Macroscopic Calculation of the Kapitza Resistance between Solids and LiquidHe4

Abstract

We treat the Kapitza thermal boundary resistance $R_K$ between a Debye solid and liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in the temperature range 0.1 to 1 K, where the phonon transmission coefficient is known to be highly anomalous. Using a continuum model, we consider the consequences of a solid van der Waals layer of helium which is acoustically absorbing. Using values of acoustic wave attenuation in the layer based on experiment, we are able to predict the correct order of magnitude and temperature dependence of $R_K$ for copper.