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Pressure-driven flow of a thin viscous sheet

Published online by Cambridge University Press:  26 April 2006

B. W. Van De Fliert ,
P. D. Howell  and
J. R. Ockenden
B. W. Van De Fliert
Affiliation:
Mathematical Institute, 24–29 St Giles’, Oxford, UK
P. D. Howell
Affiliation:
Mathematical Institute, 24–29 St Giles’, Oxford, UK
J. R. Ockenden
Affiliation:
Mathematical Institute, 24–29 St Giles’, Oxford, UK
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Abstract

Systematic asymptotic expansions are used to find the leading-order equations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatures, the Navier–Stokes equations with appropriate free-surface conditions are simplified to give a ‘shell-theory’ model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to be employed. The effects of surface tension, gravity and inertia can also be incorporated in the model.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 292 , 10 June 1995 , pp. 359 - 376
Copyright
© 1995 Cambridge University Press

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