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 δ 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 ζ 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(δ-1), the ζ potential becomes comparable to the thermal voltage, depending nonlinearly on δ and E. We obtain a uniform approximation for the ζ-potential distribution, valid for both moderate and strong fields; it holds even under intense fields, E≫δ-1, where it scales as log|E|. The induced-flow magnitude therefore undergoes a transition from an E2 dependence at moderate fields to an essentially linear variation with |E| at intense fields. Remarkably, surface conduction is negligible as long as E≪δ-2: the ζ 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.