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Self-propelled colloidal swimmers move by pushing the adjacent fluidbackwards. The resulting motion of an asymmetric body depends on the profile ofpushing velocity over its surface. We describe a method of predicting themotion arising from arbitrary velocity profiles over a given body shape, usinga discrete-source "stokeslet" representation. The net velocity and angularvelocity is a sum of contributions from each point on the surface. Thecontributions from a given point depend only on the shape. We give a numericalmethod to find these contributions in terms of the stokeslet positions definingthe shape. Each contribution is determined by linear operations on the Oseeninteraction matrix between pairs of stokeslets. We first adapt the LorentzReciprocal Theorem to discrete sources. We then use the theorem to implementthe method of Teubner[1] to determine electrophoretic mobilities ofnonuniformly charged bodies.

Adapting the Teubner reciprocal relations for stokeslet objects