  In a variety of physical situations, a bulk viscous flow is induced by a
distribution of surface velocities, for example in diffusiophoresis (as a
result of chemical gradients) and above carpets of cilia (as a result of
biological activity). When such boundary-driven flows are used to pump fluids,
the primary quantity of interest is the induced flow rate. In this letter we
propose a method, based on the reciprocal theorem of Stokes flows, to compute
the net flow rate for arbitrary flow distribution and periodic pump geometry
using solely stress information from a dual Poiseuille-like problem. After
deriving the general result we apply it to straight channels of triangular,
elliptic and rectangular geometries and quantify the relationship between bulk
motion and surface forcing.
