Electrophoretic Motion of Two Spherical Particles with Thick Double Layers

The electrophoretic mobilities of two interacting spheres are calculated numerically for arbitrary values of the double-layer thickness. A general formula for the electrophoretic translational and angular velocities of N interacting particles is derived for low-zeta-potential conditions. The present calculation complements the well-studied case of thin double layers. The results are compared with recent reflection calculations and are used to compute the O(phi) contribution to the electrophoretic mobility of a suspension. Particle interactions can be significant for values of the scaled particle radius kappaa </= 10. At kappaa = 1 the O(phi) contribution can increase by a factor of 2-3 over its thin-double-layer value. The precise values depend on the strength of the double-layer repulsions as determined by the particle size. Fluctuations in the electrophoretic velocity are also calculated but would appear to be limited to about 10% of the mean velocity. The reflection results to order R-6, where R is the particle separation, are in good agreement with the numerical results for the suspension mobility and fluctuations but higher order reflections produce worse results. Although the effects of pair interactions are noticeable, the major result is that pair interactions even for quite thick double layers are not large.