Green's functions and hydrodynamics for isotopic binary diffusion

We study classical binary fluid mixtures in which densities vary on very short time (ps) and length (nm) scales, such that hydrodynamics does not apply. In a pure fluid with a localized heat pulse the breakdown of hydrodynamics was overcome using Green's functions which connect the initial densities to those at later times. Numerically it appeared that for long times the results from the Green's functions would approach hydrodynamics. In this paper we extend the Green's functions theory to binary mixtures. For the case of isothermal isobaric mutual diffusion in isotopic binary mixtures and ideal binary mixtures, which is easier to handle than heat conduction yet still non-trivial, we show analytically that in the Green's function approach one recovers hydrodynamic behaviour at long time scales provided the system reaches local equilibrium at long times. This is a first step toward giving the Green's function theory a firmer basis because it can for this case be considered as an extension of hydrodynamics.