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Non-local kinetic theory of inhomogeneous liquid mixtures

In this work we investigate the dynamical properties of a mixture of mutually interacting spherical molecules of different masses and sizes. From an analysis of the microscopic laws governing the motion of the molecules we derive a set of non-local self-consistent equations for the singlet phase-space distribution functions. The theory is shown to reproduce the hydrodynamic equations for the densities of each species, the total momentum and the local temperature. The non-ideal gas interaction term is separated into a contribution due to the repulsive part, which is treated by means of the revised Enskog theory for hard spheres, and an attractive contribution treated within the random phase approximation. The present formulation accounts for the effects of the density and velocity inhomogeneities, both on the thermodynamic and transport properties of the fluid. In a special limit, where one species is massive and diluted, the theory leads to a description that is formally identical to the dynamic density functional equation governing the time evolution of a colloidal system. The derivation also determines the dependence of the friction coefficient, appearing in the dynamic density functional theory, on the microscopic parameters of the solvent. However, the predicted value takes into account only the collisional contributions to the friction and not the Stokes friction of hydrodynamic origin, suggesting that velocity correlations should be incorporated in a more complete treatment.