Type
ArticleKAUST Grant Number
KUK-C1-013-04Date
2012-08-10Permanent link to this record
http://hdl.handle.net/10754/597693
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Show full item recordAbstract
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.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.Publisher
Cambridge University Press (CUP)Journal
Journal of Fluid MechanicsISSN
0022-11201469-7645
ae974a485f413a2113503eed53cd6c53
10.1017/jfm.2012.275