Upper-bound error estimates for the derjaguin approximation and the linearization approximation to the double-layer interaction energy for two unequal spheres

Abstract

At present only approximate methods are available for calculating double-layer interaction energy. All of these approximate methods use the Derjaguin approximation, which is valid for large ‘plate-like’ spheres. When the linearization approximation is used in addition to the Derjaguin approximation, further computational simplification results in an analytic expression for the double-layer interaction energy. This linearization approximation is valid for small surface potentials. This work estimates the upper-bound error in the double-layer interactionenergy caused by the Derjaguin approximation and the linearization approximation. These error estimates are shown to be a function of the sphere radius and surface potential.