A new acoustic mismatch theory for Kapitsa resistance

Abstract

This paper generalizes the well-known acoustic mismatch theory of Kapitsa interface thermal resistance by taking into consideration a broad class of thermal vibrations that were excluded from that theory by the imposition of the Sommerfeld radiation condition, which is required for the theory of sound but is not relevant for the analysis of heat transport. This extension preserves the main ideas of the acoustic mismatch theory but provides much more reasonable estimates for the interface resistance. The predictions of the new theory are compared with various published experimental results for the thermal resistance between liquid helium at low temperatures and several different metals (Ag, Au, Cu, Pb and Pt). The computations are straightforward and require only well-known material parameters. The predictions agree with the experiments to within their stated range of accuracy.

Extension of Planck’s law to steady heat flux across nanoscale gaps

“…If the ensemble of electromagnetic waves in the domain G is not in thermal equilibrium but instead has a small energy flux Q along the x-axis then it cannot be described by the formula (2.5) derived from the assumption of equilibrium. However, observing that this ensemble appears to be in equilibrium in a frame which moves along the x-axis with the speed v ≈ Q/E we can verify [6,7] that its energy density can be represented as the sum…”

“…However, we recently developed a method to deal with similar problems arising in the theory of heat transport by acoustic waves, usually referred to as phonons. In particular, in [6,7] we describe the spectra of the energy density of an ensemble of acoustic waves with a steady heat flux, and using this information we obtained reasonable estimates of the so-called Kapitsa interface thermal resistance which has remained an open theoretical problem for about seven decades. Here we further develop our approach to problems of heat transport by electromagnetic waves, and we thereby get estimates of the thermal resistance of a narrow vacuum gap which agrees with recently published experimental data.…”

Extension of Planck's law of thermal radiation to systems with a steady heat flux

“…We have applied the proposed extension of Planck's law to the analysis of Kapitsa thermal resistance and obtained results [28,29] that show correct order of magnitude Kapitsa resistance for the first time without any added elements such as surface roughness or nonlinearities, and which is almost two orders of magnitude more accurate than conventional theories based on the classical Planck's law. In a closely related paper [30] we considered radiative heat transport between two dielectric half-spaces separated by a gap of small width d, and we obtained agreement with recent experimental observation, that the conductance becomes unbounded as O (1/d 2 ) between two materials at different temperatures as the gap's width d vanishes.…”

Equilibrium ensembles of electromagnetic thermal radiation in layered media

“…To illustrate the insufficiency of the information provided by Planck's law we consider an ensemble of plane electromagnetic waves described by the formula 6) where e = (e x , e y , e z ) is a random vector of unit length, c 0 is the speed of light in a vacuum, and A is a random complex-valued amplitude. Each of these random fields has the energy density E = 0 |A| 2 , where 0 is the dielectric permittivity of the vacuum.…”

“…With the goal of developing a reliable model of Kapitsa interface thermal resistance we recently revisited the conventional theory and found [6][7][8] that three things needed to be addressed to get a logically consistent model: first we needed to remove the often-used Sommerfeld radiation condition, which is not relevant in problems of heat transport; second modify Plank's distribution to make it valid for non-equilibrium systems with constant heat flux; and third understand the structure of the equilibrium ensembles of thermally excited wave fields, which can then be used as the foundation for perturbation methods. The results presented in [6][7][8] show correct orders of magnitude Kapitsa resistance for the first time without any added elements such as surface roughness.…”