Theory of thermal boundary resistance between small particles and liquid helium: Size effect on phonon conduction

Abstract

The size effect for the heat transfer between small particles and liquid helium is theoretically investigated at low temperatures. The general expression is presented for the thermal boundary resistance due to phonon conduction between a small particle and liquid helium. The resistances are calculated under some experimental conditions, which exhibit a $T^{-3\mathrm{}}$ variation above some temperature. Above this temperature the absolute magnitude of the calculated resistance also coincides with that of the acoustic mismatch theory for a bulk solid. Below its temperature the resistance increases exponentially with decreasing temperature. This temperature depends on both the size and the elastic properties of a small particle.