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

Electrophoretic Mobility and Electric Conductivity of Salt-Free Suspensions of Charged Soft Particles

A unit cell model is employed to analyze the electrophoresis and electric conduction in a concentrated suspension of spherical charged soft particles (each is a hard core coated with a porous polyelectrolyte layer) in a salt-free medium. The linearized Poisson–Boltzmann equation applicable to a unit cell is solved for the equilibrium electrostatic potential distribution in the liquid solution containing the counterions only surrounding a soft particle. The counterionic continuity equation and modified Stokes/Brinkman equations are solved for the ionic electrochemical potential energy and fluid velocity distributions, respectively. Closed-form formulas for the electrophoretic mobility of the soft particles and effective electric conductivity of the suspension are derived, and the effect of particle interactions on these transport characteristics is interesting and significant. Same as the case in a suspension containing added electrolytes under the Debye–Hückel approximation, the scaled electrophoretic mobility in a salt-free suspension is an increasing function of the fixed charge density of the soft particles and decreases with increases in the core-to-particle radius ratio, ratio of the particle radius to the permeation length in the porous layer, and particle volume fraction, keeping the other parameters unchanged. The normalized effective electric conductivity of the salt-free suspension also increases with an increase in the fixed charge density and with a decrease in the core-to-particle radius ratio, but is not a monotonic function of the particle volume fraction.

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.