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

TL;DR

This paper develops a Hamiltonian framework for thermocapillary fluid mixtures considering entropy gradient effects, revealing the existence of special acceleration waves at interfaces that propagate undistorted due to linear degeneracy.

Contribution

It introduces a novel Hamiltonian-based model incorporating entropy gradients and demonstrates the existence of undistorted acceleration waves in interfacial layers.

Findings

Existence of tangential acceleration waves in the mixture.

Waves are linearly degenerate and propagate without distortion.

Internal energy dependence on entropy gradients is essential for wave existence.

Abstract

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).