Generalized hydrodynamics of binary fluids

The k-dependent hydrodynamic fluctuations for binary classical fluids are discussed. The aim of this paper is to give the microscopic basis for the phenomenological formulation of hydrodynamics of binary fluids which was explored by the present author. The generalized Langevin equation formalism is used to derive closed equations for the fluctuations of temperature, mass, relative velocity, etc. Explicit expressions for the k-dependent thermodynamic susceptibilities are also derived. Using these quantities, it is shown that the equations for fluctuations reduce to the macroscopic equations in the long wavelength limit.