Title Page	2
	Preface	7
	Contents	10
	Chapter 1 Basic Principles of the Kinetic Theory	15
	Introduction	15
	Molecular Structure of a Gas	21
	Basic Principles	21
	The Maxwellian Distribution Function	22
	Determination of the Characteristic Velocities	26
	Molecular Flux	28
	Elementary Theory of Transport Processes	30
	Characteristic Dimensions	34
	Potentials of Molecular Interactions	35
	Brownian Motion	37
	Dynamics of a Binary Collision	40
	Conservation Laws	40
	Asymptotic Post-Collisional Velocities	42
	Asymptotic Velocities for Gas Mixtures	43
	Scattering Angle ?	44
	Differential Cross Section	46
	Appendix	49
	Chapter 2 The Boltzmann Equation	50
	The Boltzmann Equation	50
	The BBGKY Hierarchy	55
	The Liouville Theorem	55
	Equations of the BBGKY Hierarchy	57
	The Boltzmann Equation	60
	The Transfer Equation	64
	Summational Invariants	66
	Macroscopic Description	69
	Moments of the Distribution Function	69
	Balance Equations for the Moments	71
	The Definition of Equilibrium	72
	The Maxwellian Distribution Function	72
	Equilibrium States	73
	Entropy and Entropy Flux	79
	The $H$-Theorem	82
	Interactions of Gas Molecules with Solid Surfaces	82
	Scattering Kernels	84
	The $H$-Theorem	89
	The Paradoxes of Loschmidt and Zermelo	90
	The Many Faces of Entropy	91
	Appendix	92
	Chapter 3 The Chapman–Enskog Method	94
	Thermodynamics of a Single Fluid	94
	Simplified Version of the Chapman–Enskog Method	96
	The Integral Equation	96
	Solution of the Integral Equation	99
	Constitutive Equations and Transport Coefficients	102
	Formal Version of the Chapman–Enskog Method	106
	The dimensionless Boltzmann Equation	106
	The Integral Equations	107
	The Second Approximation	109
	Expansion of the Scalar Coefficients A and B	111
	Transport Coefficients	114
	The BGK Model	117
	Appendix	120
	Chapter 4 Moment Methods	121
	Balance Equations	121
	Grad’s Distribution Function	122
	Grad’s Distribution from Entropy Maximization	125
	Determination of the Non-convective Fluxes, Production Terms, Entropy Density and Entropy Flux	126
	Field Equations	129
	The Method of Maxwell and Ikenberry–Truesdell	131
	Calculation of the Production Terms	131
	The Maxwellian Iteration	132
	The Chapman–Enskog–Grad Combined Method	134
	Non-inertial Reference Frames	137
	Objective Tensors	137
	The Boltzmann Equation in Non-inertial Reference Frames	140
	Frame Dependence of the Heat Flux Vector	142
	Appendix	144
	Chapter 5 Polyatomic Gases	145
	Some Properties of Polyatomic Gases	145
	Semi-classical Model	147
	Boltzmann and Transfer Equations	147
	Macroscopic Description	150
	The Equilibrium Distribution Function	152
	Equilibrium States	154
	The Non-equilibrium Distribution Function	155
	The Laws of Navier–Stokes and Fourier	157
	A Limiting Case	161
	Classical Model	163
	Basic Fields	163
	Boltzmann and Transfer Equations	164
	Transport Coefficients	167
	Rough Spherical Molecules	168
	Dynamics of a Binary Collision	169
	Transport Coefficients	171
	Appendix	175
	Chapter 6 Dense Gases	177
	The Thermal Equation of State	177
	The Van der Waals Equation	177
	The Virial Equation of State	181
	Enskog’s Dense Gas	183
	The Enskog’s Equation	183
	The Transfer Equation	184
	Macroscopic Description	185
	Determination of the Potential Contributions	186
	Equilibrium Constitutive Equations	188
	Determination of the Kinetic Contributions	189
	The Laws of Navier–Stokes and Fourier	191
	The Modified Enskog Equation	192
	Chapter 7 Granular Gases	197
	Dynamics of a Binary Collision	197
	The Boltzmann Equation	198
	Macroscopic Description of a Granular Gas	199
	The Chapman–Enskog Method	200
	Integral Equations	200
	First Approximation f$^(0)$	202
	Second Approximation f$^(1)$	205
	Constitutive Equations for the Pressure Tensor and the Heat Flux Vector	209
	Granular Gases of Rough Spherical Molecules	211
	Chapter 8 Mixtures of Monatomic Gases	215
	Boltzmann and Transfer Equations	215
	Macroscopic Description	216
	Thermodynamics of Fluid Mixtures	220
	The Equilibrium Distribution Function	222
	Equilibrium States	225
	Grad’s Distribution Function	227
	The Combined Chapman–Enskog–Grad Method	229
	The Navier–Stokes Law	230
	The Laws of Fick and Fourier	231
	Matrices as Functions of the Collision Integrals	235
	Binary Mixtures	238
	Coefficients of Shear Viscosity and Thermal Conductivity	238
	Coefficients of Diffusion and Thermal–Diffusion Ratio	240
	Coefficients for Some Intermolecular Potentials	241
	Appendix	243
	Chapter 9 Chemically Reacting Gas Mixtures	246
	Thermodynamics of Chemically Reacting Systems	246
	Extent of Reaction and Affinity	246
	Chemical Potentials	248
	The Law of Mass Action	249
	The Arrhenius Equation	251
	Boltzmann Equations	253
	Transfer and Balance Equations	255
	Models for Differential Cross Sections	260
	Equilibrium Distribution Function	261
	Transport Coefficients for $H2 + Cl HCl + H$	263
	Chapman–Enskog Method	263
	Transport Coefficients	268
	Quaternary Mixture H2, Cl, HCl, H	271
	Remarks on the Reactive Contributions to the Transport Coefficients	278
	Trend to Equilibrium of $H2 + Cl HCl + H$	279
	Determination of the Production Terms	279
	Constituents at Same Temperature	281
	The $H$-Theorem and the Tendency to Equilibrium	286
	Symmetric Reactions	291
	The Influence of the Heat of Reaction on Slow Reactions	292
	Chemical Reactions without Activation Energy	298
	Remarks on the Geometry of the Collisions	302
	Remarks on Inelastic Reactive Collisions	304
	References	308
	Index	309