potential but also the local ionic densities and fluid velocity. The effective electric conductivity of a dilute suspension of poly-That is, one must first solve a set of coupled electrokinetic electrolyte molecules or charged flocs in an electrolyte solution is equations to obtain the distributions of electric potential, analytically studied. The model used for the particles is a porous ionic concentrations and fluid velocity in the electrolyte solusphere in which the density of hydrodynamic frictional segments, tion, and then compute the average electric current and conand therefore also that of the fixed charges, is constant. The equaductivity in the suspension.
tions which govern the electrochemical potential distributions of Theoretical studies on the effective electric conductivity ionic species and the fluid flow field inside and outside a porous of a suspension of impermeable charged spheres have been particle migrating in an unbounded solution are linearized assummade by Saville (1) and O'Brien (2), assuming that the ing that the system is only slightly distorted from equilibrium.
Using a perturbation method, these linearized equations are solved particles and their electric double layers occupy only a small for a porous sphere in a uniform applied electric field with the fraction of the total volume. Approximate formulas for the density of the fixed charges as the small perturbation parameter. conductivity were obtained using a perturbation method for An analytical expression for the effective conductivity of a dilute particles with low z potential immersed in a symmetric elecsuspension of identical charged porous spheres is obtained from trolyte correct to O(z 2 ). Their results have some discrepancthe average electric current density calculated using the solution ies with the experimental data reported by Watillon and of electrochemical potential distributions of the ions. The result Stone-Masui (3), who measured the surface conductances demonstrates that the presence of the fixed charges in the porous of a number of monodisperse polystyrene latices over a range particles can lead to an augmented or a diminished electric conof particle volume fractions. Later, Saville (4) considered ductivity of the suspension relative to that of a corresponding the effects of added counterions produced by the particle suspension of uncharged porous particles, depending on the charcharging procedure and of nonspecific adsorption which alacteristics of the electrolyte solution and the suspending particles.
When the anionic and cationic diffusion coefficients of a symmet-ters the concentrations of ions in the solution outside the ric electrolyte are the same, the correction for the effect of the double layers, and obtained better agreement between theofixed charges of the particles on the electric conductivity of the ries and experiments.
suspension is proportional to the square of the fixed charge density.
The basic equations governing the electric conductivity α§ 1997 Academic Press of a dilute suspension of colloidal particles also describe the Key Words: polyelectrolyte particles; porous spheres; electric electrophoretic phenomena. O'Brien (5) derived the analyticonductivity; dilute suspensions. cal formulas for the electrophoretic mobility and the electric conductivity of a dilute suspension of dielectric spheres with thin but polarized double layers in a general electrolyte solu-