Squirmers with arbitrary shape and slip: modeling, simulation, and optimization*

We consider arbitrary-shaped microswimmers of spherical topology and propose a framework for expressing their slip velocity in terms of tangential basis functions defined on the boundary of the swimmer. Given a microswimmer shape, we solve six Dirichlet boundary value problems and, exploiting the reciprocal theorem, show that their solution can be used to construct rigid body velocities for any prescribed time-independent slip profile. Moreover, we derive an analytical expression for the periodic motion of an isolated microswimmer suspended in free space. For a given swimmer shape, we then investigate which slip profile maximizes swimming efficiency. A six-dimensional eigenvalue problem is shown to encode the solution to this optimization problem, which can be solved easily. We showcase and analyze the slip profiles thus obtained for various shape families.