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

Escher, Joachim; Hillairet, Matthieu; Laurençot, Philippe; Walker, Christoph

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

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