The effect of concurrent geometry and roughness in interacting surfaces

TL;DR

This paper investigates how surface roughness and shape influence interaction energies, deriving an averaged expression and analyzing the combined effects for electrostatic and Casimir forces.

Contribution

It introduces a method to average interaction energy over random corrugations and applies derivative expansion to analyze shape-roughness interplay.

Findings

Derived an averaged interaction energy expression depending only on smooth surface.

Calculated leading and next-to-leading order terms in the derivative expansion.

Analyzed shape and roughness effects for specific corrugation models in electrostatic and Casimir interactions.

Abstract

We study the interaction energy between two surfaces, one of them flat, the other describable as the composition of a small-amplitude corrugation and a slightly curved, smooth surface. The corrugation, represented by a spatially random variable, involves Fourier wavelengths shorter than the (local) curvature radii of the smooth component of the surface. After averaging the interaction energy over the corrugation distribution, we obtain an expression which only depends on the smooth component. We then approximate that functional by means of a derivative expansion, calculating explicitly the leading and next-to-leading order terms in that approximation scheme. We analyze the resulting interplay between shape and roughness corrections for some specific corrugation models in the cases of electrostatic and Casimir interactions.