Cylindrical Couette flow of a vapor-gas mixture: Ghost effect and bifurcation in the continuum limit

Abstract

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 flowbifurcation. These phenomena are also demonstrated by a Monte Carlo simulation for small Knudsen numbers using the Boltzmann equation.