear Rate Dependence of the Turbidity 544
8.5 Collective Diffusion 549
8.6 Anomalous Behaviour of the Shear Viscosity 554
Appendix A 567
Appendix B 568
Exercises 569
Further Reading and References 574
CHAPTER 9. PHASE SEPARATION KINETICS 578
9.1 Introduction 580
9.2 Initial Spinodal Decomposition Kinetics 586
9.3 Initial Spinodal Decomposition of Sheared Suspensions 599
9.4 Small Angle Light Scattering by Demixing Suspensions 605
9.5 Demixing Kinetics in the Intermediate Stage 609
9.6 Experiments on Spinodal Decomposition 626
Appendix A 631
Appendix B 634
Appendix C 636
Appendix D 637
Exercises 641
Further Reading and References 649
INDEX 654