Stokes flow through a two-dimensional channel with a linear expansion

Abstract

Summary Motivated by various applications in microfluidics, we consider low-Reynolds-number flow in a two-dimensional channel with different widths in the upstream and downstream directions. The channel geometry consists of a polygonal domain with angled edges at transition points. The polygonal nature of the geometry makes it amenable to analysis via the Unified Transform Method, providing quasi-analytical solutions which can be used to compute all the physical quantities of interest. We compute the pressure drop between the ends of the expansion or constriction region as a function of the channel width ratio and the orientation of the angled edges and compare our results to extended lubrication theory.