TY - JOUR
T1 - Boundary conditions for free surface inlet and outlet problems
AU - Taroni, M.
AU - Breward, C. J. W.
AU - Howell, P. D.
AU - Oliver, J. M.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/8/10
Y1 - 2012/8/10
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/597693
UR - https://www.cambridge.org/core/product/identifier/S0022112012002753/type/journal_article
UR - http://www.scopus.com/inward/record.url?scp=84866654014&partnerID=8YFLogxK
U2 - 10.1017/jfm.2012.275
DO - 10.1017/jfm.2012.275
M3 - Article
SN - 0022-1120
VL - 708
SP - 100
EP - 110
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -