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Abstract: Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hooke’s law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method. [Copyright &y& Elsevier]

A rarefied gas flow thermally induced around a heated (or cooled) flat plate, contained in a vessel, is considered in two different situations: (i) both sides of the plate are simultaneously and uniformly heated (or cooled); and (ii) only one side of the plate is uniformly heated. The former is known as the thermal edge flow and the latter, typically observed in the Crookes radiometer, may be called the radiometric flow. The steady behaviour of the gas induced in the container is investigated on the basis of the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The flow features are clarified for a wide range of the Knudsen number, with a particular emphasis placed on the structural similarity between the two flows. The limiting behaviour of the flow as the Knudsen number tends to zero (and thus the system approaches the continuum limit) is investigated for both flows. The detailed structure of the normal stress on the plate as well as the cause of the radiometric force (the force acting on the plate from the hotter to the colder side) is also clarified for the present infinitely thin plate. [ABSTRACT FROM PUBLISHER]

A binary mixture of gases is confined in a gap between two coaxial circular cylinders rotating at different angular velocities. One of the component gases is the vapor of the substance that forms the cylinders, so that evaporation or condensation (or sublimation) of the vapor may take place on the surfaces of the cylinders. The other component is a noncondensable gas that neither evaporates nor condenses on the surfaces. Axisymmetric and axially uniform flows (the cylindrical Couette flow) of such a mixture are investigated on the basis of kinetic theory with special interest in the continuum (or fluid-dynamic) limit in which the Knudsen number goes to zero. The fluid-dynamic system that describes the behavior of the mixture is derived by a formal but systematic asymptotic analysis of the Boltzmann system. The resulting system shows some nontrivial phenomena such as the ghost effect and the flow bifurcation. These phenomena are also demonstrated by a Monte Carlo simulation for small Knudsen numbers using the Boltzmann equation. [ABSTRACT FROM AUTHOR]

This paper is the second part of the study of a steady flow of a vapor in a half space condensing onto a plane condensed phase of the vapor at incidence in the presence of a noncondensable gas near the condensed phase. The aim of the study is to clarify the behavior of the vapor and noncondensable gas on the basis of kinetic theory under the assumption that the molecules of the noncondensable gas are mechanically identical with those of the vapor. In the first part [S. Taguchi et al., Phys. Fluids 15, 689 (2003)], the case of subsonic condensation, where the Mach number corresponding to the flow-velocity component perpendicular to the condensed phase at infinity is less than unity, is considered. In the present second part, the case of supersonic condensation is investigated in detail on the same lines as the first part.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Steady flows of a vapor with evaporation and condensation on the boundary consisting of the condensed phase of the vapor are considered in the following situation: (i) the boundary is of arbitrary smooth shape; (ii) the Knudsen number Kn, the ratio of the typical mean free path of the vapor molecules to the characteristic length of the system, is small; (iii) a small amount of a noncondensable gas is contained in the system; more specifically, the amount is such that the average concentration of the noncondensable gas is of the order of Kn in the case of a closed domain (the case of an infinite domain is also discussed). The steady behavior of the vapor and the noncondensable gas, in particular, that in the continuum limit where Kn vanishes, is investigated by means of a systematic asymptotic analysis based on kinetic theory. In this situation, the average concentration of the noncondensable gas becomes infinitely small in the continuum limit in the case of a closed domain. However, it is shown that the noncondensable gas accumulates in the infinitely thin Knudsen layer on the boundary where condensation is taking place and has a significant effect on the global vapor flow in the continuum limit. An example demonstrating such an effect is also given. [Copyright &y& Elsevier]

A flow of a rarefied gas caused by a discontinuous wall temperature is investigated on the basis of kinetic theory in the following situation. The gas is confined in a two-dimensional square container, and the left and right halves of the wall of the container are kept at different uniform temperatures, so that the temperatures of the top and bottom walls are discontinuous at their respective middle points. External forces are assumed to be absent. The steady flow of the gas induced in the container by the effect of the discontinuities is analyzed numerically on the basis of the Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The features of the flow are clarified for a wide range of the Knudsen number. In particular, it is shown that, as the Knudsen number becomes small (i.e., as the system approaches the continuum limit), the maximum flow speed tends to approach a finite value, but the region with appreciable flow shrinks to the points of discontinuity; thus, the overall flow in the container vanishes nonuniformly in the continuum limit. The behavior of the molecular velocity distribution function is also investigated in detail. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]