“Force-free” electrophoresis?

When a colloidal particle is exposed to an externally applied electric field, it acquires an electrophoretic velocity, resulting from fluid slip occurring across the Debye screening layer. When the field is uniformly applied, it is usually assumed that the net neutrality of the combined particle-layer system implies that the net electric force acting on it must vanish. This assumption of “force-free” phoretic motion has been employed extensively to describe electrophoresis in both unbounded and bounded fluid domains [J. L. Anderson, Annu. Rev. Fluid Mech. 21, 61 (1989)]. A careful inspection reveals here that this intuitive premise may fail when the fluid domain is bounded, in which case a nonzero electric force (resembling dielectrophoretic forces in nonuniformly applied fields) may actually exist. Such forces (represented via surface integrals of Maxwell stresses) result in particle motion above and beyond the one driven by the phoretic slip mechanism. A positive demonstration for the existence of a such a force is provided for a standard sphere-wall configuration, where the applied field acts parallel to the wall. In that scenario, particle motion consists of a (familiar) slip-driven contribution parallel to the wall, together with a superimposed force-driven drift away from the wall. An analogy with pressure forces occurring at incompressible and inviscid potential flows is presented.