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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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References

Hansen, E. B. 1987 Stokes flow down a wall into an infinite pool. J. Fluid Mech. 178, 243–256.Google Scholar
Kelmanson, M. A. 1994 Theoretical and experimental analyses of the maximum-supportable fluid load on a rotating cylinder. Submitted.Google Scholar
Madsen, K. 1975 An algorithm for minimax solution of overdetermined systems of non-linear equations. J. Inst. Maths Applics 16, 321–328.Google Scholar
Madsen, K., Hegelund, P. & Hansen, P. C. 1991 Fortran non-gradient subroutines for non-linear optimisation. Rep. NI-91-05, Numerical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark.Google Scholar
Malone, B. 1992 An experimental investigation of roll-coating phenomena. PhD thesis, Department of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK.Google Scholar
Moffatt, H. K. 1977 Behaviour of a viscous film on the outer surface of a rotating cylinder. J. Méc. 16, 651–673.Google Scholar
Preziosi, L. & Joseph, D. D. 1988 The run-off condition for coating and rimming flows. J. Fluid Mech. 187, 99–113.Google Scholar
Pukhnachev, V. V. 1974 Problems with a free boundary for the Navier-Stokes equations. PhD thesis (in Russian), Lavrenteyev Institute of Hydrodynamics, Novosibirsk, USSR.Google Scholar
Pukhnachev, V. V. 1977 Motion of a liquid film on the surface of a rotating cylinder in a gravitational field (in Russian). Z. Prikl. Mekh. i Tekh. Fiz. 3, 78–88. English translation in (1977), J. Appl. Mech. Tech. Phys. 18, 344–351.Google Scholar
Thompson, H. M. 1992 A theoretical investigation of roll-coating phenomena. PhD thesis, Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK.Google Scholar