Proximity Effects in Radiative Transfer

TL;DR

This paper investigates how near-field radiative transfer between curved objects, specifically two spheres, depends on their size and gap, revealing scaling laws and proposing a modified proximity approximation for better predictions.

Contribution

It introduces a new scaling analysis for radiative transfer between curved objects and proposes a modified proximity approximation to improve predictive accuracy.

Findings

Radiative transfer scales as R/d when d/R approaches zero.

It follows a logarithmic dependence for larger d/R values.

The modified proximity approximation accurately predicts transfer between curved objects.

Abstract

Though the dependence of near-field radiative transfer on the gap between two planar objects is well understood, that between curved objects is still unclear. We show, based on the analysis of the surface polariton mediated radiative transfer between two spheres of equal radii $R$ and minimum gap $d$, that the near--field radiative transfer scales as $R/d$ as $d/R \rightarrow 0$ and as $\ln(R/d)$ for larger values of $d/R$ up to the far--field limit. We propose a modified form of the proximity approximation to predict near--field radiative transfer between curved objects from simulations of radiative transfer between planar surfaces.