Analytical Methods for Problems of Molecular Transport

ISBN-13: 9781402058646 / Angielski / Twarda / 2007 / 409 str.

I. N. Ivchenko; S. K Loyalka

Opis

The transport of a given species (atoms, molecules, neutrons, photons, etc. ), either through its own kind or through some other host medium, is a problem of considerable interest. Practical applications may be found in many technologically and environmentally relevant areas such as the transport of neutrons in a nuclear power reactor or in a nuclear weapon, the transport of ions and electrons in plasma, the transport of photons which constitutes radiative heat transfer in various industrial, environmental and space applications, the transport of atoms or molecules of one species either through itself or as one component of a multi-component gas mixture, and the interactions of such gas mixtures with various solid and liquid surfaces such as one might find associated with capillary tubes, aerosol particles, interstellar dust grains, etc. . These application areas are obviously quite broad and it is readily apparent that there are, indeed, few scientific activities that do not require some level of understanding of transport processes. One of the most important and influential texts in the area of transport theory has been The Mathematical Theory of Non-Uniform Gases by Sidney Chapman and T. G. Cowling that was first printed in 1939. This book, along with several other more recent texts (Hirschfelder, J. O., Curtiss, C. F. and Bird, R. B., Molecular Theory of Gases and Liquids, John Wiley and Sons, NY, 1954; Kogan, M. N.

Recenzje

From the reviews:

"The aim of the present work is to present a concise ... introduction to the field of transport theory with a fairly tight focus on a few recently successful analytical solution techniques. ... the book is useful as a reference for scientists and engineers working in the fields of rarefied gas dynamics and aerosol mechanics, of working in any applied discipline in which gas-surface interactions can be expected to play a significant role." (Claudia-Veronika Meister, Zentralblatt MATH, Vol. 1141, 2008)

Spis treści

Contents; Table of Tables; Table of Figures; Preface; Acknowledgments;

Chapter 1. The General Description of a Rarefied Gas: 1. Some Introductory Remarks; 2. Density and Mean Motion; 3. The Distribution Function of Molecular Velocities; 4. Mean Values ofFunctions of Molecular Velocities; 5. Transport of Molecular Properties; 6. The Pressure Tensor; 7. The Hydrostatic Pressure; 8. The Amount of Heat; 9. The Kinetic Temperature; 10. The Equation of State for a Perfect Gas; 11. The Thermal Flux Vector; 12. Summary; Problems; References;

Chapter 2. The Boltzmann Equation; 1. Derivation of the Boltzmann Equation; 2. The Moment Equations; 3. Another Form of the Moment Equations; 4. The Equations for a Continuum Medium; 5. Molecular Encounters; 6. The Relative Motion of Two Molecules; Problems; References;

Chapter 3. The Collision Operator; 1. The Differential and Total Scattering Cross Sections; 2. The Statistics of Molecular Encounters; 3. The Transformation of Some Integrals; Problems; References;

Chapter 4. The Uniform Steady-State of a Gas; 1. The Boltzmann H-Theorem; 2. The Maxwellian Velocity Distribution; 3. The Mean Free Path of a Molecule; Problems; References;

Chapter 5. The Non-Uniform State for a Simple Gas; 1. Expansion in Powers of a Small Parameter; 2. The First Approximation; 3. A General Formal Solution for the Second Correction; 4. The Transformation of the Non-Homogeneous Term; 5. The Second Approximation; 6. The First-Order Chapman-Enskog Solution for Thermal Conduction; 7. The First-Order Chapman-Enskog Solution for Viscosity; 8. The Thermal Conductivity and Viscosity Coefficients; 9. The First-Order Approximation for Arbitrary Intermolecular Potential; 10. The Second-Order Approximation for Arbitrary Intermolecular Potential; Problems; References;

Chapter 6. Regimes of Rarefied Gas Flows; 1. The Knudsen Number; 2. A General Analysis of the Different Gas Flow Regimes; 3. The Boundary Conditions; 4. The Boundary Dispersion Kernel; 5. Features of the Boundary Conditions for Small Knudsen number; Problems; References;

Chapter 7. The Free-Molecular Regime; 1. The Free-Molecular Distribution Function; 2. The Force on a Particle in a Uniform Gas Flow; 3. Calculation ofMacroscopic Values in the Free-Molecular Regime; 4. Thermophoresis of Particles in the Free-Molecular Regime; 5. Condensation on a Spherical Droplet; 6. Non-Stationary Gas Flows; Problems; References; 

Chapter 8. Methods of Solution of Planar Problems; 1. Maxwell’s Method; 2. Loyalka's Method; 3. The Half-Range Moment Method; 4. Features of the Boundary Conditions for the Moment Equations; 5. Solution of the Thermal-Creep Problem by the Half-Range Moment Method; 6. Influence of the Boundary Models on the Thermal-Creep Coefficient; Problems; References;

Chapter 9. The Variational Method for the Planar Geometry; 1. Another Form of the Boltzmann Equation; 2. The Variational Technique for the Slip-Flow Problem; 3. Discussion of the Slip-Flow Results; 4. The Variational Solution for the Thermal-Creep Problem; 5. Discussion of the Thermal-Creep Results; 6. Slip-Flow and Temperature-jump Coefficients for the Lennard-Jones (6-12); Potential Model; Problems; References;

Chapter 10. The Slip-Flow Regime; 1. Basic Equations; 2. The Spherical Drag Problem; 3. The Thermal Force Problem; Problems; References;

Chapter 11. Boundary Value Problems for All Knudsen Numbers; 1. The Moment Equations in Arbitrary Curvilinear Coordinates; 2. The Two-Sided Maxwellian Distribution Functions; 3. Moments of Discontinuous Distribution Functions; 4. Analytical Expressions for the Bracket Integrals; 5. Boundary Conditions for Moment Equations; 6. Thermal Conduction from a Heated Sphere; 7. Method of the ‘Smoothed’ Distribution Function; 8. The Polynomial Expansion Method; 9. Solution of One Classic Transport Problem. 10. A Simplification of Moment Systems for Curvilinear Problems. 11. The Torque Problem; Problems; References;

Chapter 12. Boundary Slip Phenomena in a Binary Gas Mixture; 1. The First-Order Chapman-Enskog Approximation for a Binary Gas Mixture; 2. The Transport Coefficients for a Binary Gas Mixture; 3. The Second-Order Chapman-Enskog Approximation for a Binary Gas Mixture; 4. Analytical Methods of Solution for Planar Boundary Value Problems Involving Binary Gas Mixtures; 5. The Slip Coefficients for a Binary Gas Mixture; 6. Discussion of the Slip Coefficient Results; Problems; References;

Appendix 1. Bracket Integrals for the Planar Geometry; 1. Bracket Integrals Involving Two Sonine Polynomials; 2. Bracket Integrals Containing Several Components of Molecular Velocity; 3. Bracket Integrals Containing Two Discontinuous Functions; 4. Bracket Integrals Containing One Discontinuous Function; References;

Appendix 2. Bracket Integrals for Curvilinear Geometries; 1. The Special Function of the First Kind for the Spherical Geometry; 2. The Special Function of the Second Kind for the Spherical Geometry; 3. The Special Function of the First Kind for the Cylindrical Geometry; 4. The Special Function ofthe Second Kind for the Cylindrical Geometry; 5. Approximate Expressions for the Special Functions; References;

Appendix 3. Bracket Integrals for Polynomial Expansion Method; 1. Calculation of the Bracket Integrals of the First Kind; 2. Analytical Expressions for the Bracket Integrals of the Second Kind; References;

Appendix 4. The Variational Principle for Planar Problems; 1. Some Definitions and Properties for Integral Operators; 2. The Variational Principle; References;

Appendix 5. Some Definite Integrals; 1. Some Frequently Encountered Integrals; 2. Some Integrals Encountered in Boundary Problems; 3. Some Integrals Connected with the Second-Order Chapman-Enskog Solution; 4. Some Integrals Connected with Non-Linear Transport Problems;

Appendix 6. Omega-Integrals for Second-Order Approximation;

References; Author Index ; Subject Index