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 electri c field is constant and parallel to the nonconducting pore wall, and t he particle and wall surfaces are assumed uniformly charged. Electrica l double layers adjacent to solid surfaces are assumed to be thinner t han particle radius and gap width between surfaces. The presence of th e pore wall affects particle velocity: 1. an electroosmotic flow of th e suspending fluid exists due to interaction between the electric fiel d and the charged wall; 2. the local electric field on the particle su rfaces is enhanced by the insulated wall, speeding up the particle, an d 3. the wall increases viscous retardation of the moving particle. To solve electrostatic and hydrodynamic governing equations, general sol utions 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 b y a collocation technique. Typical electric-field-line, equipotential- line and streamline patterns for the fluid phase are exhibited, and co rrections to the Smoluchowski equations for particle electrophoretic v elocity are presented for various relative separation distances betwee n the particle and wall. The presence of the pore wall always reduces the electrophoretic velocity; however, the net wall effect is quire we ak. even for very small gap width between the particle and wall.