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Analytical Study of Bifurcation of a Flow of a Gas Between Coaxial Circular Cylinders with Evaporation and Condensation

Analytical Study of Bifurcation of a Flow of a Gas Between Coaxial Circular Cylinders with Evaporation and Condensation

University of Kyoto

Time-independent behavior of a gas between two coaxial 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 to the bifurcation of the flow. The problem is studied analytically for small values of the speed of rotation of the cylinders and Knudsen number on the basis of the Boltzmann equation, and the solution is obtained explicitly. The bifurcation of the 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 bifurcation diagram.