Electrophoretic rotation of doublets composed of two spheres almost in contact

Colloidal doublets formed from spheres with different zeta potentials rotate as dipoles into alignment with an applied electric field. The rate of rotation is proportional to the difference in the electrophoretic mobilities of the isolated spheres times a dimensionless rotation coefficient (N). The coefficient N, which describes the interaction effects between the particles, has been previously calculated numerically under the assumptions of infinitesimal double layers and uniform zeta potentials on each sphere. These numerical values have been used to interpret experiments which probe the tangential forces between two particles almost in contact. But since these assumptions might not hold for the small gaps in actual experiments, it is important to know how N is affected when the double layers of two spheres overlap or when the charge is nonuniformly distributed on the sphere surfaces (especially in the gap region). Using an extension of the Lorentz reciprocal theorem for Stokes flow, we have developed a semi-analytical solution for N which is valid in the asymptotic limit of small (but finite) gaps of fluid between the spheres. For infinitesimal double layers and uniform zeta potentials, this result shows that N is weakly singular in the gap between the spheres. Our method also enables us to examine the effects of overlapping double layers and nonuniform zeta potentials in the gap region, and an important result of this paper is that even when these effects are considered, the result for infinitesimal double layers and uniform zeta potentials remains a very good approximation.