Boundary conditions for free surface inlet and outlet problems

M. Taroni, C. J. W. Breward, P. D. Howell, J. M. Oliver

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10 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)100-110
Number of pages11
JournalJournal of Fluid Mechanics
StatePublished - Aug 10 2012
Externally publishedYes

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