Electrophoresis of a colloidal sphere in a circular cylindrical pore

The electrophoretic motion of a dielectric sphere along the centerline of a long circular pore is studied theoretically. The imposed electric field is constant and parallel to the nonconducting pore wall, and the particle and wall surfaces are assumed uniformly charged. Electrical double layers adjacent to solid surfaces are assumed to be thinner than particle radius and gap width between surfaces. The presence of the pore wall affects particle velocity: 1. an electroosmotic flow of the suspending fluid exists due to interaction between the electric field and the charged wall; 2. the local electric field on the particle surfaces is enhanced by the insulated wall, speeding up the particle, and 3. the wall increases viscous retardation of the moving particle. To solve electrostatic and hydrodynamic governing equations, general solutions are constructed from fundamental solutions in both cylindrical and spherical coordinate systems. Boundary conditions are enforced at the pore wall by Fourier transforms and then on the particle surface by a collocation technique. Typical electric-field-line, equipotential-line and streamline patterns for the fluid phase are exhibited, and corrections to the Smoluchowski equations for particle electrophoretic velocity are presented for various relative separation distances between the particle and wall. The presence of the pore wall always reduces the electrophoretic velocity; however, the net wall effect is quire weak. even for very small gap width between the particle and wall.