In this paper, we examine how base flows affect interfacial stabilities in the presence of surfactants. A thin-film flow model, subjected to various base-flow conditions, is employed to mimic a wide class of practical interfacial flows. The base flow can be driven by an external force (e.g., pressure forcing or gravity), an interfacial stress, or their combination. For long-wave perturbations, we show that the stability is governed by a coupled set of evolution equations for the interface and surfactant concentration, so the origin of the stability can be unraveled analytically in line with simpler physical arguments. We also demonstrate that the system can exhibit a variety of stability states; it can be neutral, conditionally stable or unstable, or definitely stable or unstable, determined solely by the nature of the base flow and how it regulates surfactant transport. Two modes are found to determine the stability, the interface and surfactant modes, and characterized by the ratio of the basic interfacial shear force to the external force. The routes to the instability are also identified through the action of the base flow. The base flow plays a dual role in affecting the stability: although the imposition of an interfacial shear destabilizes the interface, an external force can cause stabilization. The competition between these two effects gives rise to stability or instability in a range of the force ratio. The underlying mechanisms are elucidated in detail. A generalized criterion for the onset of instability is also established for one- or two-fluid interfacial flows.

• Received 11 October 2006

DOI:https://doi.org/10.1103/PhysRevE.75.036306