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A vapor in a gap between two parallel plane surfaces of its condensed phase, on which evaporation or condensation may take place, is considered in the case where another gas that neither evaporates nor condenses on the surfaces (say, a noncondensable gas) is also contained in the gap. The steady flow of the vapor caused by evaporation on one surface and condensation on the other and the behavior of the noncondensable gas are investigated on the basis of kinetic theory. First, fundamental features of the flow field are clarified for small values of the Knudsen number (associated with vapor–vapor collisions) by a systematic asymptotic analysis of the Boltzmann equation. Then, the problem is analyzed numerically by means of the direct simulation Monte Carlo method, and the steady behavior of the vapor and of the noncondensable gas (e.g., the spatial distributions of the macroscopic quantities) is clarified for a wide range of the Knudsen number. In particular, it is shown that, in the limit as the Knudsen number tends to zero (the continuum limit with respect to the vapor), there are two different types of the limiting behavior depending on the amount of the noncondensable gas, and evaporation and condensation can take place only when the average density of the noncondensable gas is vanishingly small in comparison with that of the vapor.

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Articles you may be interested inNumerical analysis of the Poiseuille flow and the thermal transpiration of a rarefied gas through a pipe with a rectangular cross section based on the linearized Boltzmann equation for a hard sphere molecular gas J. Vac. Sci. Technol. A 28, 603 (2010); 10.1116/1.3449056 Temperature, pressure, and concentration jumps for a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation Phys. Fluids 18, 067102 (2006); 10.1063/1.2206220 Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation Phys. Fluids 17, 047105 (2005); 10.1063/1.1882252 Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall Diffusion slip for a binary mixture of hard-sphere molecular gases: Numerical analysis based on the linearized Boltzmann equation AIP Conf.The thermal-slip ͑thermal-creep͒ and the diffusion-slip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finite-difference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki ͓Phys. Fluids A 1, 363 ͑1989͔͒ for a single-component gas. As a result, the behavior of the mixture is clarified accurately not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, accurate formulas of the thermal-slip and the diffusion-slip coefficients for arbitrary values of the concentration of a component gas are constructed by the use of the Chebyshev polynomial approximation.

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