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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.

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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