Effect of Relaxation on Drag Forces and Diffusivities of Particles Confined in Rectangular Channels

Abstract

When a particle is moving inside a channel, its hydrodynamic interaction with channel walls increases its drag coefficient, causing a diffusivity reduction. For charged particles moving in an electrolytic solution, there is an additional drag due to the distortion of an electrical double layer caused by particle motion known as the relaxation effect. Effects of relaxation on drag forces on spheres confined in rectangular channels are computed employing perturbations involving particle Peclet number and surface charge densities. Results indicate that confinement amplifies electrokinetic retardation; increasing the relative particle size or decreasing the channel cross section area enhances the relaxation effect. With the relative particle size kept constant, the relaxation effect on the drag exerted on charged spheres in cylindrical pores with its smaller cross section area is stronger than that on charged spheres in rectangular channels and slit pores. However, for certain values of Debye length and particle size, the ratio between excess drag due to relaxation on confined charged spheres and hydrodynamic drag on uncharged spheres confined at the same location is higher for particles in rectangular channels, resulting in higher percentages of diffusivity reduction. Diffusivity reduction due to relaxation of charged particles in square ducts displays a maximum as a function of relative particle size, whereas that of charged particles in rectangular channels with higher cross section aspect ratio increases monotonically as particle size increases.