Kinetic Theory

The Chapman–Enskog Solution of the Transport Equation for Moderately Dense Gases

1st Edition - January 1, 1972
Author: S. G. Brush
Editor: D. ter Haar
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 4 5 8 5 - 3

Kinetic Theory, Volume 3: The Chapman-Enskog Solution of the Transport Equation for Moderately Dense Gases describes the Chapman-Enskog solution of the transport equation for… Read more

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Kinetic Theory, Volume 3: The Chapman-Enskog Solution of the Transport Equation for Moderately Dense Gases describes the Chapman-Enskog solution of the transport equation for moderately dense gases. Topics covered range from the propagation of sound in monatomic gases to the kinetic theory of simple and composite monatomic gases and generalizations of the theory to higher densities. The application of kinetic theory to the determination of intermolecular forces is also discussed. This volume is divided into two sections and begins with an introduction to the work of Hilbert, Chapman, and Enskog that led to the formulation of the Chapman-Enskog theory. The Chapman-Enskog results are then compared with those of earlier theories with respect to viscosity, heat conduction, diffusion, and thermal diffusion. Subsequent chapters focus on alternatives to the Chapman-Enskog method and some mathematical problems; foundations of the kinetic theory of gases; and kinetic theory of processes in dilute gases and of heat conduction, viscosity, and self-diffusion in compressed gases and liquids. This book should be of interest to graduate students and others undertaking research in kinetic theory.

Preface

Part 1

Chapter I The Work of Hilbert, Chapman, and Enskog

Hilbert

Enskog

Chapman

Chapman or Enskog

Chapter II Comparison of the Chapman-Enskog Results with those of Earlier Theories

Viscosity

Heat Conduction

Diffusion

Thermal Diffusion

Chapter III Application of Kinetic Theory to Determination of Intermolecular Forces

Lennard-Jones

The exp-6 Potential

Chapter IV Propagation of Sound in Monatomic Gases

The Newton-Laplace Theory

Early Kinetic-Theory Explanations of the Speed of Sound

Absorption and Dispersion

Applications of the Burnett Approximation

Recent Theories

Chapter V Alternatives to the Chapman-Enskog Method, and Mathematical Problems

Carleman's Results

Grad's Method

Results of Wild and Morgenstern

Ikenberry and Truesdell

Grad's Asymptotic Theory

Chapter VI Generalizations of the Kinetic Theory to Higher Densities

Early Results of Jager and Others

The BBGKY Equations

Correlation Formulas for Transport Coefficients

Transport Coefficients for the Dense Hard-Sphere Gas

Discovery of the Divergence

Bibliography

Part 2

1 Foundations of the Kinetic Theory of Gases (from Mathematische Annalen, 1912)

2 The Kinetic Theory of Simple and Composite Monatomic Gases: Viscosity, Thermal Conduction, and Diffusion (from Proceedings of the Royal Society of London, 1916-17)

Part I.—Outline of the Mathematical Method

Part II.—Application to the Theory of the Mean-Free-Path Phenomena

Part III.—Discussion of the Results in Various Special Cases

3 A Note on Thermal Diffusion (from Philosophical Magazine, 1917)

4 Kinetic Theory of Processes in Dilute Gases (Translated from Kinetische Theorie der Vorgange in massig verdunnten Gasen, 1917)

Introduction

I. Fundamentals

II. Processes in a Simple Gas

III. Processes in a Mixture of Two Diffusing Gases

IV. Numerical Results

V. Entropy and Entropy Transport to Second Approximation

VI. Calculation of Pressures to Third Approximation

Appendix

5 Kinetic Theory of Heat Conduction, Viscosity and Self-Diffusion in Compressed Gases and Liquids (Translated from Kungliga Svenska Vetenskapsakademiens Handlingar, 1922)

6 The Kinetic Theory of Gases Fifty Years Ago (from Lectures in Theoretical Physics, Boulder, 1966)

Index