Mixture of Fluids involving Entropy Gradients and Acceleration Waves in Interfacial Layers

Henri Gouin (1, 2) , Tommaso Ruggeri

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

Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the gradient of the entropies of each component. A Lagrangian associated with the kinetic energy and the internal energy allows to obtain the equations of momentum for each component and for the barycentric motion of the mixture. We obtain also the balance of energy and we prove that the equations are compatible with the second law of thermodynamics. Though the system is of parabolic type, we prove that there exist two tangential acceleration waves that characterize the interfacial motion. The dependence of the internal energy of the entropy gradients is mandatory for the existence of this kind of waves. The differential system is non-linear but the waves propagate without distortion due to the fact that they are linearly degenerate (exceptional waves).

Mots clés: Fluid mixtures; acceleration waves; interfacial layers

Domaines: Mécanique des fluides [physics.class-ph]

Henri Gouin, Tommaso Ruggeri. Mixture of Fluids involving Entropy Gradients and Acceleration Waves in Interfacial Layers. European Journal of Mechanics - B/Fluids, 2005, 24 (5), pp.596-613. ⟨10.1016/j.euromechflu.2005.01.001⟩. ⟨hal-00204143⟩