Symmetry Breaking in Induced-Charge Electrophoresis

The electrophoretic motion of a conducting particle, driven by an induced charge mechanism, is analyzed. The dependence of the motion upon particle shape is embodied in four tensorial coefficients that relate the particle velocities to the externally-applied electric field. Several families of particle shapes, whose members are unaffected by the applied field, are identified via use of symmetry arguments. Other particles translate and/or rotate in response to the imposed field, even if their net electric charge vanishes. The coefficients are represented as surface integrals of the electric potential over the particle boundary, thereby eliminating the need to solve the flow field.