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Stability of a bi-layer free film: simultaneous or individual rupture events?

Published online by Cambridge University Press:  15 July 2015

Peter S. Stewart*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, G12 8QW, UK
Jie Feng
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Laura S. Kimpton
Affiliation:
Mathematical Institute, University of Oxford, OX2 6GG, UK
Ian M. Griffiths
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Mathematical Institute, University of Oxford, OX2 6GG, UK
Howard A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
Email address for correspondence: peter.stewart@glasgow.ac.uk

Abstract

We consider the stability of a long free film of liquid composed of two immiscible layers of differing viscosities, where each layer experiences a van der Waals force between its interfaces. We analyse the different ways in which the system can exhibit interfacial instability when the liquid layers are sufficiently thin. For an excess of surfactant on one gas–liquid interface, the coupling between the layers is relatively weak and the instability is manifested as temporally separated rupture events in each layer. Conversely, in the absence of surfactant, the coupling between the layers is much stronger and the instability is manifested as rupture of both layers simultaneously. These features are consistent with recent experimental observations.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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