  Among the few methods which have been proposed to create small-scale
swimmers, those relying on self-phoretic mechanisms present an interesting
design challenge in that chemical gradients are required to generate net
propulsion. Building on recent work, we propose that asymmetries in geometry
are sufficient to induce chemical gradients and swimming. We illustrate this
idea using two different calculations. We first calculate exactly the
self-propulsion speed of a system composed of two spheres of unequal sizes but
identically chemically homogeneous. We then consider arbitrary,
small-amplitude, shape deformations of a chemically-homogeneous sphere, and
calculate asymptotically the self-propulsion velocity induced by the shape
asymmetries. Our results demonstrate how geometric asymmetries can be tuned to
induce large locomotion speeds without the need of chemical patterning.
