Shear driven micro-flows of gaseous mixtures

Abstract

A mesoscale kinetic-type approach is proposed to solve shear driven micro flows of binary gas mixtures in MEMS. The coupled linear integral-differential equations, which formally describe the flow, are solved using the discrete velocity method. The complicated collision integral term is approximated by the McCormack model. The proposed approach is applied in one and two dimensions, solving the Couette and the driven cavity problems respectively, for two binary gas mixtures (Ne-Ar and He-Xe). Numerical results are presented for a wide range of the rarefaction and for various molar concentrations. It is demonstrated that the formulation is very efficient and can be implemented as an alternative to classical approaches, such as Navier Stokes solvers with slip boundary conditions.