Developing pressure-driven liquid flow in microchannels under the electrokinetic effect

A mathematical model is developed to study the electrokinetic effect on liquid developing flow in a parallel slit including the general Nernst–Planck equation describing anion and cation distributions, the Poisson equation determining the electrical potential profile, and the modified Navier–Stokes equation governing the velocity flow field. Since these three equations are coupled, a numerical scheme based on the finite volume method is utilized to iteratively solve the proposed model. A new expression for the streaming potential in the case of the developing flow status is derived. The characteristics of the pressure-driven flow in the presence of the electrokinetic effect are examined.