Boundary effects on electrophoretic motion of colloidal spheres

An analysis is presented for electrophoretic motion of a charged non-conducting sphere in the proximity of rigid boundaries. An important assumption is that κ a → ∞, where a is the particle radius and κ is the Debye screening parameter. Three boundary configurations are considered: single flat wall, two parallel walls (slit), and a long circular tube. The boundary is assumed a perfect electrical insulator except when the applied field is directed perpendicular to a single wall, in which case the wall is assumed to have a uniform potential (perfect conductor). There are three basic effects causing the particle velocity to deviate from the value given by Smoluchowski's classic equation: first, a charge on the boundary causes electro-osmotic flow of the suspending fluid; secondly, the boundary alters the interaction between the particle and applied electric field; and, thirdly, the boundary enhances viscous retardation of the particle as it tries to move in response to the applied field. Using a method of reflections, we determine the particle velocity for a constant applied field in increasing powers of λ up to O (λ 6 ), where λ is the ratio of particle radius to distance from the boundary. Ignoring the O (λ 0 ) electro-osmotic effect, the first effect attributable to proximity of the boundary is O (λ 3 ) for all boundary configurations, and in cases when the applied field is parallel to the boundaries the electrophoretic velocity is proportional to ζ p − ζ w , the difference in zeta potential between the particle and boundary.