Dynamic electrophoresis of a sphere in a spherical cavity: arbitrary surface potential

The boundary effect on the dynamic electrophoretic behavior of a charged entity is examined by considering a sphere in a spherical cavity.
The present study extends previous analysis to the case of an arbitrary level of electrical potential where the effect of double-layer distortion
can be significant. The governing equations are solved numerically based on a pseudo-spectral method, which is found to be sufficient in
solving the corresponding electrophoresis problem when a static electric field is applied. The result of numerical simulation reveals that as the
size of a cavity decreases, both the magnitude of the mobility and the inertial force acting on a particle decrease accordingly. Also, while the
distortion of the ionic cloud should not be ignored, in general, when the surface potential of a particle is high, its influence on the magnitude
and on the phase angle of the mobility is alleviated by the presence of the cavity.