Sedimentation Velocity and Potential in a Dilute Suspension of Charged Composite Spheres

Abstract

The sedimentation of a charged composite particle composed of a solid core and a surrounding porous shell in an electrolyte solution is analytically studied. In the solvent-permeable and ion-penetrable porous surface layer of the particle, idealized hydrodynamic frictional segments with fixed charges are assumed to distribute at a uniform density. The equations which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field inside and outside the surface layer of a charged composite particle migrating in an unbounded solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a composite sphere with the charge densities of the rigid core surface and of the surface layer as the small perturbation parameters. An analytical expression for the settling velocity of the composite sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. The result demonstrates that the presence of the fixed charges in the composite sphere slows down its settling velocity relative to that of an uncharged one. A closed-form formula for the sedimentation potential in a dilute suspension of identical charged composite spheres is also derived by using the requirement of zero net electric current. The Onsager reciprocal relation is found to be satisfied between sedimentation and electrophoresis. It is shown that spherically-symmetric “neutral” composite particles (bearing no net charge) can undergo electrophoresis, induce sedimentation potential, and experience a smaller settling velocity relative to corresponding uncharged particles. The direction of the electrophoretic velocity or the induced potential gradient is determined by the fixed charges in the porous surface layers of the particles. In the limiting cases, the analytical solutions describing the sedimentation velocity and sedimentation potential (or electrophoretic mobility) for charged composite spheres reduce to those for charged solid spheres and for charged porous spheres.