Weak curvature asymptotics for Debye layers as electrohydrodynamic discontinuities.

Abstract

Important microfluidic phenomena, such as droplet deformation and cell motion, are impacted by the formation of Debye layers at charged interfaces. Previous studies examined interface problems with leaky dielectrics or the formation of diffuse charge layers. In most cases, the results are derived for weakly curved spherical geometries. Moreover, many studies of streaming-potential phenomena at fluid-solid interfaces lack a macroscale description of effects that are higher than first order. An asymptotic methodology capturing both complex surface geometries and an accurate description of higher-order phenomena is presented in this study. For this purpose, we consider a generic streaming-potential problem. As a result, the complex three-dimensional electrohydrodynamics in the Debye layer are entailed in two-dimensional discontinuity conditions. The latter contain a free parameter, the layer thickness, which mathematically represents the discontinuity position within the Debye layer. It can be used to derive an alternative definition of the Debye thickness capturing the influence of the ζ potential. We introduce a virtual particle whose outer boundary envelopes the solid particle plus a fraction of the Debye layer. It interacts with the macroscopic flow while incorporating the detailed electrohydrodynamics inside the layer.