Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory

The steady behavior of a multicomponent mixture of vapors and noncondensabl e gases between two parallel plane condensed phases for small Knudsen numbe rs, especially for the continuum limit (i.e., the limit as the Knudsen numb er vanishes), is investigated in the light of kinetic theory. By a systemat ic asymptotic analysis of the Boltzmann equation with kinetic boundary cond itions, the flow due to evaporation and condensation on the condensed phase s is shown to vanish in the continuum limit, and then the system of fluid-d ynamic-type equations and their boundary conditions which describes the beh avior in the limit is derived. On the basis of the system, it is shown that the vanishingly weak evaporation and condensation give a finite effect on the behavior of the mixture in the continuum limit. This is an example of t he ghost effect discovered recently by Sone and co-workers [e.g., Y. Sone , Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gas Dynamics, ed ited by C. Shen (Peking U.P., Beijing, 1997), p. 3]. Finally, for the case of a binary mixture of a vapor and a noncondensable gas, two typical proble ms, the simultaneous mass and heat transfer and the plane Couette flow, are considered to demonstrate the effect more concretely. The result is also c ompared with that obtained by the numerical analysis of the Boltzmann equat ion by the direct simulation Monte Carlo method. (C) 1999 American Institut e of Physics. [S1070-6631(99)00909-5].