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    Boundary conditions for free surface inlet and outlet problems

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    Type
    Article
    Authors
    Taroni, M.
    Breward, C. J. W.
    Howell, P. D.
    Oliver, J. M.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2012-08-10
    Permanent link to this record
    http://hdl.handle.net/10754/597693
    
    Metadata
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    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.
    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 Mechanics
    ISSN
    0022-1120
    1469-7645
    DOI
    10.1017/jfm.2012.275
    ae974a485f413a2113503eed53cd6c53
    10.1017/jfm.2012.275
    Scopus Count
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