Gas flows through constricted shallow micro-channels

Abstract

We study the viscous compressible flow through micro-channels of non-uniform cross-section. A lubrication approximation is applied to analyse the flow through shallow configurations whose gap width is small in comparison with the other characteristic dimensions. Focusing on channels with a symmetric constriction (or cavity) we obtain the solution to the problem by means of a Schwarz–Christoffel transformation. This analytic solution is verified by examining the convergence of numerical simulations with diminishing Reynolds number and gap width. Explicit closed-form expressions for the pressure-head and mass-flow-rate losses in terms of the geometrical parameters characterizing the constriction are presented and discussed in the context of experimental data existing in the literature.