Electrophoretic motion of a charged particle in a charged cavity

Abstract

A theoretical investigation of the electrophoresis of a dielectric colloidal sphere located at an arbitrary position inside a charged spherical cavity filled with an ionic fluid is presented. The applied electric field is perpendicular to the line through the centers of the particle and cavity, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and any gap width between the surfaces. The general solutions to the Laplace and Stokes equations governing the electric potential and fluid velocity fields, respectively, are established from the superposition of their basic solutions in the two spherical coordinate systems about the two centers, and the boundary conditions are satisfied by a multipole collocation method. Results for the translational and angular velocities of the confined particle are obtained for various cases. When the particle is positioned at the center of the cavity, these results are in excellent agreement with the available analytical solution. The effects of the cavity wall on the electrokinetic motion of the particle are interesting, complicated, and significant. In general, the electrophoretic translational/rotational mobility of the particle decreases/increases with increases in the particle-to-cavity radius ratio and the relative distance between the particle and cavity centers (the direction of rotation is opposite to that of a corresponding settling particle), but there exist some exceptions. The direct and recirculating cavity-induced electroosmotic flows can strengthen or weaken the electrophoretic translation and rotation of the particle and even reverse their directions, depending on the cavity-to-particle zeta potential ratio and geometric parameters. The effect of the cavity wall on the electrokinetic translation of a particle perpendicular to the line connecting their centers is slightly weaker than that parallel to this line.