Electrophoresis of a charge-regulated soft sphere in a charged cylindrical pore

The boundary effect on the electrophoresis of a soft spherical particle, which comprises a rigid core and a porous layer, along the axis of a cylindrical pore is analyzed under the conditions of low surface potential and weak applied electric field. The porous layer of the particle is of charge-regulated nature where the distribution of fixed charge depends on the degree of dissociation/association reaction of the ionizable function groups contained in the porous layer. The pore might be charged, implying that the effect of electroosmotic flow can play a role. The influences of the nature of the porous layer of a particle, the thickness of the double layer, the pH of the bulk liquid, and the relative size of a pore on the electrophoretic behavior of the particle are investigated. Several unexpected and interesting results are obtained. For instance, if the pH value of the bulk liquid or the thickness of the membrane layer takes a medium large value, the electrophoretic mobility of the particle has a local maximum as the thickness of the double layer varies.