Electrophoresis of a thin charged disk

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Abstract
The electrophoretic velocity of a charged disk of zero thickness is computed in the limit of small surface potentials, but with arbitrary double layer thickness. The disk represents an idealized clay particle, and has uniform surface charge over its flat surface, together with a uniform line charge around its edge. The contributions of these two charges to the electrophoretic velocity are considered separately. Asymptotic results are obtained for thin and thick double layers, and intermediate results are obtained by numerical integration. The singularities in both the electrical and hydrodynamic fields at the edge of the particle enhance the importance of the edge charge when the double layer thickness κ−1 is small compared to the disk radius a.

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