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The electrophoresis of a rigid, charge-regulated, spherical particle normal to a large disk is investigated under the conditions of low surface potential and weak applied electric field. We show that, although the presence of a charged disk does not generate an electroosmotic flow, it affects particle motion appreciably through inducing charge on its surface and establishing an osmotic pressure field. The competition between the hydrodynamic force and the electric force may yields a local extremum in mobility; it is also possible that the direction of particle movement is reversed. In general, if a particle remains at constant surface potential, a decrease in the thickness of double layer has the effect of increasing the electrostatic force acting on it so that its mobility increases. However, this might not be the case for a charged-regulated particle because an excess hydrodynamic force is enhanced. For a fixed separation distance, the influence of a charged disk on mobility may reduce to a minimum if the bulk concentration of hydrogen ion is equal to the dissociation constant of the monoprotic acidic functional groups on particle surface.

The electrophoresis of two finite, identical cylinders along the axis of an uncharged cylindrical pore is analyzed under the conditions of low electrical potential and weak applied electric field. This geometry allows us to examine simultaneously the effects of the presence of a boundary and the interaction between particles on the electrophoretic behavior of particles. The result of numerical simulation reveals that the effect of particle−particle interaction on the pair mobility of particles can be significant if the thickness of the double layer surrounding a particle is comparable to half the separation distance between them. However, this effect is less significant compared with that arising from the presence of the pore. We show that the boundary effect on electrophoresis for the case of nonuniformly charged particles is more important than that for the case of uniformly charged particles. The effect of particle−particle interaction on electrophoresis for the case of two cylinders is stronger than that for the case of two spheres.