Elliptic function representation of doubly periodic two-dimensional Stokes flows

Abstract

We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find the mean flow through an arbitrary lattice in response to a pressure gradient in an arbitrary direction, and show in a typical example that the shorter of the two period lattice vectors is an "easy direction" for the flow, an eigenvector of the conductance tensor corresponding to maximal conductance.