THE GHOST EFFECT IN THE CONTINUUM LIMIT FOR A VAPOR–GAS MIXTURE AROUND CONDENSED PHASES: ASYMPTOTIC ANALYSIS OF THE BOLTZMANN EQUATION

Abstract

A binary mixture of a vapor and a noncondensable gas around arbitrarily shaped condensed phases of the vapor is considered. Its steady behavior in the continuum limit (the limit where the Knudsen number vanishes) is investigated on the basis of kinetic theory in the case where the condensed phases are at rest, and the mixture is in a state at rest with a uniform pressure at infinity when an infinite domain is considered. A systematic asymptotic analysis of the Boltzmann equation with kinetic boundary condition is carried out for small Knudsen numbers, and the system of fluid-dynamic type equations and their appropriate boundary conditions that describes the behavior in the continuum limit is derived. The system shows that the flow of the mixture vanishes in the continuum limit, but the vanishing flow gives a finite effect on the behavior of the mixture in this limit. This is an example of the ghost effect discovered recently by Sone and coworkers [e.g., Y. Sone et al., Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gas Dynamics, edited by C. Shen (Peking University Press, Beijing, 1997), p. 3]. It is shown that there are several new source factors of the ghost effect that are peculiar to a gas mixture, i.e., that originate from the nonuniformity of the concentration.

ACKNOWLEDGMENTS

The authors express their cordial thanks to Professor Yoshio Sone for his interest in the present work and valuable advice. The first author is also grateful to Professor François Golse for the discussion and valuable comments on the subject of Appendix 1. This work is partially supported by the grants-in-aid (No. 12750053 and No. 10045040) for Scientific Research from the Japan Society for the Promotion of Science.