Effect of surfactants on the inertialess instability of a two-layer film flow

Abstract

The effect of insoluble surface and interfacial surfactants on the inertialess instability of a two-fluid film flow down an inclined plane is investigated based on a normal mode analysis. The results reveal that the inertialess instability of relatively long waves can be predominantly weakened by a surface surfactant and enhanced by an interfacial surfactant. For sufficiently large viscosity ratio of the upper layer to the lower one, a destabilizing influence of the surface surfactant is also detected; this is thus a rare example demonstrating the possible destabilizing effect of the surfactant on the flow with a free surface. When the upper layer is less viscous and hence the instability due to the viscosity stratification disappears, a new instability can be triggered by the presence of an interfacial surfactant. Both the surfactants on the surface and the interface can stabilize or destabilize the short-wave instabilities, which occur for negligible surface and interfacial tensions.