The dynamics of the Rayleigh-Taylor instability of a two-dimensional thin liquid film placed on the underside of a planar substrate subjected to either normal or tangential harmonic forcing is investigated here in the framework of a set of long-wave evolution equations accounting for inertial effects derived earlier by Bestehorn, Han, and Oron [“Nonlinear pattern formation in thin liquid films under external vibrations,” Phys. Rev. E 88, 023025 (2013)]. In the case of tangential vibration, the linear stability analysis of the time-periodic base state with a flat interface shows the existence of the domain of wavenumbers where the film is unstable. In the case of normal vibration, the linear stability analysis of the quiescent base state reveals that the instability threshold of the system is depicted by a combination of distinct thresholds separate for the Rayleigh-Taylor and Faraday instabilities. The nonlinear dynamics of the film interface in the case of the static substrate results in film rupture. However, in the presence of the substrate vibration in the lateral direction, the film interface saturates in certain domains in the parameter space via the mechanism of advection induced by forcing, so that the continuity of the film interface is preserved even in the domains of linear instability while undergoing the time-periodic harmonic evolution. On the other hand, sufficiently strong forcing introduces a new inertial mode of rupture. In the case of the normal vibration, the film evolution may exhibit time-periodic, harmonic or subharmonic saturated waves apart of rupture. The enhancement of the frequency or amplitude of the substrate forcing promotes the destabilization of the system and a tendency to film rupture at the nonlinear stage of its evolution. A possibility of saturation of the Rayleigh-Taylor instability by either normal or unidirectional tangential forcing in three dimensions is also demonstrated.
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Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration
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Research Article|
May 30 2017
Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration
Elad Sterman-Cohen;
Elad Sterman-Cohen
1
Advanced Defense Systems Ltd.
, P.O. Box 2250(19), Haifa 3102102, Israel
2Department of Mechanical Engineering,
Technion-Israel Institute of Technology
, Haifa 32000, Israel
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Michael Bestehorn;
Michael Bestehorn
3Department of Theoretical Physics,
Brandenburg University of Technology
, 03044 Cottbus, Germany
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Alexander Oron
Alexander Oron
2Department of Mechanical Engineering,
Technion-Israel Institute of Technology
, Haifa 32000, Israel
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Physics of Fluids 29, 052105 (2017)
Article history
Received:
April 06 2017
Accepted:
May 11 2017
Connected Content
A correction has been published:
Erratum: “Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration” [Phys. Fluids 29, 052105 (2017)]
Citation
Elad Sterman-Cohen, Michael Bestehorn, Alexander Oron; Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration. Physics of Fluids 1 May 2017; 29 (5): 052105. https://doi.org/10.1063/1.4984082
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