Nonsymmetric thin film equations with surfactants

Thin film equations are utilised in many different areas of fluid dynamics when there exists a direction in which the length scale can be considered small. Real world examples include bubble caps, tear films, ice sheets and lubrication. We consider thin films with Marangoni effects in the extensional flow regime, where the variations in the small direction are ignored to leading order. In practice, nonsymmetric distributions of surfactants, or surface tension, are possible, for example at the surface of bubbles (Lhuissier and Villermaux 2009) and the rupture of thin films by the deposition of surfactants on one side (Néel and Villermaux 2018). In this talk, we derive the nonsymmetric thin film equations with surfactants. We discuss the effects of the Marangoni number and the Ohnesorge number on the resulting thin film dynamics.