Self-electrophoresis of spheroidal electrocatalytic swimmers

Using the method of matched asymptotic expansions, we derive a general expression for the speed of a prolate spheroidal electrocatalytic nanomotor in terms of interfacial potential and physical properties of the motor environment in the limit of small Debye length and Péclet number. This greatly increases the range of geometries that can be handled without resorting to numerical simulations, since a wide range of shapes from spherical to needle-like, and in particular the common cylindrical shape, can be well-approximated by prolate spheroids. For piecewise-uniform distribution of surface cation flux with fixed average absolute value, the mobility of a prolate spheroidal motor with a symmetric cation source/sink configuration is a monotonically decreasing function of eccentricity. A prolate spheroidal motor with an asymmetric sink/source configuration moves faster than its symmetric counterpart and can exhibit a non-monotonic dependence of motor speed on eccentricity for a highly asymmetric design.