Universal Electrokinetic Mobility of Highly-Charged Particles of Arbitrary Shape, Size and Concentration

In the limit of thin double-layers and negligible surface conduction, Morrison showed the electrophoretic mobility of a uniformly-charged particle to depend only on its zeta potential ζ -- not on its shape, size, or even concentration. Finite surface conduction causes this argument to fail. We treat the opposite limit, wherein particles are so highly charged that surface conductivity dominates completely (Bikerman-Dukhin number Du→∞), and show their electrokinetic mobility to be again independent of shape, size or concentration. Significantly, our result holds for any mean-field model of the double-layer and for any `phoretic' forcing, including electrophoresis and diffusiophoresis. The (standard) Guoy-Chapman model gives a Du →∞ electrokinetic mobility of εln 4 k_BT/eη, independent even of ζ.