The ghost effect in the continuum limit for a vapor-gas mixture around condensed phases: Asymptotic analysis of the Boltzmann equation

A binary mixture of a vapor and a noncondensable gas around arbitrarily sha ped condensed phases of the vapor is considered. Its steady behavior in the continuum limit (the limit where the Knudsen number vanishes) is investiga ted on the basis of kinetic theory in the case where the condensed phases a re at rest, and the mixture is in a state at rest with a uniform pressure a t infinity when an infinite domain is considered. A systematic asymptotic a nalysis of the Boltzmann equation with kinetic boundary condition is carrie d out for small Knudsen numbers, and the system of fluid-dynamic type equat ions and their appropriate boundary conditions that describes the behavior in the continuum limit is derived. The system shows that the flow of the mi xture vanishes in the continuum limit, but the vanishing flow gives a finit e effect on the behavior of the mixture in this limit. This is an example o f the ghost effect discovered recently by Sone and coworkers [e.g., Y. Sone ct al., Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gets Dyn amics, edited by C. Shen (Peking University Press, Beijing, 1997), p. 3]. I t is shown that there are several new source factors of the ghost effect th at are peculiar to a gas mixture, i.e., that originate from the nonuniformi ty of the concentration.