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Resonance in viscous film flow over topography
Author(s) -
Heining Christian,
Wierschem Andreas,
Bontozoglou Vasilis,
Aksel Nuri,
Uecker Hannes
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700021
Subject(s) - harmonics , bistability , resonance (particle physics) , dimensionless quantity , nonlinear system , flow (mathematics) , nonlinear resonance , mechanics , coupling (piping) , physics , condensed matter physics , materials science , atomic physics , optoelectronics , composite material , voltage , quantum mechanics
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)