Stokes flows past gaps in a wall

Abstract

This paper presents a conformal mapping approach to the study of planar Stokes flows near a wall with either one or two gaps. The technique reproduces, in a unified fashion, analytical solutions for various Stokes flows past a single gap in a wall found by previous authors using different methods. These include purely pressure-driven flows, shear flows and stagnation point flows near a gap in a wall. It is then shown how the conformal mapping method can be generalized to find new analytical solutions for the analogous flows when there are two gaps in the wall. Features of the new two-gap solutions are studied in detail.