  A multicomponent extension of our recent theory of simple fluids [ U.M.B.
Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is
proposed to describe miscible and immiscible liquid mixtures under
inhomogeneous, non steady conditions typical of confined fluid flows. We first
derive from a microscopic level the evolution equations of the phase space
distribution function of each component in terms of a set of self consistent
fields, representing both body forces and viscous forces (forces dependent on
the density distributions in the fluid and on the velocity distributions).
Secondly, we solve numerically the resulting governing equations by means of
the Lattice Boltzmann method whose implementation contains novel features with
respect to existing approaches. Our model incorporates hydrodynamic flow,
diffusion, surface tension, and the possibility for global and local viscosity
variations. We validate our model by studying the bulk viscosity dependence of
the mixture on concentration, packing fraction and size ratio. Finally we
consider inhomogeneous systems and study the dynamics of mixtures in slits of
molecular thickness and relate structural and flow properties.
