Fluids with internal degrees of freedom. I. Extended thermodynamics approach

Abstract

Extended irreversible thermodynamics (EIT) is used to derive a complete set of time evolution equations for the state variables describing a general polyatomic fluid. The internal degrees of freedom of the fluid are represented by suitable nonconserved variables. In particular, these time evolution equations are shown to resemble relaxation-type equations. The sign of the unknown coefficients included in such equations is undetermined. However, when a comparison is made with the results obtained from the moment solution method of a kinetic equation for a dilute polyatomic fluid, several of the general features of the phenomenological results are clarified. Indeed, the predictions of kinetic theory fully agree with the basic equations of EIT. This provides a mesoscopic foundation for the theory. The sign of the unknown coefficients appearing in the relaxation-type equations for the nonconserved variables is such that the corresponding relaxation times are positive definite. Therefore, such equations are indeed relaxation equations. Other features of the phenomenological theory are also discussed on the light of the kinetic theoretical results. Further, the usefulness of the theory will be addressed in connection with a subsequent paper where the results here obtained will be used to compute the Rayleigh–Brillouin spectrum for a polyatomic fluid.