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Spatial formulation of the Orr‐Sommerfeld equation for thin liquid films flowing down a plane
Author(s) -
Krantz William B.,
Owens W. Brechner
Publication year - 1973
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690190613
Subject(s) - plane (geometry) , stability (learning theory) , flow (mathematics) , mechanics , plane wave , space (punctuation) , harmonic , wavenumber , mathematical analysis , falling (accident) , classical mechanics , physics , mathematics , optics , geometry , computer science , acoustics , machine learning , operating system , medicine , environmental health
The linear stability problem for thin liquid films flowing down a plane is formulated in terms of disturbance which are harmonic in space and time and grow or decay spatially. A closed‐form analytical solution to the resulting spatial formulation of the Orr‐Sommerfeld equation is shown to compare more favorable with wave property data than do solutions to the classical temporal formulation of this stability problem. The predictions of Gaster that the spatial and temporal formulations will be equivalent only for weakly amplified nondispersive disturbances are confirmed for falling film flow.