Boundary effects on electrophoresis of colloidal cylinders

Abstract

An exact analytical study is presented for the electrophoresis of an infinite insulating cylinder in the proximity of an infinite plane wall parallel to its axis. The electric field is exerted perpendicular to the particle axis in two fundamental cases: normal to a conducting plane and parallel to a non-conducting wall. The electrical double layers adjacent to solid surfaces are assumed to be thin with respect to the particle radius and the gap thickness between surfaces. The two-dimensional electrostatic and hydrodynamic governing equations are solved in the quasi-steady limit using bipolar coordinates and the typical electric-field-line, equipotential-line and streamline patterns are exhibited. Corrections to Smoluchowski's equation for the electrophoretic velocities of the particle are determined in simple closed forms as a function of λ, the ratio of particle radius to distance of the particle axis from the wall. Interestingly, the electrophoretic mobility of the cylinder in the direction parallel to a dielectric plane increases monotonically as the particle approaches the wall and becomes infinity when the particle touches the wall. For the motion of a cylinder normal to a conducting plane, the presence of the wall causes a reduction in the electrophoretic velocity, which goes to zero as λ → 1. It is found that boundary effects on the electrophoresis of a cylinder are much stronger than for a sphere at the same value of λ. The boundary effects on the particle mobility and on the fluid flow pattern in electrophoresis differ significantly from those of the corresponding sedimentation problem with which comparisons are made.