Stability of gravity-driven thin-film flow in the presence of an adjacent gas phase

The stability of a falling liquid film flowing down an inclined channel is revisited. The classical Kapitza criterion for the onset of long wave instability ignored the presence of the adjacent gas phase and provided the critical liquid Reynolds number, Re_cr=5/6cot(β) for the flow destabilization. In the current study, the impact of the adjacent gas on Re_cr is studied via solution of the Orr-Sommerfeld equations in both the liquid and gas phases. The particular case of zero net (recirculating) gas flow is investigated, though this case is shown to be relevant to a wider range of concurrent and countercurrent gas flows. The results obtained confirm the recent finding that Kapitza instability may be fully suppressed in sufficiently small channels. However, in large channels, where the critical perturbation for the flow destabilization is long wave, the Kapitza criterion largely over predicts the critical Reynolds number. This is shown to be related to the increasing impact of the dynamic interactions between the gas and liquid at the interface, whereas the role of the liquid inertia diminishes. A revised analytical expression for Re_cr is derived, which accounts for those interactions in gravity driven thin film flows.