Electric conductivity in a fibrous porous medium with thin but polarized double layers

Electroosmosis and Electric Conduction of Electrolyte Solutions in Charge-Regulating Fibrous Media

An analytical study of the electroosmosis and electric conduction of electrolyte solutions in a fibrous medium composed of parallel charge-regulating cylinders with arbitrary electric double layer thickness is presented. A linearized charge regulation model was adopted for the association and dissociation reactions occurring at the amphoteric functional groups over the surfaces of the cylinders, and a unit cell model was employed to accommodate interactions among the cylinders. The electrokinetic equations governing the ionic concentration, electric potential, and liquid flow fields were solved at low zeta potential for the cylinders. Explicit formulas for the electroosmotic mobility and effective electric conductivity in the fiber matrix were obtained. The results indicate that the charge regulation characteristics, such as the equilibrium constants of the reactions occurring at the cylinders’ surfaces and the bulk concentration of the charge-determining ions, influence the surface charge density and potential, electroosmotic mobility, and effective electric conductivity substantially.

Electrokinetic Flow of Salt-Free Solutions in a Fibrous Porous Medium

The electrokinetic flow of a salt-free solution in the fibrous porous medium constituted by an array of parallel charged circular cylinders subject to a pressure gradient and an electric field imposed in the axial direction is analytically studied via the use of a unit cell model. The Poisson-Boltzmann equation and modified Navier-Stokes equation applicable to a unit cell accommodating the salt-free solution around an individual cylinder are solved to determine the electric potential profile and fluid velocity distribution. Results of the electroosmotic velocity and effective electric conductivity in the fiber matrix are obtained as functions of the surface charge density of the dielectric cylinders and the porosity of the fiber matrix. The effects of the porosity or interactions among the cylinders on the electric potential distribution, electroosmotic velocity, and effective electric conductivity are significant and interesting under practical conditions. The apparent zeta potential, electroosmotic velocity, and effective electric conductivity increase monotonically with an increase in the surface charge density of the cylinders. When the porosity of the fiber matrix and surface charge density of the cylinders are high, the increases of the apparent zeta potential and electroosmotic velocity with the surface charge density are substantially suppressed due to the counterion condensation effect. However, this effect becomes weak when the porosity is low.

Electroosmotic velocity and electric conductivity in a fibrous porous medium in the transverse direction

The steady electroosmosis and electric conduction in a fibrous medium constructed by a homogeneous array of parallel, identical, charged, circular cylinders filled with an electrolyte solution is analytically examined. The imposed electric field is constant and normal to the axes of the cylinders. The electric double layer surrounding each dielectric cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model that allows for the overlap of the double layers of adjacent cylinders is employed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged cylinder in a cylindrical cell are linearized assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the cylinder as the small perturbation parameter. Analytical expressions for the electroosmotic velocity of the fluid solution and the effective electric conductivity in the array of cylinders are obtained in closed forms as functions of the porosity of the fiber matrix and other characteristics of the porous system. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The cell model predicts that, under otherwise identical conditions, the electric conductivity in a porous medium composed of an array of parallel cylinders in the transverse direction in general is smaller than that of a suspension of spheres, but there are some exceptions. The effect of interactions among the cylinders or spheres on the effective conductivity can be significant under appropriate conditions.