Electrokinetic flow and electric current in a fibrous porous medium

An analytical study is presented for the steady electrokinetic flow of electrolyte solutions in the fibrous medium constructed by an ordered array of identical, parallel, charged, circular cylinders. The electric field and/or pressure gradient are applied uniformly in the direction along the axes of the cylinders. The dielectric cylinders may have either a constant surface potential or a constant surface charge density of an arbitrary value. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model, which allows for the overlap of the double layers of adjacent cylinders, is employed to account for the effect of fiber interactions. The electrostatic potential distribution in the fluid phase is determined by solving the Poisson-Boltzmann equation, and the fluid velocity profile is obtained as the analytical solution of a modified Navier-Stokes equation. Explicit formulas for the flow rate, electroosmotic velocity, electric current, effective electric conductivity, and streaming potential are derived as functions of the porosity of the fiber matrix and other characteristics of the system. The effect of interactions among the cylinders on the fluid velocity and effective conductivity is interesting and can be significant under appropriate conditions.