Chapter 7 - Electrophoresis of Porous Particles

Abstract

Abstract Electrophoresis of charged porous particles is investigated in this chapter for either a single particle suspended in an infinite medium of electrolyte solution or particle suspensions, either dilute or concentrated. Due to the permeability of the particle, the hydrodynamic drag force is drastically reduced. Moreover, as the fixed charges carried by the particle are distributed all over the entire interior of the particle, the total amount of particle charges in general are significantly larger than the corresponding rigid particle situation discussed in Chapter 1, where the particle charges are distributed on the particle surface only. As a result, the electric driving force is much larger as well. Based on the above two hydrodynamic and electrostatic features pertinent to charged porous particles, the electrophoretic mobility is much larger than the rigid particle situation in general, especially for a porous particle both highly charged and highly permeable. In general, the electrostatic phenomenon of “counterion condensation,” or equivalently the “shielding effect” of fixed charges by the driven-in counterions, reduces the nominal fixed charge density significantly at the same time when κa is large due to the strong double layer suppression effect. The higher the particle charge level is, the more profound this shielding effect is due to the stronger Coulomb attraction force. Moreover, the convection-induced component of the motion-deterring double layer polarization effect dominates in the electrophoresis of porous particles due to the much faster particle motion in general compared with the rigid particles. These two coupled and inseparable nonlinear effects are the two major factors underlying the electrophoretic behavior of porous particles. A modified Brinkman equation with an extra local electric body force term is used to describe the electrokinetic response within the porous particle. General Henry's charts are provided under various electrokinetic conditions. There is no stagnant inner Stern layer for a porous particle as the entire particle is permeable. The no-slip hydrodynamic boundary conditions on the surface of a rigid particle fail to apply here either. We actually have only one diffuse “single layer” instead of the double layer structure introduced in Chapter 1. The terminology is borrowed or extended from there, nonetheless, as the conceptual or analogous double layer here as well as the double layer polarization, with the understanding that the focus is on the diffuse single layer only. Intriguing phenomena pertinent to highly charged porous particles are discussed such as a less charged particle may move faster than a highly charged one, and porous particles may move faster in a concentrated suspension than in a dilute one under some electrokinetic circumstances. Permeability of the porous particles is the underlying crucial factor.