Electrokinetic Effects on Pressure-Driven Liquid Flows in Rectangular Microchannels

Abstract

The effects of the electrical double layer near the solid-liquid interface and the induced electrokinetic field on the pressure-driven liquid flow through a rectangular microchannel are analyzed in this work. A nonlinear, two-dimensional Poisson–Boltzmann equation governing the electrical double layer field in the cross section of rectangular channels is numerically solved with the use of a finite-difference scheme. A body force caused by the electrical double field and the flow-induced electrokinetic field is considered in the equation of motion. An exact solution to this equation of motion in rectangular microchannels is obtained by employing the Green function formulation. The effects of the ionic concentration of the liquid, the zeta potential of the solid surface, and the size and the shape of microchannels on the fluid velocity distribution, streaming potential, volumetric flow rate, friction coefficient, and apparent viscosity are discussed. The results clearly show that for a liquid solution of low ionic concentration and a solid surface of high zeta potential the liquid flow in rectangular microchannels is significantly influenced by the presence of the electrical double layer field and hence deviates from the flow characteristics described by classical fluid mechanics.