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Falling liquid films in narrow tubes: occlusion scenarios. (English) Zbl 1460.76045
Summary: We study a gravity-driven wavy liquid film falling down the inner surface of a narrow cylindrical tube in the presence of an active core gas flow. We employ the model of the first author and the third author [ibid. 762, 68–109 (2015; Zbl 1335.76011)] to investigate the role of surface waves in the occlusion of the tube. We consider four real working liquids and reproduce several experiments from the literature, focusing on conditions where the Bond number is greater or equal to unity. We prove that occlusion is triggered by spatially growing surface waves beyond the limit of saturated travelling-wave solutions, and delimit three possible regimes for a naturally evolving wavy film: (i) certain occlusion, when the liquid Reynolds number is greater than the limit of the spatially most amplified travelling waves. Occlusion is caused by surface waves emerging from linear wave selection (scenario I); (ii) conditional occlusion, when the most amplified waves possess travelling states but longer waves do not. Occlusion is triggered by secondary instability, generating long waves through nonlinear coarsening dynamics (scenario II); and (iii) impossible occlusion, when travelling waves always exist, no matter how great their wavelength. We show that certain occlusion is delayed by gravity and precipitated by a counter-current gas flow, axial viscous diffusion (high-viscosity liquids) and inertia (low-viscosity liquids). The latter two effects are also found to determine whether the occlusion mechanism is dictated by loss of travelling-wave solutions or absolute instability. Finally, we show that occlusion can be prevented through coherent inlet forcing. As a side benefit, we introduce an augmented version of our model based on a localized additional force term that allows representing stable travelling liquid pseudo-plugs.
MSC:
76A20 Thin fluid films
Software:
Gerris
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