Abstract
A general theory is developed for the time dependent transient electrophoretic mobility of spherical colloidal particles in a salt-free liquid medium containing only counterions when a step external electric field is suddenly applied to the colloidal suspension. It is found that as in the case of the steady electrophoretic mobility in a salt-free medium, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case. In the latter case the counterion condensation takes place near the particle surface. For the low-surface charge case, the transient electrophoretic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations. For the high-surface-charge case, however, the transient mobility becomes independent of the particle surface charge because of the counterion condensation effects. A simple expression is derived for the ratio of the transient electrophoretic mobility to the steady electrophoretic mobility, which is found to take the same form irrespective of the magnitude of the particle surface charge. Using this equation, it is now possible to predict how the system will approach its final steady state.