D. Velegol et al., ELECTROPHORETIC ROTATION OF DOUBLETS COMPOSED OF 2 SPHERES ALMOST IN CONTACT, Colloids and surfaces. A, Physicochemical and engineering aspects, 140(1-3), 1998, pp. 59-74
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.