  We present the detailed analysis of the diffusive transport of spatially
inhomogeneous fluid mixtures and the interplay between structural and dynamical
properties varying on the atomic scale. The present treatment is based on
different areas of liquid state theory, namely kinetic and density functional
theory and their implementation as an effective numerical method via the
Lattice Boltzmann approach. By combining the first two methods it is possible
to obtain a closed set of kinetic equations for the singlet phase space
distribution functions of each species. The interactions among particles are
considered within a self-consistent approximation and the resulting effective
molecular fields are analyzed. We focus on multispecies diffusion in systems
with short-range hard-core repulsion between particles of unequal sizes and
weak attractive long-range interactions. As a result, the attractive part of
the potential does not contribute explicitly to viscosity but to diffusivity
and the thermodynamic properties. Finally, we obtain a practical scheme to
solve the kinetic equations by employing a discretization procedure derived
from the Lattice Boltzmann approach. Within this framework, we present
numerical data concerning the mutual diffusion properties both in the case of a
quiescent bulk fluid and shear flow inducing Taylor dispersion.
