THE ELECTRIC-CONDUCTIVITY OF DILUTE SUSPENSIONS OF CHARGED POROUS SPHERES

The effective electric conductivity of a dilute suspension of polyelec trolyte molecules or charged flocs in an electrolyte solution is analy tically studied. The model used for the particles is a porous sphere i n which the density of hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The equations which gove rn the electrochemical potential distributions of ionic species and th e fluid flow field inside and outside a porous particle migrating in a n unbounded solution are linearized assuming that the system is only s lightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a porous sphere in a uniform appl ied electric field with the density of the fixed charges as the small perturbation parameter. An analytical expression for the effective con ductivity of a dilute suspension of identical charged porous spheres i s obtained from the average electric current density calculated using the solution of electrochemical potential distributions of the ions. T he result demonstrates that the presence of the fixed charges in the p orous particles can lead to an augmented or a diminished electric cond uctivity of the suspension relative to that of a corresponding suspens ion of uncharged porous particles, depending on the characteristics of the electrolyte solution and the suspending particles. When the anion ic and cationic diffusion coefficients of a symmetric electrolyte are the same, the correction for the effect of the fixed charges of the pa rticles on the electric conductivity of the suspension is proportional to the square of the fixed charge density. (C) 1997 Academic Press.