Sedimentation velocity and potential in a concentrated suspension of charged soft spheres

An analytical study of sedimentation in a suspension of charged spherical soft particles, each with the structure of a rigid core surrounded by a porous shell, in an electrolyte solution is presented. The porous shell of the particle is treated as a solvent-permeable and ion-penetrable surface layer of finite thickness, in which hydrodynamic frictional segments with fixed charges distribute uniformly. A unit cell model that allows the overlap of the electric double layers of adjacent particles is employed to account for the effect of particle interactions. When the system is slightly distorted from equilibrium, the electrokinetic equations governing the electric potential, ion concentration, and fluid velocity distributions are linearized and solved using a perturbation method with the fixed charge densities of the core surface and porous layer of each soft sphere as the small parameters. Explicit formulas for the sedimentation velocity and potential in the suspension are obtained to the second orders of these fixed charge densities with the relaxation effect of the double layers included. The sedimentation velocity and potential are not necessarily monotonic functions of the volume fraction of the particles; the particle concentration effects are significant, even in dilute suspensions. In the limiting cases, the analytical solutions of the sedimentation velocity and potential for charged soft spheres reduce to those for charged rigid spheres and charged porous spheres. It is shown that a suspension of charged but neutral soft spheres can produce sedimentation potential, and their sedimentation velocity differs from that of the uncharged soft spheres.