Electrophoresis of a Sphere at an Arbitrary Position in a Spherical Cavity

The boundary effect on electrophoresis is of both fundamental and practical significance. Here, we consider the case when a sphere is placed at an arbitrary position in a spherical cavity. We show that the qualitative behavior of the particle depends largely on the charged conditions on both particle surface and cavity surface, and the presence of the latter may have the effect of increasing the mobility of the particle. For example, for the case when both particle and cavity are maintained at constant surface potential, if the particle is close to the cavity surface, charge reversal may occur on the latter. In this case, the closer the particle to cavity surface, the greater its mobility. It is found that the thicker the double layer surrounding the particle and/or the greater the difference between the surface potential of the particle and that of the cavity, the easier it is for the charge reversal to occur.