Parametrically driven surface waves in surfactant–covered liquids

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Kumar Satish and Matar Omar K. 2002Parametrically driven surface waves in surfactant–covered liquidsProc. R. Soc. Lond. A.4582815–2828http://doi.org/10.1098/rspa.2002.1017SectionRestricted accessResearch articleParametrically driven surface waves in surfactant–covered liquids Satish Kumar Satish Kumar Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Ave. SE, Minneapolis, MN 55455, USA Google Scholar Find this author on PubMed Search for more papers by this author and Omar K. Matar Omar K. Matar Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK Google Scholar Find this author on PubMed Search for more papers by this author Satish Kumar Satish Kumar Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Ave. SE, Minneapolis, MN 55455, USA Google Scholar Find this author on PubMed Search for more papers by this author and Omar K. Matar Omar K. Matar Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2002https://doi.org/10.1098/rspa.2002.1017AbstractVertical vibration will excite standing waves on a liquid free surface. We perform a linear–stability analysis for viscous and viscoelastic liquids of arbitrary depth to determine the role that insoluble surfactants play in the formation of these parametrically driven surface waves. We find that in order to obtain time–periodic solutions which involve Marangoni forces in a non–trivial way, it is necessary to consider the high–Peclet number limit of the surfactant transport equation. Floquet theory is applied to the linearized governing equations to obtain a recursion relation for the temporal modes of the free–surface deflection. The recursion relation is then solved numerically to obtain the critical vibration amplitude needed to excite the surface waves, and the corresponding wavenumber. The results show that the presence of surfactants raises or lowers the critical amplitude and wavenumber depending on the spatial phase shift between the surfactant–concentration variations and surface deflections. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited bySamanta A (2020) Effect of porous layer on the Faraday instability in viscous liquid, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476:2239, Online publication date: 1-Jul-2020. Jia B, Xie L, Yang L, Fu Q and Cui X (2020) Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations, Physics of Fluids, 10.1063/5.0016311, 32:8, (083104), Online publication date: 1-Aug-2020. Zhu Z, Song Y, Liu X, Xiao D, Yang L and Huang L (2019) Observation of alternately localized Faraday waves in a narrow tank, Physical Review Fluids, 10.1103/PhysRevFluids.4.014807, 4:1 Mikishev A, Friedman B and Nepomnyashchy A (2016) Generation of transverse waves in a liquid layer with insoluble surfactant subjected to temperature gradient, Fluid Dynamics Research, 10.1088/0169-5983/48/6/061403, 48:6, (061403), Online publication date: 1-Dec-2016. Ibrahim R (2015) Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems, Journal of Fluids Engineering, 10.1115/1.4029544, 137:9, Online publication date: 1-Sep-2015. Strickland S, Shearer M and Daniels K (2015) Spatiotemporal measurement of surfactant distribution on gravity–capillary waves, Journal of Fluid Mechanics, 10.1017/jfm.2015.352, 777, (523-543), Online publication date: 25-Aug-2015. This Issue08 November 2002Volume 458Issue 2027 Article InformationDOI:https://doi.org/10.1098/rspa.2002.1017Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/11/2002Published in print08/11/2002 License: Citations and impact Keywordsviscoelasticitywavesinstabilitysurfactantfree surface