  We study the instability of a thin film composed of two miscible fluids
(binary fluid) placed on a solid planar surface. We include the fact that both
the free surface and wetting energies depend on the mixture concentration. By
assuming a linear relationship between these energies and both the bulk and
surface concentrations, we analyze their effect on the phase separation of the
constituent fluids. The problem is formulated within the gradient dynamics
formulation applied to the thin film limit of the Cahn-Hilliard Navier-Stokes
equations. The dependence of the free surface energy on concentration leads to
a Marangoni type of effect, while the wetting energy resulting from
fluid--solid interaction between the film and the substrate is described by a
concentration dependent Hamaker constant. The linear stability analysis
uncovers that both monotonous and oscillatory evolution is possible. While our
problem formulation applies to any binary mixture that can be consistently
modeled via the presented approach, a particular interpretation of the results
is provided for the case of liquid metal alloy films on nanoscale. In this
context, we find that rich dynamics is possible, including the evolution that
may lead to formation of drops of the Janus--type as well as of core-shell
configurations.
