Electrophoresis of a sphere normal to a plane at arbitrary electrical potential and double layer thickness

The electrophoretic movement of a sphere normal to an uncharged, planar surface is analyzed theoretically, taking the effect of double layer polarization into account. Here, both the surface potential of the particle and the thickness of the double layer surrounding it can be arbitrary. We show that if double layer polarization is neglected, the effect of the surface potential of a particle on its electrophoretic velocity is inappreciable. On the contrary, it becomes significant if double layer polarization is present. However, if the distance between the particle and the surface is sufficiently close, since the hydrodynamic effect dominates, the influence of the surface potential and double layer polarization becomes insignificant.