Formation of patterns induced by thermocapillarity and gravity

The authors consider a liquid film on a slightly inclined plane driven by gravity and thermocapillarity. They derive an equation describing the nonlinear evolution of the interface between the liquid and the atmosphere. In line with an approach introduced previously by them they preserve the full impact of the curvature that contributes towards the formation of bubbles and together with convection induced by the inclined plane contributes towards either wave breaking or the prevention of rupture that otherwise occurs. Travelling waves are also possible. A variety of possible equilibrium states is also discussed.