Kremer G.M. An Introduction to the Boltzmann Equation and Transport Processes in Gases

Springer-Verlag Berlin Heidelberg, 2010. 328 p. ISSN: 1860-6245, e-ISSN: 1860-6253, ISBN: 978-3-642-11695-7, e-ISBN: 978-3-642-11696-4.This book deals with the classical kinetic theory of gases. Its aim is to present the basic principles of this theory within an elementary framework and from a more rigorous approach based on the Boltzmann equation. The subjects are presented in a self-contained manner such that the readers can understand and learn some methods used in the kinetic theory of gases in order to investigate the Boltzmann equation. This book can be useful as a textbook for students and researchers who are interested in the foundations of the Boltzmann equation and in the classical methods used in the kinetic theory for the determination of the transport coefficients of the gasesBasic Principles of the Kinetic TheoryMolecular Structure of a Gas
Basic Principles
The Maxwellian Distribution Function
Determination of the Characteristic Velocities
Molecular Flux
Elementary Theory of Transport Processes
Characteristic Dimensions
Potentials of Molecular Interactions
Brownian Motion
Dynamics of a Binary Collision
Conservation Laws
Asymptotic Post-Collisional Velocities
Asymptotic Velocities for Gas Mixtures
Scattering Angle χ
Differential Cross Section
Appendix
The Boltzmann Equation
The Boltzmann Equation
The BBGKY Hierarchy
The Liouville Theorem
Equationsof the BBGKY Hierarchy
The Boltzmann Equation
TheTransfer Equation
Summational Invariants
Macroscopic Description
Momentsof the Distribution Function
Balance Equations for the Moments
The Definition of Equilibrium
The Maxwellian Distribution Function
Equilibrium States
Entropy and Entropy Flux
The H-Theorem
Interactions of Gas Molecules with Solid Surfaces
Scattering Kernels
The H-Theorem
The Paradoxes of Loschmidtand Zermelo
The Many Facesof Entropy
Appendix
The Chapman–Enskog Method
Thermodynamics of a Single Fluid
Simplified Version of the Chapman–Enskog Method
The Integral Equation
Solution of the Integral Equation
Constitutive Equations and Transport Coefficients
Formal Version of the Chapman–Enskog Method
The dimensionless Boltzmann Equation
The Integral Equations
The Second Approximation
Expansion of the Scalar Coefficients A and B
Transport Coefficients
The BGK Model
Appendix
Moment Methods
Grad’s Moment Method
Balance Equations
Grad’s Distribution Function
Grad’s Distribution from Entropy Maximization
Determination of the Non-convective Fluxes,
Production Terms, Entropy Density and Entropy
Flux
FieldEquations
The Method of Maxwell and Ikenberry–Truesdell
Calculationof theProductionTerms
The Maxwellian Iteration
The Chapman–Enskog–Grad Combined Method
Non-inertialReference Frames
Objective Tensors
The Boltzmann Equation in Non-inertial Referenc Frames
Frame Dependence of the Heat Flux Vector
Appendix
Polyatomic Gases
Some Properties of Polyatomic Gases
Semi-classical Model
Boltzmann and Transfer Equations
Macroscopi cDescription
The Equilibrium Distribution Function
Equilibrium States
The Non-equilibrium Distribution Function
The LawsofNavier–Stokes and Fourier
ALimiting Case
Classical Model
BasicFields
Boltzmann and Transfer Equations
Transport Coefficients
Rough Spherical Molecules
Dynamics of a Binary Collision
Transport Coefficients
Appendix
Dense Gases
TheThermal Equation of State
The Vander Waals Equation
The Virial Equation of State
Enskog’s Dense Gas
The Enskog’s Equation
The Transfer Equation
Macroscopic Description
Determination of the Potential Contributions
Equilibrium Constitutive Equations
Determination of the Kinetic Contributions
The LawsofNavier–Stokes and Fourier
The Modified Enskog Equation
Granular Gases
Dynamics of a Binary Collision
The Boltzmann Equation
Macroscopic Description of a Granular Gas
The Chapman–Enskog Method
Integra lEquations
First Approximation f(0)
Second Approximation f(1)
Constitutive Equations for the Pressure Tensor and the Heat Flux Vector
Granular Gases of Rough Spherical Molecules
Mixtures of Monatomic Gases
Boltzmann andTransfer Equations
Macroscopic Description
Thermodynamics of Fluid Mixtures
The Equilibrium Distribution Function
Equilibrium States
Grad’s Distribution Function
The Combined Chapman–Enskog–Grad Method
The Navier–Stokes Law
The Laws of Fickand Fourier
Matrices as Functions of the Collision Integrals
Binary Mixtures
Coefficients of Shear Viscosity and Thermal Conductivity
Coefficients of Diffusion and Thermal–Diffusion Ratio
Coefficients for Some Intermolecular Potentials
Appendix
Chemically Reacting Gas Mixtures
Thermodynamics of Chemically Reacting Systems
Extent of Reaction and Affinity
Chemical Potentials
The Law o fMass Action
The Arrhenius Equation
Boltzmann Equations
Transfer and Balance Equations
Models for Differential Cross Sections
Equilibrium Distribution Function
Transport Coefficients for H2 + Cl HCl + H
Chapman–EnskogMethod
Transport Coefficients
Quaternary Mixture H2, Cl, HCl, H
Remarks on the Reactive Contributions to the TransportCoefficients
Trend to Equilibrium of H2 + Cl HCl + H
Determination of the Production Terms
ConstituentsatSameTemperature
The H-Theorem and the Tendency to Equilibrium
Symmetric Reactions
The Influence of the Heat of Reaction on Slow Reactions
Chemical Reactions without Activation Energy
Remarks on the Geometry of the Collisions
Remarks on Inelastic Reactive Collisions