Slow flows of a vapor-gas mixture with large density and temperature variations in the near-continuum regime

Abstract

A binary mixture of a vapor and a noncondensable gas in contact with the boundary made of the condensed phase (liquid or solid) of the vapor is considered in the following situation: the amount of the noncondensable gas contained in the system is of the same order of magnitude as that of the vapor; the temperature variation along the boundary may be large; the boundary is at rest, and there is no flow at infinity when an infinite domain is considered; and the Knudsen number is small (i.e., near-continuum regime). Slow steady flows (with Mach number of the order of Knudsen number, or equivalently, with Reynolds number of the order of unity) of the mixture, mainly caused by evaporation and condensation of the vapor on the boundary, are investigated on the basis of kinetic theory. The basic system used in this work is the fluid-dynamic-type system that was derived systematically from the Boltzmann system in a previous paper [S. Takata and K. Aoki, Transp. Theor. Stat. Phys. 30, 205 (2001); erratum, Transp. Theor. Stat. Phys. 31, 289 (2002)] in connection with the ghost effect, and it is solved numerically by a finite-volume method. Some additional computation using the direct simulation Monte Carlo method, based on the original Boltzmann system, is also performed for comparison. The behavior of the mixture in the continuum limit in which the Knudsen number vanishes is discussed with special interest in the ghost effect.