Approximate expressions for retarded van der waals interaction

Abstract

Several approximations for retarded van der Waals interaction between plates, between spheres, and for the sphere-plate system are considered. For the interaction of flat plates, a single expression is shown to be an adequate substitute for two empirical formulae of Overbeek. This expression is then used to derive a simple result for retarded interaction between unequal spheres at close approach which agrees fairly well with “exact” computations up to separations of about 10% of the sphere radius. An equivalent expression applies to the sphere-plate system but in this case an even simpler result is shown to give reasonable agreement with exact computations up to distances of about 20% of the sphere radius. These approximations take the form of simple unretarded Hamaker formulae, together with a correction factor which depends on the separation distance and the characteristic wavelength of the dispersion interaction. They should find application in problems of colloid stability and particle deposition.