Simplified calculation of electrophoretic mobility of non-spherical particles when the electrical double layer is very extended

Abstract

Experiments in our laboratories (1) have shown tha t some dispersions in nonpolar solvents exhibit very large differences in mobility (sometimes as much as an order of magnitude) from particle to particle. Naturally, the question arises as to why this is so. Generally, since the ion concentration is low in these liquids, the diffuse part of the electrical double layer is very extended and does not contribute appreciably to the (i.e., the electrophoretic drag and relaxation effect (2) are negligible). Therefore, to calculate the mobility of a particle of charge Q, one may simply balance the force EQ, due to the applied electric field E, against the opposing force due to ordinary hydrodynamic drag. Using this approximation, which greatly simplifies the calculations, we can investigate whether the observed large variations in mobility can be caused by variations in shape. The answer is no, as is shown by the following calculations for el]ipsoidal particles}