Surfactant-induced fingering phenomena in thin film flow down an inclined plane

We consider the dynamics of a thin liquid film covered with insoluble surfactant flowing down an inclined plane. A coupled pair of nonlinear partial differential equations for the film height and surfactant concentration are derived using lubrication theory. Two configurations of fluid and surfactant are considered: constant flux and constant volume. Examination of the base states reveals the presence of propagating wave fronts in both configurations. Application of a transient growth analysis demonstrates the existence of an instability near the leading edge of the fluid that is found to be vulnerable to transverse disturbances of intermediate wavenumber. Our results illustrate that several features of the much studied uncontaminated film flow problem are modified due to the inclusion of surfactant.