Electric conductivity of a suspension of charged colloidal spheres with thin but polarized double layers

An analytical study of the effective electric conductivity of a homogeneous suspension of identical, charged, spherical particles in the solution of a symmetrically charged electrolyte is presented. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between two neighboring particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. The effects of interactions among individual particles are taken into explicit account by employing a unit cell model that is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of electrochemical potential energies of ionic species are solved for each cell, in which a spherical particle is envisaged as surrounded by a concentric shell of the suspending fluid. Analytical expressions for the electric conductivity are obtained in closed form as functions of the volume fraction of the particles and other characteristics of the suspension. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The effects of particle interactions on the effective conductivity can be quite significant in general cases.