Streaming Potential and Associated Electrokinetic Effects through a Channel Filled with Electrolyte Solution Surrounded by a Layer of Immiscible and Dielectric Liquid.

The present article deals with the streaming potential-mediated pressure-driven flow across a channel in which the electrolyte solution is surrounded by a layer of cell membrane. Such a membrane of a biological cell may be modeled as an immiscible and dielectric liquid, which may bear free lipid molecules or charged surfactants. The presence of such additional charged molecules may lead to formation of liquid-liquid interfacial charge. In addition, the dielectric gradient-mediated ion partitioning effect further plays an important role in two-phase electrokinetic motion. We aim to study the generation of streaming potential and electrokinetic conversion efficiency as well as associated electroviscous effect for the undertaken problem. The mathematical model is based on the Poisson-Boltzmann equation for electrostatic potential and the Stokes equation for fluid flow, and the problem is studied considering suitable interfacial conditions for the flow variables along the liquid-liquid interface. The explicit analytical results for velocity and streaming field, electrokinetic energy conversion efficiency, and the parameter indicating the electroviscous effect are derived under the Donnan limit and within the Debye-Hückel electrostatic framework. We further numerically calculated the aforementioned intrinsic electrokinetic parameter associated with the problem undertaken for a wide range of pertinent parameters. The results are illustrated to indicate the impact of pertinent parameters on the generation of the streaming potential and associated electrokinetic effects.