  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).
