Electrokinetic properties of suspensions of colloidal particles with thin, polarized double layers

Electrokinetic properties of concentrated colloidal dispersions of charged spherical particles are studied in the limit of thin, polarized double layers. In this limit the problem of multiparticle interactions is decoupled from the details of double layer dynamics, and the macroscopic properties depend on relatively few variables. The linearized equations for the fluid motion and ionic potentials are solved to determine conductivity, resistivity, and mobility of charged particles in random as well as ordered suspensions as a function of volume fraction c of particles and the surface conductivity K_s . The particle-interaction effects are shown to be relatively weak and insensitive to the details of the spatial arrangement of the particles. The analytic formulas for accurately predicting these properties for a wide range of values of c and K_s are given. Expressions for relating macroscopic electrokinetic properties, such as the electrophoretic mobility, electro-osmotic velocity, and conductivity, to the mobility and resistivity functions are also given. In addition, the results are also given for the effect of polydispersity, high-frequency dielectric dispersion, and the two-dimensional case of long aligned cylinders.