Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory
Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory
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根据动力学理论，连续介质极限下蒸汽和不凝气体多组分混合物的两个表面问题
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
K. Aoki
中科院分区：
文献类型：
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作者：
S. Takata;K. Aoki
本文研究了在小Knudsen数，特别是连续极限（即，极限为克努森数消失），研究了在光动力学理论。通过对具有动力学边界条件的Boltzmann方程的系统渐近分析，证明了在连续极限下，由于凝结相的蒸发和凝结引起的流动为零，从而导出了描述该极限下流动行为的流体动力学型方程组及其边界条件。在此基础上，证明了在连续极限下，弱蒸发和凝结对混合物的影响是有限的。这是Sone及其同事最近发现的幽灵效应的一个例子[例如，Y. Sone等人，Phys. Fluids 8，628和3403（1996）; Y. Sone，在稀薄气体动力学中，由C. Shen（Peking U.P.，北京，1997年），第3页]。最后，对于蒸汽和不凝性气体的二元混合物的情况下，两个典型的问题，同时的质量和热量传递和平面Couette流，被认为是更具体地证明效果。结果还与用直接模拟Monte Carlo方法对Boltzmann方程进行数值分析所得的结果进行了比较。研究了小Knudsen数时，特别是在连续极限（即，极限为克努森数消失），研究了在光动力学理论。通过对具有动力学边界条件的Boltzmann方程的系统渐近分析，证明了在连续极限下，由于凝结相的蒸发和凝结引起的流动为零，从而导出了描述该极限下流动行为的流体动力学型方程组及其边界条件。在此基础上，证明了在连续极限下，弱蒸发和凝结对混合物的影响是有限的。这是Sone及其同事最近发现的幽灵效应的一个例子[例如，Y. Sone等人，Phys. Fluids 8，628和3403（1996）; Y. Sone，在稀薄气体动力学中，由C. Shen（Peking U.P.，北京，...
The steady behavior of a multicomponent mixture of vapors and noncondensable gases between two parallel plane condensed phases for small Knudsen numbers, especially for the continuum limit (i.e., the limit as the Knudsen number vanishes), is investigated in the light of kinetic theory. By a systematic asymptotic analysis of the Boltzmann equation with kinetic boundary conditions, the flow due to evaporation and condensation on the condensed phases is shown to vanish in the continuum limit, and then the system of fluid-dynamic-type equations and their boundary conditions which describes the behavior 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 the ghost effect discovered recently by Sone and co-workers [e.g., Y. Sone et al., Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gas Dynamics, edited 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 problems, the simultaneous mass and heat transfer and the plane Couette flow, are considered to demonstrate the effect more concretely. The result is also compared with that obtained by the numerical analysis of the Boltzmann equation by the direct simulation Monte Carlo method.The steady behavior of a multicomponent mixture of vapors and noncondensable gases between two parallel plane condensed phases for small Knudsen numbers, especially for the continuum limit (i.e., the limit as the Knudsen number vanishes), is investigated in the light of kinetic theory. By a systematic asymptotic analysis of the Boltzmann equation with kinetic boundary conditions, the flow due to evaporation and condensation on the condensed phases is shown to vanish in the continuum limit, and then the system of fluid-dynamic-type equations and their boundary conditions which describes the behavior 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 the ghost effect discovered recently by Sone and co-workers [e.g., Y. Sone et al., Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gas Dynamics, edited by C. Shen (Peking U.P., Beijing, ...