Influence of non-linear slip dependent zeta potential on the bi-layered electrohydrodynamic flow in an electrically actuated microsystem

Abstract

In this paper, the electro-osmotic flow (EOF) of two immiscible fluids through an electrically actuated micro-slit with a non-linear slip-dependent zeta potential is considered. The main objective of this work is to enhance the EOF velocity of non-polar fluid with an intensive flow variation in micro-confinements. We present the comparison between the Poisson–Nernst–Planck (P–N–P) and the Poisson–Boltzmann model and illustrate the impact of different parameters, such as Debye–Hückel parameter, slip coefficient, and interfacial potential drop, on the ionic concentration and the induced potential in detail. In this study, the interface between two immiscible fluids is considered to be planar, and a potential drop is observed close to the interface due to the development of back-to-back diffuse layers. At the interface between two layers, the continuity of the velocity and total stresses (Maxwell stress and shear stress) are taken into account to investigate the flow field in the system of immiscible electrolytes. The P–N–P model, linked with the ion transport equation and the Poisson equation, is employed to describe the motion of electrolyte solutions. The non-linear governing equations are numerically computed using a pressure-correction-based finite volume technique based on a staggered grid algorithm. Closed-form analytical solutions are derived for both steady and unsteady EOF field of two immiscible fluids for the low wall zeta potential and non-overlapping electrical double layer. The analytical solutions are well validated with our numerical results under suitable assumptions. It is also observed that the slip-dependent zeta potential successfully provides a considerable enhancement in EOF velocity over a broad range of parameters such as zeta potential, Debye–Hückel parameter, as well as boundary slip parameter. The results for both layers are highly affected by unequal wall potential, and the ion concentrations are highly actuated by the external electric field.