Analysis of the dispersion force between a layered sphere and a cylinder

The continuum theory developed by Lifshitz and coworkers predicts the van der Waals forces acting between colloidal or macroscopic bodies from knowledge of the dielectric spectra of the individual materials. Formal exact solutions, accounting for the effect of retardation, exist for planar geometries such as flat plates and multilayers and discrete particles such as spheres and cylinders. Each comprises a complicated nested set of sums and/or integrals over a spectrum of wavenumbers and frequencies of the fluctuating electromagnetic modes. The power of the theory lies in the natural accommodation of the many-body effects responsible for the quantitative failure for condensed media of the pairwise additive Hamaker theory. The price is the need for complete dielectric spectra for the component materials and involved numerical calculations which obscure the relationship between these dielectric properties and the essential features of the force. This report contains the analysis of and numerical results for the dispersion force between a coated cylinder and sphere based on rigorous expressions available from the Lifshitz theory for interactions between half spaces. The Derjaguin approximation satisfactorily accounts for the curvature of the bodies since the dimensions are large with respect to the relevant wavelengths.