5R39. Kinetic Theory and Fluid Dynamics. - Y Sone (Kyoto Univ, 230-133 Iwakura-Nagatani-cho, Sakyo-ku Koyto, 606-0026, Japan). Birkhauser Boston, Cambridge MA. 2002. 353 pp. ISBN 0-8176-4284-6. \$69.95.

Reviewed by C Michaelis (Space, Mission Concept and Anal Group, Appl Phys Lab, Johns Hopkins Univ, 11100 Johns Hopkins Rd, Laurel MD 20723-6099).

Kinetic Theory and Fluid Dynamics provides a comprehensive description of the relationship between kinetic theory and continuum fluid dynamics. The author applies asymptotic analysis to the governing kinetic equations in the continuum limit in an attempt to bridge the gap between kinetic theory and continuum theory.

The author first derives the appropriate set of equations governing the flow in the form of a series expansion on Knudsen number. The Knudsen number is a measure of the degree of rarefaction in the flow, defined as the ratio of mean free path to some scale length. If the Knudsen number is very small, then the flow may be described as a continuum. The author then reduces the system of equations by applying limits for various applications, such as small Reynolds number, small temperature variations, etc. Finally, the appropriate kinetic theory-based boundary conditions are derived and applied. An extensive discussion of the Knudsen-layer, a region that extends a few mean free paths from a boundary, is given. It is shown that for weakly rarefied flows, continuum theory can be used with a modification of the boundary conditions to account for rarefaction effects.

The mathematical relationship between kinetic theory and continuum theory is studied by looking at several examples. The linear limit as the Reynolds number becomes small is explored. Generally, for all problems, the author discusses both the solid wall and gas phase/condensed phase interface boundary conditions. Several examples of rarefied flows induced by temperature fields are discussed. Such flows cannot be found in a gas in the continuum limit. By far the most interesting application discussed is the Knudsen compressor, a pumping system that is created by applying a temperature gradient across a pipe connecting two reservoirs. An extensive discussion of both optimal configurations and experimental set-ups is included.

The author discusses weakly nonlinear flows where the Reynolds number is finite and temperature variations are small. Nonlinear theory is explored by systematically eliminating restrictions on temperature variations, Mach number, and speed of evaporation and condensation. One of the thrusts of the author is his finding that classical gas dynamics is found to be incomplete in describing the behavior of a gas in the continuum limit. The book concludes with a discussion of bifurcation of cylindrical Couette flow with evaporation and condensation.

The author approaches the book from the point of view of applied mathematics. Heavy emphasis on mathematical derivations deducts from the overall readability of the book. The book would be more complete if it included physics-based discussion to support the mathematical analysis and augment the theory. Further, more illustrative figures should have been included to explain the problems of interest. The figure captions were not sufficient to understand many of the figures. The target audience for the book is scientists and mathematicians working in kinetic theory. Practicing engineers will find the book to be too mathematical to be useful. Graduate students should find this to be a useful reference for theoretical work. Kinetic Theory and Fluid Dynamics is an excellent compilation of Yoshio Sone’s lifetime works in kinetic theory and asymptotic methods. The book provides a comprehensive theoretical foundation for those interested in bridging kinetic and continuum theory.