Marangoni convection in a thin film on a vertically oscillating plate.
Thermocapillary (Marangoni) convection in a thin film on a plate oscillating with a frequency ranging from ultralow to high is considered. By adjusting the vibration amplitude, the impact of the vibration is kept non-negligible. Using the long-wave approximation framework, the amplitude equations are derived for each frequency interval, and linear and weakly nonlinear stability analyses are performed, supplemented by computations where necessary. In the case of a high vibration frequency, the surface tension effectively increases due to vibration, but the film still ruptures. When the frequency is ultralow, the vibration provides gravity modulation, and the surface deformation emerges subcritically, grows fast, and then decays, all during less than half of the vibration period. In the intermediate regime, the vibration either results in a short-wavelength instability or it does not affect the Marangoni convection.
Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, Perm 614013, Russia.
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Shklyaev
Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, Perm 614013, Russia.|Department of Theoretical Physics, Perm State University, Perm 614990, Russia.
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Alabuzhev
Department of Mathematics, Western Kentucky University, 1906 College Heights Boulevard, Bowling Green, Kentucky 42101, USA.
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Khenner