Dynamics of a thin film driven by a moving pressure source

Motivated by the liquid metal coating on a divertor in a tokamak, we investigate the flow of a thin film of incompressible fluid on an inclined substrate subjected to a localised external pressure that oscillates parallel to the substrate. When the movement of the pressure occurs on a time scale significantly longer than the characteristic time for the thin film to equilibrate, the system is quasi steady. In the opposite extreme, where the pressure oscillates much faster than the response time of the free surface, a multiple scales analysis shows that the free surface is exposed to an effective time-averaged pressure profile. Thus the oscillations can act to spread the momentum load of the applied pressure, resulting in smaller deformations of the liquid film.
In the intermediate case, where the intrinsic and external time-scales are similar, we find that there exists a critical speed of oscillations which maximises the free-surface deflection and results in a possibly dangerous thinning of the film. Further local maxima in the free-surface deflection are caused by a fascinating non-local wave interaction mechanism.