Taroni, M. and Breward, C. J. W. and Howell, P. D. and Oliver, J. M.
(2012)
Boundary conditions for free surface inlet and outlet
problems.
Journal of Fluid Mechanics
.
(Submitted)

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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 filmforming meniscus. In the limit of vanishing capillary number Ca it is wellknown that the flux scales with Ca2/3, but this classical result is nonuniform as the contact angle approaches . By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the farfield behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes overdetermined. The implications of this result for the modelling of coating flows are discussed.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1540 
Deposited By:  Peter Hudston 
Deposited On:  04 Jul 2012 08:05 
Last Modified:  29 May 2015 19:14 
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