Dynamic electrophoretic mobility of a sphere in a spherical cavity.

Dynamic electrophoresis is a powerful analytical tool for the description of the surface properties of the charged entities in a concentrated dispersion. In our study the boundary effect on this dynamic phenomenon is investigated theoretically for the case, when the surface potential is low. In particular, the dynamic electrophoresis of a sphere in a spherical cavity is discussed as are the effects of the key factors on the phenomenon under consideration, which include the thickness of the double layer, the frequency of the applied electric field, the ratio of particle radius to cavity radius, and the boundary conditions of the surfaces of the particle and the cavity. The results of numerical simulation reveal that these key factors can have both quantitative and qualitative influence on the electrophoretic behavior of the particle. As an example, for the case of a positively charged particle placed in a negatively charged cavity if the double layer surrounding the particle is thin, the magnitude of the electrophoretic mobility of the particle increases with an increase in the frequency of the applied electric field and a phase lead may occur, but the opposite is true if the double layer is thick. These effects are not observed for the case of a positively charged particle placed in an uncharged cavity or for a positively charged particle placed in a positively charged cavity.