ELECTROPHORETIC ROTATION OF DOUBLETS COMPOSED OF 2 SPHERES ALMOST IN CONTACT

Colloidal doublets formed from spheres with different zeta potentials rotate as dipoles into alignment with an applied electric field. The r ate of rotation is proportional to the difference in the electrophoret ic mobilities of the isolated spheres times a dimensionless rotation c oefficient (N). The coefficient N, which describes the interaction eff ects 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 i nterpret experiments which probe the tangential forces between two par ticles almost in contact. But since these assumptions might not hold f or 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 theo rem 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 unifor m zeta potentials, this result shows that N is weakly singular in the gap between the spheres. Our method also enables us to examine the eff ects of overlapping double layers and nonuniform zeta potentials in th e gap region, and an important result of this paper is that even when these effects are considered, the result for infinitesimal double laye rs and uniform zeta potentials remains a very good approximation. (C0 1998 Elsevier Science B.V. All rights reserved.