Electrophoresis in suspensions of charged porous spheres in salt-free media

Abstract

Electrophoresis in either dilute or concentrated suspensions of charged porous spheres in salt-free media is investigated theoretically in this study. The Brinkman model and the Kuwabara’s unit cell model are adopted to simulate the porous structure and the suspensions, respectively. We found, among other things, that the polarization effect due to the convection flow within the porous sphere is a crucial factor in determining its electrophoretic behavior. An induced electric field opposite to the applied electric field is generated, which deters the particle motion significantly when the particle is highly permeable. Approximate analytical prediction for dilute suspensions neglecting convection flow can overestimate the mobility severely in this situation. The approximate analytical prediction is satisfactory when the permeability of particle is low, though. Counterion condensation happens at high fixed charge density which decreases the mobility drastically and the mobility approaches a constant value asymptotically. The mobility profile of the particles with increasing volume fraction can exhibit local minimum if the corresponding dimensionless parameter Q fix /( λa) 2 is high, where Q fix and λa are, respectively, the fixed charge density and the friction coefficient of the porous particles in dimensionless form. This is due to the overlapping of counterion clouds surrounding particles, which offsets the polarization effect, becomes significant as the suspension gets concentrated. No such phenomenon for low Q fix /( λa) 2, where the mobility profile decreases monotonously with increasing volume fraction. Comparison with experimental data available in the literature for polyelectrolyte suspensions is excellent, indicating the reliability of this analysis, as well as the success of using charged porous sphere to model a polyelectrolyte system.