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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.200700660
Subject(s) - dimensionless quantity , resonance (particle physics) , bistability , harmonics , flow (mathematics) , nonlinear system , capillary action , mechanics , viscous liquid , nonlinear resonance , capillary wave , materials science , viscoelasticity , physics , optics , composite material , optoelectronics , atomic physics , voltage , surface wave , 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 capillary‐gravity waves traveling against the flow. Nonlinear terms produce higher harmonics resonance which in particular may lead to bistable resonance similar to that of the driven Duffing oscillator. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)