Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics. Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid, as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.