Transient electrophoresis of a spherical soft particle

A theory is developed on the time-dependent transient electrophoresis of a spherical soft particle (i.e., a spherical polyelectrolyte-coated particle) when a step electric field is applied. The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of the particle. A simple approximate analytic mobility expression is derived which is applicable for the practically important case where the electrolyte is symmetrical, the particle core radius and the polyelectrolyte layer thickness are both much larger than the Debye length and the Brinkman screening length, and the polyelectrolyte layer is much thinner than the particle core radius (a thin polyelectrolyte layer). The other limiting case of a thick polyelectrolyte layer is also considered.