proteins, which is frequently carried out on systems with
The electrophoretic motion of a charged sphere in the presence low ka values and low surface potentials.
of a rigid boundary is analyzed for low surface z potentials but
The assumption of sphericity can be relaxed (7-9), as arbitrary ka, where a is the particle radius and k is the inverse can the assumption of uniform surface potential (10)(11)(12). A Debye length. The boundary configurations considered are a single further important generalization is to particles which are not flat wall, a slit, and a long cylindrical tube. Using a method of isolated, for in practice electrophoresis is often carried out reflections, we obtain the particle velocity for a constant applied in semi-dilute suspensions, when other particles are relaelectric field in powers of l up to O(l 6 ), where l is the ratio of tively close by, or in the presence of rigid boundaries, as the particle radius to the distance from the boundary. This analysis in the case of membrane separation techniques. In these is valid as long as the double layer around the particle does not overlap significantly with the double layer at the boundary. The circumstances a colloid particle experiences perturbations to effect of finite ka is to enhance the viscous retardation of the the uniform electric field and to the surrounding flow field particle, although for large separations the first effect due to the due to the presence of the other particles or boundaries.
proximity of the boundary is still at O(l 3 ) in all cases. When the Most of the work done so far has employed the thin double applied field is parallel to the boundary, the electrophoretic veloclayer approximation, since then the specific effects of the ity is not proportional to the difference in zeta potential between double layer enter the hydrodynamic equations only as a slip the particle and the boundary (as occurs for ka r ฯฑ), and the boundary condition. Numerical solutions have been obtained proximity of the boundary may increase the particle velocity or for a sphere moving near a plane wall (13, 14), for a sphere change its direction. An important result of the analysis is that moving axially toward a circular hole or disk (15), for a line the hindrance to the electrophoretic velocity of a particle in a of identical spheres with thin polarized double layers moving cylindrical pore increases significantly as ka is reduced below 10.
along the centerline of a cylindrical pore (16), for a prolate