Dynamical Effects and Phase Separation in Thin Films

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.