Interplay of roughness/modulation and curvature at proximity

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.

5 pages, 2 figures

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• Isolelectronic apparatus to probe the thermal Casimir force
• Observing the Casimir-Lifshitz Force Out of Thermal Equilibrium
• Heat transfer in granular media with weakly interacting particles
• Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force
• Exact formulas for radiative heat transfer between planar bodies under arbitrary temperature profiles: modified asymptotics and sign-flip transitions
• A robust superconducting setup to probe the thermal Casimir effect
• The effect of concurrent geometry and roughness in interacting surfaces