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Parametric instability of the interface between two fluids

Published online by Cambridge University Press:  26 April 2006

Krishna Kumar  and
Laurette S. Tuckerman
Krishna Kumar
Affiliation:
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'ltalie, 69364 Lyon Cedex 07, France
Laurette S. Tuckerman
Affiliation:
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'ltalie, 69364 Lyon Cedex 07, France Permanent address: Department of Mathematics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, TX 78712, USA.
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Abstract

The flat interface between two fluids in a vertically vibrating vessel may be parametrically excited, leading to the generation of standing waves. The equations constituting the stability problem for the interface of two viscous fluids subjected to sinusoidal forcing are derived and a Floquet analysis is presented. The hydrodynamic system in the presence of viscosity cannot be reduced to a system of Mathieu equations with linear damping. For a given driving frequency, the instability occurs only for certain combinations of the wavelength and driving amplitude, leading to tongue-like stability zones. The viscosity has a qualitative effect on the wavelength at onset: at small viscosities, the wavelength decreases with increasing viscosity, while it increases for higher viscosities. The stability threshold is in good agreement with experimental results. Based on the analysis, a method for the measurement of the interfacial tension, and the sum of densities and dynamic viscosities of two phases of a fluid near the liquid-vapour critical point is proposed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 279 , 25 November 1994 , pp. 49 - 68
Copyright
© 1994 Cambridge University Press

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