Start-Up of Electrokinetic Flow in a Fibrous Porous Medium

Abstract

The transient response of ionic solutions in the porous medium constructed by a homogeneous assemblage of parallel charged circular cylinders to the step application of an electric field and a pressure gradient in the axial direction is analyzed through the use of a unit cell model. By solving the Poisson–Boltzmann equation and modified Navier–Stokes equation applicable to the system, the electric potential distribution and time-evolving velocity profile in the fluid phase are determined for arbitrary electric double layer thickness and zeta potential associated with the dielectric cylinders. Results for the flow rate, electroosmotic velocity, and effective electric conductivity of the fluid are obtained as functions of the elapsed time and the porosity of the fibrous medium. The effects of the relevant parameters on the transient starting electrokinetic flow in the fiber array are significant and interesting. For a fibrous medium with smaller porosity, a much shorter elapsed time is needed for the fluid ...