Generalised hydrodynamics and Langevin equations for viscoelastic binary liquid mixtures

For viscoelastic binary liquid mixtures, generalised hydrodynamic equations are set up, in which the relaxation of the chemical potential due to structural relaxation is taken into account. A generalised diffusion equation is obtained, and the spectra of thermal fluctuations of concentration and mass density are derived. For very asymmetric mixtures of a mobile species in a very viscous solvent, such as a glass-forming liquid near its glass transition, coupled Langevin equations for concentration and mass density are derived, which may be applied to the calculation of the intensity of non-equilibrium fluctuations as observed in quench experiments.