Relaxation Effect on Intrapore Diffusivities of Highly Charged Colloidal Particles Confined in Porous Membranes

During the particle intrapore diffusion, the particle–pore hydrodynamic interaction enhances the drag on the particle, resulting in a particle diffusivity reduction. For charged particles submerged in an electrolytic solution, the distortion of electrical double layer caused by particle motion creates an additional drag: a phenomenon known as the relaxation effect. Such effect on intrapore diffusivities of rigid spherical particles confined in long cylindrical pores is determined by employing a perturbation scheme involving particle Peclet number. Comparison between present simulation results and previous results from perturbations involving both particle Peclet number and surface charge density indicates that the perturbation involving surface charge density overestimates the electrokinetic retardation. Our results demonstrate that, whereas a particle surface charge density increase always amplifies the excess drag due to relaxation, effects of pore surface charge density are more complicated and dependent on values of particle surface charge density and Debye length. If a highly charged particle is confined in a charged pore, this additional drag increases as a function of Debye length if the Debye length is small, but becomes constant despite the increasing Debye length if the Debye length is comparable or larger than the pore radius. For particles confined in uncharged pores, however, the Debye length increase always amplifies the electrokinetic retardation, causing the particle diffusivity reduction of a highly charged particle in an uncharged pore to be larger than that of a similar particle confined in a charged pore if the Debye length is comparable to or larger than the pore radius.