Resonance in viscous film flow over topography |
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| Authors: | Christian Heining Andreas Wierschem Vasilis Bontozoglou Nuri Aksel Hannes Uecker |
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| Institution: | 1. University of Bayreuth, Department of Applied Mechanics and Fluid Dynamics, 95440 Bayreuth, Germany;2. Technische Universität München, Lehrstuhl für Systemverfahrenstechnik, 85350 Freising, Germany;3. Department of Mechanical and Industrial Engineering, University of Thessaly, Pedion Areos, 38334 Volos, Greece;4. Institute of Analysis, Dynamics and Modelling, University of Stuttgart, 70569 Stuttgart, Germany |
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| Abstract: | We study viscous gravity-driven films flowing over periodically undulated substrates. Linear analysis describes resonance in steady flow along small bottom corrugations for films of arbitrary thickness. Depending on the dimensionless film thickness we find different regimes for the resonance, which is associated with the interaction of the undulated film with capillarygravity waves traveling against the flow. Nonlinear resonance produces higher harmonics and bistable resonance. The higher harmonics are due to higher harmonics resonance and due to the nonlinear coupling to lower harmonics. For the bistable resonance we derive a minimum model showing that the bistability corresponds essentially to that of the driven Duffing oscillator. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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