J. Non-Equilib. Thermodyn. 2003  Vol. 28  pp. 69–84 Thermodynamics and Second Sound in a Two-Fluid Model of Helium II; Revisited M. Fabrizio 1 , A. Morro 2 1 Department of Mathematics, University of Bologna, Bologna, Italy 2 DIBE, University of Genova, Genoa, Italy Registration Number 940 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. 1. Introduction Helium II is currently considered to consist of two phases. One phase is designated the superfluid and is composed of atoms in their energetic ground state. The other phase, the normal fluid, is composed of atoms in energetically elevated states. The superfluid has no entropy, is non-viscous and has no dynamic interaction with the normal fluid. Among the early works on the description of helium II we mention references [1–4]. F. London [2] envisaged the formation of liquid helium II from liquid helium I at the !-point as a peculiar type of quantum condensation known as Bose-Einstein condensation. This phenomenon is framed in momentum space where the condensed particles have zero-point energy and momentum. Next Feynman [5] succeeded in deriving, on the basis of quantum statistics, the energy level and energy gap picture of Landau, while at the same time retaining the Bose-Einstein condensation idea of London. J. Non-Equilib. Thermodyn.  2003  Vol. 28  No. 1 # Copyright 2003 Walter de Gruyter  Berlin  New York Brought to you by | Georgetown University Authenticated Download Date | 5/22/15 6:45 AM