On the simultaneous effects of gas rarefaction, wall porosity, and inertia in microchannel flows

Abstract

The superposition of two effects that cause the flow to slip over the walls of a microchannel: Gas rarefaction and wall porosity, is treated in the paper. At that, in order to account for moderately high values of the Reynolds number, observed in some experiments, the effect of inertia is included into the analysis as a second order effect. The approach is fully analytic and consists in the development of a simple perturbation scheme in which the Knudsen number plays the role of a unique small parameter. The obtained results are in qualitative agreement with experiments, and may be usefully applied for the design of aerostatic bearings in which a porous material is used as the flow restrictor.