Strong electro-osmotic flows about dielectric surfaces of zero surface charge

We analyze electro-osmotic flow about a dielectric solid of zero surface charge, using the prototypic configurations of a spherical particle and an infinite circular cylinder. We assume that the ratio delta of Debye width to particle size is asymptotically small, and consider the flow engendered by the application of a uniform electric field; the control parameter is E-the voltage drop on the particle (normalized by the thermal scale) associated with this field. For moderate fields, E = O(1), the induced zeta potential scales as the product of the applied-field magnitude and the Debye width; being small compared with the thermal voltage, its resolution requires addressing one higher asymptotic order than that resolved in the comparable analysis of electrophoresis of charged particles. For strong fields, E = O(delta(-1)), the zeta potential becomes comparable to the thermal voltage, depending nonlinearly on delta and E. We obtain a uniform approximation for the zeta-potential distribution, valid for both moderate and strong fields; it holds even under intense fields, E >> delta(-1), where it scales as log vertical bar E vertical bar. The induced-flow magnitude therefore undergoes a transition from an E-2 dependence at moderate fields to an essentially linear variation with vertical bar E vertical bar at intense fields. Remarkably, surface conduction is negligible as long as E << delta(-2): the zeta potential, albeit induced, remains mild even under intense fields. Thus, unlike the related problem of induced-charge flow about a perfect conductor, the theoretical velocity predictions in the present problem may actually be experimentally realized.