No abstract

An analytical study of the electrophoretic motion of two freely-suspended, nonconducting spheres with thin electrical double layers is presented using a method of reflections. The particles may differ in radius and/or in zeta potential at the surface, and they are oriented arbitrarily relative to the direction of applied electric field. Corrections to Smoluchowski's equation due to particle interactions are determined in a power series of 1 up to O(rG7), where r,2 is the center-to-center distance between the particles. It is found that the electrophoretic particles do not interact with one another when they have equal zeta potentials. For the specific case of spheres with identical radii, our results agree well with the exact calculations using bipolar coordinates. Based on a microscopic model, the results for two particles are used to find the effect of volume fractions of particles of each type on the mean particle velocities in a bounded dispersion. Of particular interest is the electrophoresis of a suspension of particles with arbitrary size distribution but with identical zeta potentials, in which the sole factor influencing the mean particle velocity is the volume fraction of all particles. In general, the effect of particle interactions on electrophoresis is much weaker than that on sedimentation.