  We study phase separation in thin films using the Navier--Stokes
Cahn--Hilliard equations in the lubrication approximation, modeling
substrate-film interactions with a van der Waals potential. We investigate the
thin-film equations numerically and compare them with experimental results. We
find that the model captures the qualitative features of real phase-separating
fluids, in particular the tendency of concentration gradients to produce film
thinning and surface roughening. The ultimate outcome of the phase separation
depends strongly on the dynamical backreaction of concentration gradients on
the flow, as we demonstrate when a shear stress is applied at the film's
surface. When the backreaction is small, the phase domain boundaries align with
the direction of the imposed stress, while as the backreaction is made larger,
the domains begin to align in the perpendicular direction.
