Electrophoresis of a Cylindrical Particle with a Nonuniform Zeta Potential Distribution Parallel to a Charged Plane Wall

Abstract

An analytical study is presented for the steady, transverse electrophoretic motion of a circular cylindrical particle with an arbitrary angular distribution of its surface potential parallel to a plane wall prescribed with the potential distribution consistent with the applied electric field. The electric double layers adjacent to the solid surfaces are assumed to be very thin with respect to the particle radius and spacing between the surfaces. The two-dimensional electrostatic and hydrodynamic governing equations are solved using cylindrical bipolar coordinates, and the typical electric field line, equipotential line, and streamline patterns are exhibited. The explicit formulas for the electrophoretic and angular velocities of the particle are obtained with the contribution from the electroosmotic flow produced by the interaction between the applied electric field and the thin double layer adjacent to the plane wall. To apply these formulas, one only has to calculate the leading multipole moments of the...