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Thin film equations with soluble surfactant and gravity: Modeling and stability of steady states

Escher, Joachim; Hillairet, Matthieu; Laurençot, Philippe; Walker, Christoph (2012), Thin film equations with soluble surfactant and gravity: Modeling and stability of steady states, Mathematische Nachrichten, 285, 2-3, p. 210-222. http://dx.doi.org/10.1002/mana.201010009

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1002.1785v1
Date
2012
Journal name
Mathematische Nachrichten
Volume
285
Number
2-3
Publisher
Wiley
Pages
210-222
Publication identifier
http://dx.doi.org/10.1002/mana.201010009
Metadata
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Author(s)
Escher, Joachim
Hillairet, Matthieu
Laurençot, Philippe
Walker, Christoph
Abstract (EN)
A thin film on a horizontal solid substrate and coated with a soluble surfactant is considered. The governing degenerate parabolic equations for the film height and the surfactant concentrations on the surface and in the bulk are derived using a lubrication approximation when gravity is taken into account. It is shown that the steady states are asymptotically stable.
Subjects / Keywords
Thin films; lubrication approximation; degenerate parabolic equations; linearized stability

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