Direct simulation of concentration creep in a binary gas-filled enclosure

Abstract

A Cartesian, two-dimensional enclosure containing an isothermal rarefied binary gas mixture is studied as a limiting-case model for actual crystal growth experiments conducted in reduced gravity environments. By employing a microscopic approach related to the Boltzmann equation, it is demonstrated that in the presence of appreciable partial concentration gradients a steady-state flow pattern develops, driven by kinetic boundary layers adjacent to solid boundaries. In contrast, a macroscopic analysis based on the continuum transport equations and the classical no-slip boundary condition would predict no flow whatsoever. For the case of equal mass species, the velocity scales involved are shown to increase with the disparity in accommodation coefficients, in agreement with expectations based on one-dimensional, linearized Knudsen sublayer theory, while quantitative comparison between simulations and the latter theory reveals significant confinement effects. Simulation of concentration creep in binary mixtures composed of disparate mass species requires an alternative computational procedure, motivated by surface recombination/dissociation reactions. For this case, flow fields and creep coefficient values for a range of mass ratios are also reported. It is concluded that future continuum-level modelling efforts should more fully exploit the detailed information now available from relevant microscopic simulations.