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.