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Hydrodynamic stability of a sheared liquid film

Published online by Cambridge University Press:  26 April 2006

Rob Miesen  and
Bendiks Jan Boersma
Rob Miesen
Affiliation:
Koninklijke/Shell-Laboratorium, Amsterdam, Postbus 38000, 1030 BN Amsterdam, The Netherlands Present address: Shell Internationale Petroleum Maatschappij, Postbus 162, 2501 AN Den Haag, The Netherlands.
Bendiks Jan Boersma
Affiliation:
University of Twente, Postbus 217, 7500 AE Enschede, The Netherlands Present address: Laboratory for Aero- and Hydrodynamics, Rotterdamseweg 145, 2628 AL Delft, The Netherlands.
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Abstract

We study the hydrodynamic stability of a thin layer of liquid that is sheared by a gas. First, the interface conditions for the free surface approximation of the problem are discussed. We then study the stability of the flow to disturbances with phase speeds smaller than the maximum velocity in the liquid film, i.e. the internal mode, extending previous results and resolving some apparent contradictions.

The dynamic effect of the gas is studied by dropping the free surface approximation and solving the Orr-Sommerfeld equation for the gas together with that for the liquid. The effect on the stability of the liquid film is very large, which is explained by the fact that the imaginary part of the wave speed (which determines the stability of the film) is very small. Consequently the free surface approximation is, in general, not correct.

We then study the dependence of the critical Reynolds number on the Weber number, on the curvature of the liquid velocity profile and on the properties of the gas. With the gas included, a second mode of instability is found which has a phase velocity that is, in general, larger than the maximum liquid velocity and corresponds to capillary-gravity waves. We compare results with experiments from the literature; good agreement is found. Finally, a suggestion on the relevance of this study to the generation of ‘roll waves’, which are important from a practical point of view, is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 301 , 25 October 1995 , pp. 175 - 202
Copyright
© 1995 Cambridge University Press

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