Symmetry properties of the electrophoretic motion of patterned colloidal particles

In sedimentation experiments at low Reynolds numbers there are general restrictions for the motion of particles. We show that some of them do not apply for electrophoresis in ionic solutions. In particular, we construct specific examples of objects with patterned shape and surface charge, that (1) undergo a permanent motion of rotation without translation, or (2) move perpendicularly to the applied electric field, whatever the direction of the latter. This demonstrates the broad spectrum of possible electrically induced motions, and could guide the design of microengines and the understanding of biological systems.