Two sphere interactions were first explicitly dealt with by The electrophoretic mobilities of two interacting spheres are reflections for identical spheres (3) and for dissimilar calculated numerically for arbitrary values of the double-layer spheres (4). These calculations were checked against exact thickness. A general formula for the electrophoretic translational solutions in bispherical coordinates (5, 6) and boundary coland angular velocities of N interacting particles is derived for lowlocation techniques, which can be extended to multiparticle zeta-potential conditions. The present calculation complements interactions (7). These calculations are reviewed in (8). the well-studied case of thin double layers. The results are com-Similar techniques can be used for the case of polarized pared with recent reflection calculations and are used to compute thin double layers where ka ำท 1 but the O(f) contribution to the electrophoretic mobility of a suspension. Particle interactions can be significant for values of the scaled particle radius ka ยฃ 10. At ka ร
1 the O( f) contribution can exp(eรz i zร/2kT ) ka ร O(1), 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 electro-
where z is the zeta potential of the particle, e is the protonic phoretic velocity are also calculated but would appear to be limited charge, z i is the valence of ionic species i in the electrolyte, k to about 10% of the mean velocity. The reflection results to order is the Boltzmann constant, and T is the temperature. Results R 06 , where R is the particle separation, are in good agreement have appeared for clusters of a few spherical particles (9) and with the numerical results for the suspension mobility and fluctuafor both ordered and random clusters of up to 64 particles (10).
tions but higher order reflections produce worse results. Although
The chief conclusions of such studies are that particle the effects of pair interactions are noticeable, the major result is concentration has a relatively weak effect on electrophoretic that pair interactions even for quite thick double layers are not mobilities and that identical particles with thin double layers large. แญง 1997 Academic Press feel no interaction (8). The reason is that, for thin double Key Words: particle interactions; two sphere electrophoresis;
layers, the charge on the particle is canceled by the charge electrophoretic mobility; thick double layers.
in the double layer so there is no body force acting on the fluid, unlike the sedimentation problem. The particle moves due to a surface stress caused by the slip velocity boundary U ร
e 0 e r z h f (ka)E 0 , [1]