Boundary effects on electrophoretic motion of colloidal spheres

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Abstract
An analysis is presented for electrophoretic motion of a charged non-conducting sphere in the proximity of rigid boundaries. An important assumption is that κa → ∞, 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(λ6), where λ is the ratio of particle radius to distance from the boundary. Ignoring the O(λ0) electro-osmotic effect, the first effect attributable to proximity of the boundary is O(λ3) for all boundary configurations, and in cases when the applied field is parallel to the boundaries the electrophoretic velocity is proportional to ζp − ζw, the difference in zeta potential between the particle and boundary.

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