Regular hexagons and stripes on Marangoni and Rayleigh-Taylor unstable volatile thin films

Thin volatile Newtonian liquid films with a free surface on a cooled horizontal substrate are studied theoretically and numerically. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase, regular surface deformation patterns in the form of long-wave hexagons or stripes having a well defined lateral length scale are observed, depending on the instability mechanism. This is different to the case without evaporation where rupture or coarsening to larger and larger spatially disordered patterns is seen in the long time limit. We propose to use such a system to create a regular structuring of the film's surface. Heat production by latent heat and the influence of a temperature dependent surface tension (Marangoni effect) are included as well. Special emphasis is laid on the so-called anomalous Marangoni effect. In this case a parameter region where stripes should occur already at threshold is found by means of a systematic weakly non-linear analysis.