Ewald summing irreducible components of flow around active particles

Abstract

We present a method to compute the Ewald summation for the irreducible components of flow around active particles to study hydrodynamic interactions in active colloidal suspensions. An active particle is modeled as a colloidal sphere with a surface slip velocity. Using this model, we obtain an irreducible representation of the fluid flow produced by an active particle in the periodic geometry of Stokes flow for an arbitrary surface slip. The solution of the active flow is obtained in terms of the lattice sum of the Oseen tensor and its derivatives. The lattice sum is accelerated using the Ewald summation technique. We apply the method to compute explicit expressions for the rigid body motion of hydrodynamically interacting active particles. Our method presents a way for the dynamic simulation of active particles due to arbitrary modes of active slip in the periodic geometry of Stokes flow.