Boundary conditions for free surface inlet and outlet problems

Handle URI:
http://hdl.handle.net/10754/597693
Title:
Boundary conditions for free surface inlet and outlet problems
Authors:
Taroni, M.; Breward, C. J. W.; Howell, P. D.; Oliver, J. M.
Abstract:
We 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.
Citation:
Taroni 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.
Publisher:
Cambridge University Press (CUP)
Journal:
Journal of Fluid Mechanics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
10-Aug-2012
DOI:
10.1017/jfm.2012.275
Type:
Article
ISSN:
0022-1120; 1469-7645
Sponsors:
This 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.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorTaroni, M.en
dc.contributor.authorBreward, C. J. W.en
dc.contributor.authorHowell, P. D.en
dc.contributor.authorOliver, J. M.en
dc.date.accessioned2016-02-25T12:44:32Zen
dc.date.available2016-02-25T12:44:32Zen
dc.date.issued2012-08-10en
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.en
dc.identifier.issn0022-1120en
dc.identifier.issn1469-7645en
dc.identifier.doi10.1017/jfm.2012.275en
dc.identifier.urihttp://hdl.handle.net/10754/597693en
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.en
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.en
dc.publisherCambridge University Press (CUP)en
dc.subjectcapillary flowsen
dc.subjectlubrication theoryen
dc.subjectthin filmsen
dc.titleBoundary conditions for free surface inlet and outlet problemsen
dc.typeArticleen
dc.identifier.journalJournal of Fluid Mechanicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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