Abstract
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.
Highlights
When charged particles are suspended in an ionic solution and subjected to an external electric field, both the particles and their neighboring ions move owing to electrophoresis and electric migration, respectively
The electrophoresis and electric conduction of dilute salt-free suspensions of charged hard and soft spheres were analyzed by Ohshima [20,21,22] using a unit cell model and the electrophoretic mobility and electric conductivity in the suspensions are found to be proportional to the fixed charges of the particles when these charges are lower than some critical values, but approach constants due to the effect of counterion condensation around the fixed charges when they are higher than the critical values
The equilibrium electrostatic potential distribution ψeq (r ) inside a unit cell for a suspension of charged soft spheres in a salt-free solution is given by Equations (5) and (6)
Summary
When charged particles are suspended in an ionic solution and subjected to an external electric field, both the particles and their neighboring ions move owing to electrophoresis and electric migration (together with diffusion), respectively. The electrophoresis and electric conduction of dilute salt-free suspensions of charged hard and soft spheres were analyzed by Ohshima [20,21,22] using a unit cell model and the electrophoretic mobility and electric conductivity in the suspensions are found to be proportional to the fixed charges of the particles (and coincide with those in salt-containing suspensions) when these charges are lower than some critical values, but approach constants due to the effect of counterion condensation around the fixed charges when they are higher than the critical values. Carrique et al [23] numerically solved for the electrophoretic mobility and electric conductivity of concentrated salt-free suspensions of hard spherical particles via the unit cell model and confirmed the effect of counterion condensation at high surface charge density of the particles. (47), respectively, in terms of the dimensionless fixed charge density and concentration of the particles and other relevant parameters
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