Linear theory of Faraday instability in viscous liquids
1996; Royal Society; Volume: 452; Issue: 1948 Linguagem: Inglês
10.1098/rspa.1996.0056
ISSN1471-2946
Autores Tópico(s)Characterization and Applications of Magnetic Nanoparticles
ResumoRestricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Kumar Krishna 1996Linear theory of Faraday instability in viscous liquidsProc. R. Soc. Lond. A.4521113–1126http://doi.org/10.1098/rspa.1996.0056SectionRestricted accessArticleLinear theory of Faraday instability in viscous liquids Krishna Kumar Google Scholar Find this author on PubMed Search for more papers by this author Krishna Kumar Google Scholar Find this author on PubMed Published:01 January 1996https://doi.org/10.1098/rspa.1996.0056AbstractThe linear stability of the plane free surface of a viscous liquid on a horizontal plate under vertical sinusoidal oscillation is analysed theoretically. The free surface of a laterally unbounded liquid of any depth h may always be excited to standing waves if the external acceleration is raised above a critical value ac. For a fixed external frequency ω, solutions are possible only within certain bands of wave numbers k for a given forcing amplitude above ac, that is, within tongue-like stability zones in the a-k plane. The analysis for a shallow layer of viscous fluids shows new qualitative behaviours compared to the nearly inviscid theory. It predicts a series of bicritical points, where both harmonic and subharmonic solutions exist for the same forcing amplitude and forcing frequency. This makes harmonic solutions possible at the onset in a laterally large container, which is qualitatively different from the results of nearly inviscid theory. For a low viscosity fluid of small depths, the damping coefficient may be considered proportional to (vω)1/2/h in contrast to vk2 predicted by the nearly inviscid theory. An approximate analytic expression is derived for the lower part of the lowest marginal curve in cases when the depth of the liquid is much larger than the thickness of the viscous boundary layer formed at the bottom plate. This approximate threshold agrees well with that of recent experiments with viscous liquids.FootnotesThis text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Zhang S, Orosco J and Friend J (2023) Onset of Visible Capillary Waves from High-Frequency Acoustic Excitation, Langmuir, 10.1021/acs.langmuir.2c03403, 39:10, (3699-3709), Online publication date: 14-Mar-2023. 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