Translational hydrodynamics for binary mixtures: Memory from internal molecular relaxation

We consider a binary fluid mixture made up of a monatomic species and a two level molecular species and investigate the decay of correlations in the hydrodynamic variables. By restricting our considerations to the translationally hydrodynamic situations, we deduce a set of generalised hydrodynamic equations in which the frequency, ω, and wavenumber, k, dependent memory arises solely from the internal molecular relaxation. From these generalised hydrodynamic equations, we identify various (k, ω) dependent transport coefficients and the relaxation time which depends on k. We also compute the spectrum of (polarised) light scattered from such a binary mixture. We illustrate the dependence on k, ω and concentration in the problem by a numerical calculation of the generalised transport coefficients, the Rayleigh-Brillouin spectrum and the dispersion of various modes in this spectrum for the case of thermal relaxation in a parahydrogen-helium mixture.