Non-linear constitutive and diffusion equations in the Burnett regime

A phenomenological method is presented to obtain the hydrodynamic equations for a multicomponent, isotropic, non-reactive fluid to any order in the spatial inhomogeneities. Two assumptions are made, the existence of a local equilibrium state and a non-linear dependence of the fluxes on the thermodynamic forces. In particular, the generalized form for the diffusion equation, to fourth order in the gradients, is obtained. Also, we derive the hydrodynamic equations for a binary mixture in a non-linear Burnett regime. The comparison of our results with others given in the literature and, in particular with those recently derived using the time-dependent correlation function formalism, is given. Finally some remarks are made in connection with the question about the existence of the transport coefficients beyond the Navier-Stokes regime.