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Instability of a gravity current within a soap film

Published online by Cambridge University Press:  21 July 2014

Raymond E. Goldstein ,
Herbert E. Huppert ,
H. Keith Moffatt  and
Adriana I. Pesci
Raymond E. Goldstein*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK School of Earth Sciences, University of Bristol, Bristol BS8 1TW, UK School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
H. Keith Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Adriana I. Pesci
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: R.E.Goldstein@damtp.cam.ac.uk
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Abstract

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One of the simplest geometries in which to study fluid flow between two soap films connected by a Plateau border is provided by a catenoid with a secondary film at its narrowest point. Dynamic variations in the spacing between the two rings supporting the catenoid lead to fluid flow between the primary and secondary films. When the rings are moved apart, while keeping their spacing within the overall stability regime of the films, after a rapid thickening of the secondary film the excess fluid in it starts to drain into the sloped primary film through the Plateau border at which they meet. This influx of fluid is accommodated by a local thickening of the primary film. Experiments described here show that after this drainage begins the leading edge of the gravity current becomes linearly unstable to a finite-wavelength fingering instability. A theoretical model based on lubrication theory is used to explain the mechanism of this instability. The predicted characteristic wavelength of the instability is shown to be in good agreement with experimental results. Since the gravity current advances into a film of finite, albeit microscopic, thickness this situation is one in which the regularization often invoked to address singularities at the nose of a thin film is physically justified.

JFM classification

Interfacial Flows (free surface): Fingering instability Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Lubrication theory
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 753 , 25 August 2014 , R1
Copyright
© 2014 Cambridge University Press 

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Goldstein et al. supplementary movie

High-speed movie of the collapse of a catenoid soap film with a secondary film at its waist.

Download Goldstein et al. supplementary movie(Video)
Video 8.2 MB

Goldstein et al. supplementary movie

High-speed movie of the onset of fingering instability when the rings supporting a catenoid soap film, with a secondary film, are moved apart.

Download Goldstein et al. supplementary movie(Video)
Video 8.8 MB