Thermodynamics and Second Sound in a Two-Fluid Model of Helium II; Revisited

Abstract

Helium II is modelled as a mixture, within macroscopic hydrodynamics, with two partial pressures and a single temperature. The temperature-dependency of concentrations of the superfluid and the normal fluid is accounted for by regarding the mixture as reacting. Moreover, a force of interaction between the superfluid and the normal fluid which traces back to Landau is considered. Accounting for dissipative processes turns out to be a standard application of classical descriptions of viscosity and heat conduction. A detailed analysis of the thermodynamic restrictions is developed. The effciency of the resulting model is tested by revisiting the main phenomena in helium II and evaluating the expression of the wave speed of sound. The mass production has no effect on the wave speed, while the force of interaction affects the propagation of second sound. Also, a simple non-local model is given for the description of persistent currents.