Analytical study of bifurcation of a flow of a gas between coaxial circular cylinders with evaporation and condensation

Abstract

Time-independent behavior of a gas between two coaxial circular cylinders made of the condensed phase of the gas, where the cylinders are rotating around their common axis and evaporation or condensation is taking place, is considered with special attention given to bifurcation of the flow. The problem is studied analytically for small values of the speeds of rotation of the cylinders and the Knudsen number on the basis of the Boltzmann equation, and the solution is obtained explicitly. The bifurcation of flow occurs even in a simple case where the gas is axially symmetric and uniform (or the flow field depends only on the radial coordinate). The comprehensive feature of the bifurcation of flow is clarified with the explicit forms of solutions and the bifurcation diagram.