Transport Coefficients of Fluids (eBook)

Preface 6
Contents 9
1 Introduction 14
References 20
Transport Coefficients of Dilute Gases 23
2 Boltzmann Equation for Dilute Monatomic Gases 24
2.1 Boltzmann Equation and Boltzmann Entropy 25
2.2 Equilibrium Solution 27
2.3 Linear Transport Processes 29
References 38
3 Transport Processes in Monatomic Gases 40
3.1 Diffusion Processes 40
3.2 Thermal Conduction 42
3.3 Viscous Phenomena 43
3.4 Nonlinear Transport Processes 44
3.5 Applications of Nonlinear Transport Coefficients 57
References 66
4 Boltzmann Equation for Dilute Polyatomic Gases 68
4.1 Kinetic Equation for Polyatomic Gases 69
4.2 The H Theorem 72
4.3 Generalized Hydrodynamic Equations 74
4.4 Linear Transport Processes 82
4.5 Remarks 82
References 83
5 Transport Processes in Dilute Polyatomic Gases 84
5.1 Ultrasonic Absorption in Rigid Diatomic Gases 84
5.2 Nonlinear Transport Coefficients and Shock Waves 95
References 102
Transport Coefficients of Liquids 105
6 Equation of State and Equilibrium Properties of Liquids 106
6.1 Virial Equation of State 107
6.2 Generic van der Waals Equation of State 107
6.3 Free Volume 113
6.4 Temperature and Density Dependence of A and B 114
6.5 Model Canonical Equation of State 117
6.6 Integral Equations for Pair Correlation Functions 125
6.7 Equation for Inverse Correlation Length 142
6.8 Application to Hard Sphere Fluids 143
6.9 Concluding Remarks 158
References 159
7 Generalized Boltzmann Equation 162
7.1 Grand Ensemble and Kinetic Equation 163
7.2 Conservation Laws 168
7.3 Constitutive Equations 171
7.4 Generalized Hydrodynamics 177
7.5 Linear Transport Coefficients 180
7.6 Formal Consideration of the Collision Bracket Integrals 182
7.7 A Monte Carlo Method for the Stress Tensor 185
References 189
8 Generalized Boltzmann Equation for Polyatomic Liquids 192
8.1 Notational Preliminary 192
8.2 Evolution Equations for Macroscopic Variables 198
8.3 Kinetic Theory of Reacting Fluids 206
8.4 Kinetic Equation for Reacting Fluids 208
8.5 Collision Operators 211
8.6 Density Evolution Equations and Chemical Kinetics 212
8.7 Scattering Theory and Rate Coefficients 220
8.8 The R Matrix Theory of Collision 222
8.9 Collision Complexes and Rate Coefficient 227
8.10 Characterization of Collision Complexes 229
References 232
9 Dynamic Ornstein–Zernike Equation 234
9.1 Nonequilibrium Ensemble Distribution Function 234
9.2 Dynamic Ornstein–Zernike Equation 236
9.3 Connection with Existing Theory 243
9.4 Local Equilibrium Equation of State 245
References 252
10 Density Fluctuation Theory: Simple Fluids 254
10.1 Excess Normal Stress 255
10.2 Shear Stress 263
10.3 Heat Flux 279
10.4 Concluding Remarks 297
References 298
11 Density Fluctuation Theory: Complex Fluids 300
11.1 Nonequilibrium Ensemble Distribution Function 301
11.2 Excess Normal Stress 302
11.3 Shear Stress 323
11.4 Heat Flux 334
11.5 Concluding Remarks on the Density Fluctuation Theory 351
References 353
12 Free Volume Theory and Transport Coefficients 356
12.1 Modified Free Volume Theory of Diffusion 357
12.2 Comparison with Experiments 362
12.3 Modified Free Volume Theory of Mixtures 369
12.4 Validation of the Mixture Theory 377
12.5 Transport Coefficients of Ordinary Liquids 385
12.6 Conclusion 393
References 396
A Grand Ensemble Kinetic Equation 398
A.1 Derivation of the Kinetic Equation 398
A.2 Relation Between Collision and Transition Operators 403
B The Constitutive Equation for Velocity 408
References 411
Index 412