Hamiltonian Principle in Binary Mixtures of Euler Fluids with Applications to the Second Sound Phenomena

Henri Gouin (1, 2) , Tommaso Ruggeri

1 LMMT - Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596
2 IUSTI - Institut universitaire des systèmes thermiques industriels

In the present paper we compare the theory of mixtures based on Rational Thermomechanics with the one obtained by Hamilton principle. We prove that the two theories coincide in the adiabatic case when the action is constructed with the intrinsic Lagrangian. In the complete thermodynamical case we show that we have also coincidence in the case of low temperature when the second sound phenomena arises for superfluid Helium and crystals.

Mots clés: Fluid mixtures; Super fluidity; Second sound; Hamilton principle

Domaines: Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]

Henri Gouin, Tommaso Ruggeri. Hamiltonian Principle in Binary Mixtures of Euler Fluids with Applications to the Second Sound Phenomena. Rendiconti Lincei. Matematica e Applicazioni, 2003, 14 (s 9), pp.69-83. ⟨hal-00283148⟩