Primary electroviscous effect in a moderately concentrated suspension of charged spherical colloidal particles

On the basis of the standard theory of the primary electroviscous effect in a moderately concentrated suspension of charged spherical particles in an electrolyte solution presented by Ruiz-Reina et al. (Ruiz-Reina, E.; Carrique, F.; Rubio-Hernandez, F. J.; Gomez-Merino, A. I.; Garcia-Sanchez, P. J. Phys. Chem. B 2003, 107, 9528), which is applicable for the case where overlapping of the electrical double layers of adjacent particles can be neglected, the general expression for the effective viscosity or the primary electroviscous coefficient p of the suspension is derived. This expression is applicable for a suspension of spherical particles of radius a carrying arbitrary zeta potentials at the particle volume fraction phi <= 0.3 for the case of nonoverlapping double layers, that is, at kappa a > 10 (where K is the Debye-Huckel parameter). A simple approximate analytic expression for p applicable for particles with large kappa a and arbitrary is presented. The obtained viscosity expression is a good approximation for moderately concentrated suspensions of the particle volume fraction phi <= 0.3, where the relative error is negligible for kappa a >= 100 and even at kappa a = 50 the maximum error is similar to 20%. It is shown that a maximum of p, which appears when plotted as a function of the particle zeta potential, is due to the relaxation effect as in the case of the electrophoresis problem.