Theoretical analysis of Stokes flow through a sharp-cornered cross-slot

We consider the flow of a viscous fluid through a two-dimensional symmetric cross-slot geometry with sharp corners. The problem is analysed using the unified transform method in the complex plane, providing a quasi-analytical solution that can be used to compute all the physical quantities of interest. This study is a novel application of this method to a complicated geometry featuring multiple sharp corner singularities and multiple inlets and outlets. Our approach offers the advantage of resolving unbounded domains, as well as providing quantities of interest, such as the velocity and stress profiles, and the Couette pressure correction, from the solution of low-order linear systems. Our results agree well with the existing literature, which has largely used truncated bounded geometries with rounded or curved corners.