Non-equilibrium steady state of the superfluid mixtures of helium isotopes at classical temperatures

TL;DR

This paper investigates the non-equilibrium steady states and size effects in superfluid helium isotope mixtures, considering thermal excitations and phonon-impuriton interactions, and proposes an experiment to study the Knudsen effect.

Contribution

It develops a kinetic model for superfluid helium mixtures including thermal excitations and proposes an experimental setup for studying the Knudsen effect.

Findings

Derived conditions for steady non-equilibrium states in helium mixtures.

Analyzed the size effect and Knudsen effect in impuriton gases.

Proposed a model for collision operators in superfluid mixtures.

Abstract

The size effect in the gas of impuritons of the superfluid mixtures of helium isotopes is investigated by taking into consideration the contribution of thermal excitations. The solution is obtained for the set of kinetic equations describing a non-equilibrium state of the phonon-impuriton system of a superfluid mixture situated in the volume filled with the macroparticles. It allows to find the condition describing a steady, thermodynamically non-equilibrium state of $^3{He}-^4{He}$ mixture in confined geometry. The Knudsen effect in the gas of impuritons of a superfluid mixture is investigated by taking into account the contribution of phonons. A model for the collision operator has been proposed to analyze the exact results in the context of the concrete physical situations. An experiment for the investigation of the Knudsen effect in a superfluid mixture of helium isotopes is proposed.