Interplay of roughness/modulation and curvature at proximity

TL;DR

This paper investigates how surface roughness and modulations influence the distance dependence of interactions between curved objects, revealing modified scaling laws that can predict behaviors like heat transfer saturation at short distances.

Contribution

It introduces a framework linking surface modulation characteristics to changes in power-law interaction scaling laws at proximity.

Findings

Roughness alters the power-law scaling of interactions.

Modified scaling laws relate to the Taylor expansion of surface separation distributions.

Predictions include heat transfer saturation and Casimir force behavior at small separations.

Abstract

We show that roughness or surface modulations change the distance dependence of (power-law) interactions between curved objects at proximity. The modified scaling law is then simply related to the order of the first non-vanishing coefficient of the Taylor expansion of the distribution of separations between the surfaces. The latter can in principle be estimated by scanning measurements, or computed for well characterized modulations, and then used to predict short-distance scaling behavior in disparate experiments. For example, we predict that the radiative heat transfer between a rough sphere and a plate approaches a constant with decreasing separation. Similar saturation is expected for the Casimir force between dielectric or metallic surfaces with appropriate modulations over distinct length scales.