Abstract 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, Recr=5/6cot(β) for the flow destabilization. In the current study, the impact of the adjacent gas on Recr 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 Recr is derived, which accounts for those interactions in gravity driven thin film flows.

中文翻译：

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存在相邻气相时重力驱动的薄膜流动的稳定性

摘要 重新研究了沿倾斜通道流动的下降液膜的稳定性。长波不稳定性开始的经典 Kapitza 标准忽略了相邻气相的存在，并提供了临界液体雷诺数 Recr=5/6cot(β) 用于流动不稳定。在当前的研究中，相邻气体对 Recr 的影响是通过求解 Orr-Sommerfeld 方程的液相和气相来研究的。研究了零净（再循环）气流的特殊情况，尽管这种情况被证明与更广泛的并发和逆流气流相关。获得的结果证实了最近的发现，即在足够小的通道中可以完全抑制 Kapitza 不稳定性。但是，在大型渠道中，在流动不稳定的临界扰动是长波的情况下，Kapitza 准则在很大程度上过度预测了临界雷诺数。这被证明与界面处气体和液体之间动态相互作用的影响越来越大有关，而液体惯性的作用则减弱了。推导出了 Recr 的修正分析表达式，它解释了重力驱动的薄膜流中的那些相互作用。