Sedimentation velocity and potential in a suspension of charge-regulating colloidal spheres

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 reaction s of functional groups on the particle surface is approximated by a lineari zed regulation model, which specifies a linear relationship between the sur face-charge density and the surface potential. The effects of particle inte ractions are taken into account by employing a unit cell model. The overlap of the double layers of adjacent particles is allowed and the relaxation e ffect in the double layer surrounding each particle is considered. The elec trokinetic equations which govern the ionic concentration distributions, th e electrostatic potential profile, and the fluid flow field in the electrol yte 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 electroly te with the equilibrium surface potential of the particle as the small pert urbation parameter. Closed-form formulas for the settling velocity of the c harge-regulating spheres and for the sedimentation potential in the suspens ion are derived. Our results show that the charge regulation effects on the sedimentation in a suspension appear starting from the leading order of th e equilibrium surface potential, which is determined by the regulation char acteristics of the suspension. (C) 2001 Academic Press.