Sedimentation of a charged porous particle in a charged cavity

The sedimentation of a charged porous sphere at the center of a charged spherical cavity filled with an electrolyte solution is analyzed. The thickness of the electric double layers around the particle and cavity wall is arbitrary, and their relaxation effect is considered. Through the use of a set of linearized electrokinetic equations and a perturbation method, the ionic electrochemical potential energy, electric potential, and velocity fields in the fluid are solved with the fixed space charge density of the particle and surface charge density of the cavity as the small perturbation parameters, and an explicit formula for the sedimentation velocity is obtained. Due to the electroosmotic enhancement on the fluid recirculation in the cavity caused by the sedimentation-induced electric field, the presence of the surface charges on the cavity wall increases the sedimentation velocity of the porous particle. For the sedimentation of a porous particle in a cavity with their fixed charges of the same sign, the effect of electric interaction between the particle and cavity wall in general increases the sedimentation velocity. For the case of their fixed charges with opposite signs, the sedimentation velocity is increased/reduced if the magnitude of the fixed charge density of the cavity wall is relatively large/small. The effect of the surface charges at the cavity wall on the sedimentation of the porous particle increases with an increase in the permeability for fluid flow within the particle and with a decrease in the particle-to-cavity radius ratio (i.e., an increase in the surface area of the cavity wall relative to a given size of the particle, which enhances the fluid recirculation effect).