Fluid Creep Effects on Near-Wall Solute Transport for Non-Isothermal Ampoules

There is a growing practical and theoretical interest in developing accurate macroscopic modelling for flows arising in chemical or physical vapor transport (VT) crystal growth experiments, including those conducted in reduced gravity environments. Rosner was the first person to point out that previously neglected rarefield gas dynamics phenomena (Stefan and bouyancy-driven flows) become rather important sources of convection. In particular, the combination of rarefaction and strong gradients of temperature (and/or concentration) tangential to the side-walls of the ampoule induces convective flows known as thermal (and concentration) 'creep' respectively. His order-of-magnitude estimates revealed that thermal creep effects can be non-negligible even at normal gravitational levels. On the macroscopic level, the bulk fluid mechanics can be adequately described by the familiar macroscopic equations as long as the boundary conditions are modified to account for the integrated effect of kinetic boundary layers adjacent to solid boundaries. Motivated by the growing importance of these phenomena, we have embarked on a series of computational studies to elucidate these fundamental creep-induced effects for a rarefied gas in simple, two-dimensional confined geometries. However, unlike previous related studies, we resort to a microscopic description of the gas, mathematically expressed by the Boltzmann integro-differential equation. We employ the direct simulation Monte Carlo (DSMC) method of Bird, the theoretical foundations and several practical applications. In the case of thermally induced flows, the no-time counter method of Bird is used, as implemented for a hard-sphere gas. The scheme has been also extended to account for realistic molecular interaction models, an extension necessary if the diffusion physics underlying concentration creep are to be captured.