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Steady, viscous, free-surface flow on a rotating cylinder

Published online by Cambridge University Press:  26 April 2006

Hansen Erik B.  and
Kelmanson Mark A.
Hansen Erik B.
Affiliation:
Mathematical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark
Kelmanson Mark A.
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK
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Abstract

The commonly observed phenomenon of steady, viscous, free-surface flow on the outer surface of a rotating cylinder is investigated by means of an iterative, integral-equation formulation applied to the Stokes approximation of the Navier-Stokes equations. The method of solution places no restriction on the thickness of the fluid layer residing on the cylinder surface; indeed, results are presented for cases where the layer thickness is of the same order of magnitude as the cylinder radius.

Free-surface profiles and free-surface velocity distributions are presented for a range of flow parameters. Where appropriate, comparisons are made with the results of thinfilm theory; excellent agreement is observed.

For all film thicknesses and surface tensions, results show a high degree of symmetry about a horizontal axis even though the gravity field is vertical. A proof is presented that, for vanishing surface tension, this is a consequence of the Stokes approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 91 - 108
Copyright
Copyright © Cambridge University Press 1994

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