Dynamic mobility of two spherical particles with thick double layers

The dynamic electrophoretic mobility of a pair of nearby spherical particle s is analyzed in the case when the thickness of the electrical double layer around each particle is comparable to the particle radius. By means of an integral reciprocal relation, a formal expression is obtained for the force and torque on N spheres subject to an oscillating electric field which may be spatially varying, Upon linearizing in the surface potential, this expr ession is shown to depend upon a set of purely hydrodynamic problems involv ing N neutral spheres, the calculation of the electric field around N neutr al spheres, and the equilibrium charge distribution around N charged sphere s. In the case of a single particle, the known analytic formula for the dyn amic mobility is recovered. For a pair of identical particles, the dynamic mobility is calculated numerically, using known solutions to the required s ubproblems, An analytical expression for the mobility of a pair of widely s eparated spheres is also obtained by a method of reflections, and this is i n excellent agreement with the numerical results outside the range of doubl e layer overlap. (C) 2000 Academic Press.