Electric Conductivity and Electrophoretic Mobility in Suspensions of Charged Porous Spheres

The electric conduction and electrophoresis of a suspension of charged porous spheres in an electrolyte solution with an arbitrary thickness of the electric double layers are analytically studied. The porous particle can be a solvent-permeable and ion-penetrable polyelectrolyte molecule or charged floc with uniformly distributed frictional segments and fixed charges. The effect of particle interactions is taken into account by employing a unit cell model, and the overlap of the electric double layers of adjacent particles is allowed. The electrokinetic equations, which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell, are linearized by assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the dimensionless density of the fixed charges as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of each charged porous sphere and for the effective electric conductivity of the suspension correct to the first and second orders, respectively, of the fixed charge density arc obtained in closed forms. The effect of particle interactions on the electrophoresis and electric conduction of the suspension can be significant in typical situations. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The dependence of the electrophoretic mobility and the electric conductivity on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.