Gas flow and heat transfer simulation in MEMS via a mesoscopic approach

Abstract

The flow problem of binary gaseous mixtures in rectangular micro channels due to small pressure, temperature and molar concentration gradients over the whole range of the Kn number is solved. The solution is based on a meso scale approach, formally described by two coupled kinetic equations, subject to diffuse boundary conditions. The model proposed by McCormack substitutes the complicated collision term and the resulting kinetic equations are solved by an accelerated version of the discrete velocity method. Typical results are presented for the flow rates and the heat fluxes of two different binary mixtures (He-Ar and Ne-Ar) in 2-D micro-channels of various concentration and aspect (height to width) ratios, for the whole range of rare-faction. The formulation is very efficient and can be implemented as an alternative to the classical method of solving the Navier-Stokes equations with slip boundary conditions, which in any case is restricted by the hydrodynamic regime, as well as to particle-based simulations, which often become computationally inefficient.