Sedimentation Velocity and Potential in a Suspension of Charge-Regulating Colloidal Spheres

Abstract

Body-force-driven migration in a homogeneous suspension of spherical charge-regulating particles with electrical double layers of arbitrary thickness is analyzed. The charge regulation due to association/dissociation reactions of functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface-charge density and the surface potential. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the equilibrium surface potential of the particle as the small perturbation parameter. Closed-form formulas for the settling velocity of the charge-regulating spheres and for the sedimentation potential in the suspension are derived. Our results show that the charge regulation effects on the sedimentation in a suspension appear starting from the leading order of the equilibrium surface potential, which is determined by the regulation characteristics of the suspension.