Geometrical Performance of Self-Phoretic Colloids and Microswimmers

Within a unified formulation - encompassing self-electrophoresis, self-diffusiophoresis, and self-thermophoresis - we provide a simple integral kernel transforming the relevant surface flux to particle velocity for any spheroid with axisymmetric surface activity and uniform phoretic mobility. Appropriate scaling of the speed allows a dimensionless measure of the motion-producing performance of the motor shape and activity distribution across the surface. For bipartite designs with piecewise uniform flux over complementary surface regions, the performance is mapped out over the entire range of geometry (from discotic through spherical to rodlike shapes) and of bipartitioning, and intermediate aspect ratios that maximize performance are identified. Comparisons are made to experimental data from the literature.