Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles

The electrophoretic mobility of spherical soft particles in concentrated colloidal suspensions is numerically calculated. The particle is modeled as a hard core coated with an ion-penetrable membrane bearing a uniform distribution of fixed charges, while the high particle concentration is taken into account by means of a cell model. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as particle concentration, membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of ionic species, electrolyte concentration, etc. The theoretical model used is similar to the one presented by Ohshima [H. Ohshima, J. Colloid Interface Sci. 225 (2000) 233], except for the use of the Shilov-Zharkikh, rather than the Levine-Neale, boundary condition for the electric potential, and the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle [J.J. López-García, C. Grosse, J. Horno, J. Colloid Interface Sci. 265 (2003) 327]. The obtained results only coincide with existing analytical expressions for low particle concentrations, low particle charge, and when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high. This suggests that most interpretations of the electrophoretic mobility of soft particles in concentrated suspensions require numerical calculations.