Book contents
- Frontmatter
- Dedication
- Contents
- List of Figures
- List of Tables
- Acknowledgements
- Nomenclature
- 1 Introduction
- 2 The Boltzmann Equation 1: Fundamentals
- 3 The Boltzmann Equation 2: Fluid Dynamics
- 4 Transport in Dilute Gas Mixtures
- 5 The Dilute Lorentz Gas
- 6 Basic Tools of Nonequilibrium Statistical Mechanics
- 7 Enskog Theory: Dense Hard-Sphere Systems
- 8 The Boltzmann–Langevin Equation
- 9 Granular Gases
- 10 Quantum Gases
- 11 Cluster Expansions
- 12 Divergences, Resummations, and Logarithms
- 13 Long-Time Tails
- 14 Transport in Nonequilibrium Steady States
- 15 What’s Next
- Bibliography
- Index
7 - Enskog Theory: Dense Hard-Sphere Systems
Published online by Cambridge University Press: 18 June 2021
- Frontmatter
- Dedication
- Contents
- List of Figures
- List of Tables
- Acknowledgements
- Nomenclature
- 1 Introduction
- 2 The Boltzmann Equation 1: Fundamentals
- 3 The Boltzmann Equation 2: Fluid Dynamics
- 4 Transport in Dilute Gas Mixtures
- 5 The Dilute Lorentz Gas
- 6 Basic Tools of Nonequilibrium Statistical Mechanics
- 7 Enskog Theory: Dense Hard-Sphere Systems
- 8 The Boltzmann–Langevin Equation
- 9 Granular Gases
- 10 Quantum Gases
- 11 Cluster Expansions
- 12 Divergences, Resummations, and Logarithms
- 13 Long-Time Tails
- 14 Transport in Nonequilibrium Steady States
- 15 What’s Next
- Bibliography
- Index
Summary
The Enskog equation was the first extension of the Boltzmann transport equation to higher densities. It applies only to hard sphere systems and takes into account excluded volume and collisional transport effects. While useful for one component gases, it has serious shortcomings, in particular, for mixtures it leads to expressions for transport coefficients that are inconsistent with the general Onsager reciprocal relations and it has no H-theorem. The Revised Enskog equation is presented and shown to satisfy an H-theorem, and, for mixtures, to have transport coefficients that satisfy the Onsager relations. The revised equation describes spatio-temporal fluctuations in a hard sphere fluid about equilibrium. It 8 is possible to extend the Revised Enskog equation to high densities where hard sphere fluids form a crystal, and to show that this solid has transport properties appropriate for an elastic solid. Explicit expressions for the appropriate transport coefficients are given.
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- Contemporary Kinetic Theory of Matter , pp. 255 - 316Publisher: Cambridge University PressPrint publication year: 2021