Stability of a bi-layer free film: Simultaneous or individual rupture events?

We consider the stability of a long free film of liquid composed of two immiscible layers of differing viscosities, where each layer experiences a van der Waals force between its interfaces. We analyse the different ways in which the system can exhibit interfacial instability when the liquid layers are sufficiently thin. For an excess of surfactant on one gas-liquid interface, the coupling between the layers is relatively weak and the instability is manifested as temporally separated rupture events in each layer. Conversely, in the absence of surfactant, the coupling between the layers is much stronger and the instability is manifested as rupture of both layers simultaneously. These features are consistent with recent experimental observations.