Thin liquid films on a slightly inclined heated plate

The behavior of a thin liquid film on a uniformly heated substrate is considered. When the substrate is horizontal and the Marangoni number sufficiently large the film breaks up into a periodic array of drops. When the substrate is slightly inclined this drop-like state slides down the substrate. The relation between these states is discussed and their stability properties with respect to longitudinal perturbations are determined. The results shed light on the multiplicity of states accessible to systems of this type and on the possible transitions among them.