Traveling waves for a thin film with gravity and insoluble surfactant

Joachim Escher (1) , Matthieu Hillairet (2, 3) , Philippe Laurencot (4) , Christoph Walker (5)

1 IFAM - Institute for Applied Mathematics
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 ICJ - Institut Camille Jordan
4 IMT - Institut de Mathématiques de Toulouse UMR5219
5 IFAM - Institut für Angewandte Mathematik

Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully surfactant-coated film to an uncoated film. The regularity of the traveling wave depends on whether or not surface diffusion of the insoluble surfactant is included.

Mots clés: Thin films; surfactant; traveling wave

Domaines: Equations aux dérivées partielles [math.AP]

Joachim Escher, Matthieu Hillairet, Philippe Laurencot, Christoph Walker. Traveling waves for a thin film with gravity and insoluble surfactant. SIAM Journal on Applied Dynamical Systems, 2015, 14 (4), pp.1991--2012. ⟨10.1137/140963613⟩. ⟨hal-00931037⟩