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dc.contributor.authorGoodnight, Randall James Truetten_US
dc.date.accessioned2013-06-02T08:00:30Z
dc.date.available2013-06-02T08:00:30Z
dc.date.issued2013-06-01en_US
dc.identifier.othervt_gsexam:1280en_US
dc.identifier.urihttp://hdl.handle.net/10919/23125
dc.description.abstractWe examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectThin Filmsen_US
dc.subjectUndercompressive Shocken_US
dc.subjectNon-Convex Fluxen_US
dc.subjectMarangoni Stressen_US
dc.subjectSurface Tensioen_US
dc.titleDerivation of an Evolution Equation for Two-Dimensional Waves on Thin Filmsen_US
dc.typeThesisen_US
dc.contributor.departmentEngineering Science and Mechanicsen_US
dc.description.degreeMaster of Scienceen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineEngineering Mechanicsen_US
dc.contributor.committeechairCramer, Mark S.en_US
dc.contributor.committeememberRagab, Saad A.en_US
dc.contributor.committeememberJung, Sunghwanen_US


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