Relaxation of internal energy and bulk viscosities in fluid models

We investigate internal energy relaxation processes and the corresponding volume viscosity coefficients in fluids. We successively consider a simplified two temperature model, a two-mode two temperature model, and finally a well as state-to-state model for a mixture of polyatomic species. The apparition of volume - or bulk - viscosity coefficients in relaxation regimes is studied as well as the relations with the limiting equilibrium one-temperature bulk viscosity coefficients. Monte Carlo numerical simulations from the literature are next addressed and found to be in agreement with the kinetic theory analysis. New numerical simulations of state-to-state mixtures of Hydrogen and Helium are presented and found to be in full agreement with the theory. The impact of volume viscosity in the mechanics of fluids and the success of the wrong Stokes approximation are also discussed.