Nonlocal Internal Variable and Superfluid State in Liquid Helium II

Vito Antonio Cimmelli ()
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Vito Antonio Cimmelli: Department of Fundamental and Applied Sciences, University of Basilicata, Viale dell’Ateneo Lucano, 10, 85100 Potenza, Italy

Mathematics, 2025, vol. 13, issue 19, 1-16

Abstract: We present a model of superfluidity based on the internal variable theory. We consider a two-component fluid endowed with a scalar internal variable whose gradient is the counterflow velocity. The restrictions imposed by the second law of thermodynamics are obtained by applying a generalized Coleman–Noll procedure. A set of constitutive equations of the Landau type, with entropy, entropy flux and stress tensor depending on the counterflow velocity, is obtained. The propagation of acceleration waves is investigated as well. It is shown that the first-and-second sound waves may propagate along the system with speeds depending on the physical parameters of the two fluids. First sound waves may propagate in the same direction or in the opposite direction of the counterflow velocity, depending on the concentration of normal and superfluid components. The speeds of second sound waves have the same mathematical form of those propagating in dielectric crystals.

Keywords: superfluid state; counterflow velocity; first sound waves; second sound waves; internal variables; extended Coleman–Noll procedure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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