Effect of Ionic Advection on Electroosmosis over Charge Modulated Surfaces: Beyond the Weak Field Limit

Abstract

The present study deals with the effect of ionic advection on electroosmotic flow over charge modulated surfaces in a generalized paradigm when the classically restrictive "weak field" limit may be relaxed. Going beyond the commonly portrayed weak field limit (i.e, the externally applied electric field is over-weighed by the surface-induced electrical potential, towards charge distribution in an electrified wall-adhering layer) for electroosmotic transport, we numerically solve the coupled full set of Poisson-Nernst-Planck (PNP) and Navier-Stokes equations, in a semi-infinite domain, bounded at the bottom by a charged wall. Further, in an effort to obtain deeper physical insight, we solve the simplified forms of the relevant governing equations for low surface potential in two separate asymptotic limits: (i) a regular perturbation solution for Low Ionic Peclet number (Pe), where Pe is employed as the gauge function and (ii) a matched asymptotic solution for O(1) Pe in the Thin Electric Double Layer (EDL) limit. We demonstrate that reasonably good agreement is observed between the analytical and numerical solutions. Our analysis reveals that the primary effect of Pe on the flow is to slow down the "free stream velocity", adding to the periodicity of the flow, while it also induces significant changes in the overall potential. We further show that the electrical double layer thickness strongly dictates the "free stream velocity", and a simple Smoluchowski type of slip boundary condition cannot be used, if the effect of advection is taken into account. These results can be of significant importance in designing microfluidic and nanofluidic systems with surface charge modulation.