weakly interacting that the electric potential due to both The superposition formula for the electrical double-layer interspheres can be approximated by the sum of the potentials action between two uniformly charged spherical particles imof each sphere in isolation. This approach is commonly remersed in an unbounded electrolyte has been used extensively ferred to as the ''superposition approximation.'' The supersince its formulation some 50 years ago. However, the correspondposition formula for the double-layer interaction between ing result for two heterogeneously charged spherical particles has two uniformly charged spheres was originally derived by to date remained elusive. In this paper, we present such analytical Verwey and Overbeek some 50 years ago (10) and has found results and also consider the special case of a heterogeneously widespread use in numerous applications, ranging from colcharged spherical particle interacting with a uniformly charged loidal stability calculations (10) to Brownian dynamics simplate. In the sphere-plate case we suggest a simple modification to the superposition result, based on the incorporation of image ulations (11). Studies have shown, however, that in many effects, that can dramatically improve its regime of validity. We situations the assumption of a uniform charge distribution assess the validity and accuracy of the superposition formulae by on the particles is not justified and, furthermore, that the comparison with results of a rigorous boundary element calculainclusion of surface charge heterogeneities can have a dration of the electrostatic interaction. α§ 1998 Academic Press matic effect on the double-layer interaction (12-16).
In contrast to the uniformly charged case, there is a distinct lack of analytical results pertaining to the interaction of two 1 To whom correspondence should be addressed. Work performed while on leave at University of Delaware.
of the moments of the surface charge distributions of each 233