Statistical Microhydrodynamics

Statistical Microhydrodynamics......Page 4
Contents......Page 8
Preface......Page 12
Nomenclature......Page 16
1.1 Events, Set of Events, and Probability......Page 40
1.2 Random Variables, Probability Distribution Function, Average Value, and Variance......Page 43
1.3 Generalized Functions......Page 44
1.4 Methods of Averaging......Page 47
1.5 Characteristic Functions......Page 51
1.6 Moments and Cumulants of Random Variables......Page 53
1.7 Correlation Functions......Page 55
1.8 Bernoulli, Poisson, and Gaussian Distributions......Page 57
1.9 Stationary Random Functions, Homogeneous Random Fields......Page 61
1.10 Isotropic Random Fields. Spectral Representation......Page 64
1.11 Stochastic Processes. Markovian Processes. The Chapman–Kolmogorov Integral Equation......Page 67
1.12.1 Derivation of the Differential Chapman–Kolmogorov Equation......Page 70
1.12.3 Diffusion Processes. The Fokker–Planck Equation......Page 74
1.12.4 Deterministic Processes. The Liouville Equation......Page 79
1.13.1 The Langevin Equation......Page 82
1.13.2 The Diffusion Equation......Page 83
1.13.2.1 The Diffusion Equation with Chemical Reactions Taken into Account......Page 84
1.13.2.2 Brownian Motion of a Particle in a Hydrodynamic Medium......Page 85
1.14 Variational (Functional) Derivatives......Page 87
1.15 The Characteristic Functional......Page 92
2 Elements of Microhydrodynamics......Page 98
2.1 Motion of an Isolated Particle in a Quiescent Fluid......Page 100
2.2 Motion of an Isolated Particle in a Moving Fluid......Page 109
2.3.1 Fluid is at Rest at the Infinity (v = 0)......Page 117
2.3.2 Fluid is Moving at the Infinity (v 0)......Page 131
2.4 Multi-Particle Motion......Page 134
2.5 Flow of a Fluid Through a Random Bed of Particles......Page 137
3 Brownian Motion of Particles......Page 148
3.1 Random Walk of an Isolated Particle......Page 149
3.1.1 Isotropic Distribution......Page 152
3.1.2 Gaussian Distribution......Page 153
3.1.3 An Arbitrary Distribution τ(r) in the Limiting Case N»1......Page 154
3.2 Random Walk of an Ensemble of Particles......Page 155
3.3 Brownian Motion of a Free Particle in a Quiescent Fluid......Page 156
3.4 Brownian Motion of a Particle in an External Force Field......Page 161
3.5 The Smoluchowski Equation......Page 163
3.6 Brownian Motion of a Particle in a Moving Fluid......Page 165
3.7 Brownian Diffusion with Hydrodynamic Interactions......Page 169
3.8 Brownian Diffusion with Hydrodynamic Interactions and External Forces......Page 175
3.8.1 High Peclet Numbers: Pe(ij)»1......Page 178
3.8.2 Small Peclet Numbers, Pe(ij)«1......Page 179
3.9 Particle Sedimentation in a Monodisperse Dilute Suspension......Page 181
3.10 Particle Sedimentation in a Polydisperse Dilute Suspension, with Hydrodynamic and Molecular Interactions and Brownian Motion of Particles......Page 190
3.11 Transport Coefficients in Disperse Media......Page 196
3.11.1 Infinitely Dilute Suspension with Non-interacting Particles......Page 200
3.11.2 The Influence of Particle Interactions on Transport Coefficients......Page 203
3.12 Concentrated Disperse Media......Page 206
4.1 General Information on Laminar and Turbulent Flows......Page 222
4.2 The Momentum Equation for Viscous Incompressible Fluids......Page 223
4.3 The Equations of Heat Inflow, Heat Conduction and Diffusion......Page 226
4.4 The Conditions for the Beginning of Turbulence......Page 228
4.5 Hydrodynamic Instability......Page 229
4.6 The Reynolds Equations......Page 231
4.7 The Equation of Turbulent Energy Balance......Page 236
4.8 Isotropic Turbulence......Page 241
4.9 The Local Structure of Fully Developed Turbulence......Page 251
4.10 Turbulent Flow Models......Page 262
4.10.1 Semi-empirical Theories of Turbulence......Page 263
4.10.2 The Use of Transport Equations......Page 269
4.11 Use of the Characteristic Functional in the Theory of Turbulence......Page 273
4.12 Intermittency in a Turbulent Flow......Page 283
5.1 The Eulerian and Lagrangian Approaches to the Description of Fluid Flow and Particle Motion......Page 290
5.2 Lagrangian Statistical Characteristics of Turbulence......Page 295
5.3 Turbulent Diffusion......Page 306
5.4 A Semiempirical Model of Turbulent Diffusion......Page 316
5.5 Models of Two-phase Disperse Turbulent Flows......Page 321
5.6 Deposition of Particles from a Turbulent Flow......Page 331
5.7 Interaction of Particles in a Turbulent Flow......Page 343
5.8 Chemical Reactions in a Turbulent Flow......Page 345
5.8.1 Concepts of Chemical Kinetics......Page 348
5.8.2 Method of Moments......Page 351
5.8.3 Approximations for Chemical Reaction Rates......Page 358
5.9 The PDF Method......Page 361
6.1 Kinetic Equations of Coagulation......Page 374
6.2 Fundamental Features of the Coagulation of Particles......Page 383
6.3 A Model of Turbulent Diffusion......Page 388
6.4 Hydrodynamic, Molecular, and Electrostatic Forces......Page 396
6.5 Conducting Particles in an Electric Field......Page 404
6.6 Coagulation of Particles in a Turbulent Flow......Page 409
6.7 Breakup of Particles......Page 423
7 Motion and Collision of Inertial Particles in a Turbulent Flow......Page 434
7.1 Motion of Particles without Mutual Collisions......Page 435
7.2 Motion of Particles with Mutual Collisions......Page 452
7.3 Frequency of Collisions of Particles......Page 460
7.4 Preferential Concentration of Particles in Isotropic Turbulence......Page 472
Author Index......Page 494
Subject Index......Page 498