The behavior of a gas in the continuum limit in the light of kinetic theory: The case of cylindrical Couette flows with evaporation and condensation

• Published in: Physics of fluids (1994) Vol. 8; no. 12; pp. 3403 - 3413
• Main Authors: Sone, Yoshio, Takata, Shigeru, Sugimoto, Hiroshi
• Format: Journal Article
• Language: English
• Published: 01.12.1996
• Subjects: Asymptotic stability; Boundary conditions; Boundary value problems; Condensation; Continuum mechanics; Evaporation; Fluid dynamics; Gases; Heat conduction; Heat convection; Kinetic theory; Navier Stokes equations
• ISSN: 1070-6631; 1089-7666; 1527-2435; 1089-7666
• DOI: 10.1063/1.869125

Cylindrical Couette flows of a rarefied gas between two concentric circular cylinders consisting of the condensed phase of the gas, where evaporation or condensation occurs, are considered on the basis of kinetic theory, with interest in the behavior of the gas in the continuum limit. The limiting solution is obtained by asymptotic analysis of the Boltzmann equation. In some range of the parameters of the problem, neither evaporation nor condensation occurs. The limiting solution in this case is different from the continuum solution (the conventional Couette flow without evaporation and condensation on the cylinders) and is subject to the effect of the flow that is induced if the effect of gas rarefaction is taken into account. This paradoxical result is confirmed by investigating the behavior of the numerical solution of the kinetic equation as the Knudsen number approaches zero.