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dc.contributor.authorTaroni, M.
dc.contributor.authorBreward, C. J. W.
dc.contributor.authorHowell, P. D.
dc.contributor.authorOliver, J. M.
dc.date.accessioned2016-02-25T12:44:32Z
dc.date.available2016-02-25T12:44:32Z
dc.date.issued2012-08-10
dc.identifier.citationTaroni M, Breward CJW, Howell PD, Oliver JM (2012) Boundary conditions for free surface inlet and outlet problems. Journal of Fluid Mechanics 708: 100–110. Available: http://dx.doi.org/10.1017/jfm.2012.275.
dc.identifier.issn0022-1120
dc.identifier.issn1469-7645
dc.identifier.doi10.1017/jfm.2012.275
dc.identifier.urihttp://hdl.handle.net/10754/597693
dc.description.abstractWe investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.
dc.description.sponsorshipThis publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). In addition, the authors are grateful to EPSRC and Du Pont (UK) Ltd. for their financial support via grant CASE 2006/015.
dc.publisherCambridge University Press (CUP)
dc.subjectcapillary flows
dc.subjectlubrication theory
dc.subjectthin films
dc.titleBoundary conditions for free surface inlet and outlet problems
dc.typeArticle
dc.identifier.journalJournal of Fluid Mechanics
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04
dc.date.published-online2012-08-10
dc.date.published-print2012-10


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