Electric conductivity of a dilute suspension of charged composite spheres

An analytical study of the effective electric conductivity of a dilute suspension of charged composite particles, each composed of a solid core and a surrounding porous shell, in an electrolyte solution is presented. The model used for the porous shell of each composite particle is a solvent-permeable and ion-penetrable surface layer in which the density of hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The equations which govern the electrochemical potential distributions of ionic species and the fluid flow field inside and outside the surface layer of a composite particle migrating in an unbounded solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a composite sphere in a uniform applied electric field with the charge densities of the rigid core surface and of the porous surface layer as the small perturbation parameters. An analytical expression for the effective conductivity of a dilute suspension of identical charged composite spheres is obtained from the average electric current density calculated using the solution of electrochemical potential distributions of the ions. The results demonstrate that the presence of the fixed charges in the composite particles can lead to an augmented or a diminished electric conductivity of the suspension relative to that of a corresponding suspension of uncharged composite particles, depending on the characteristics of the electrolyte solution and the suspending particles. In the limiting cases, the analytical solutions describing the effective electric conductivity of a dilute suspension of charged composite spheres reduce to those of dilute suspensions of charged solid spheres and of charged porous spheres.