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Thin liquid films on a slightly inclined heated plate. (English) Zbl 1063.76032
The authors revisit the problem of a heated thin liqid film on a slightly inclined substrate with two motivations in mind: a) they are interested in the multiplicity of solutions to the nonlinear evolution equation and their stability properties, and b) the authors wish to understand the effects of small inclination of the substrate. The essence of the problem is captured by a simplified model that omits complications due to effective molecular interactions and the effects of inertia and evaporation. The authors focus on one-dimensional films, and examine the consequences of a long wavelength longitudinal instability of a flat film that sets in when the Maragoni number exceeds a critical value. They are able to explore the sequence of transitions that takes place with increasing inclination of the substrate before the Kuramoto-Sivashinsky-like behaviour is recovered.

76E17 Interfacial stability and instability in hydrodynamic stability
76A20 Thin fluid films
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI
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