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Local effects of gravity on foams

Published online by Cambridge University Press:  15 November 2013

Michael J. Davis ,
Peter S. Stewart  and
Stephen H. Davis
Michael J. Davis*
Affiliation:
Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
Peter S. Stewart
Affiliation:
Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, The University of Oxford, Oxford OX1 3LB, UK
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: davis@u.northwestern.edu
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Abstract

The stability of a two-dimensional surfactant-free (gas–liquid) foam in a gravitational field is considered. The foam is assumed to have low liquid fraction, so the gas phase can be divided into approximately polygonal bubbles separated by thin liquid films. These free films drain toward accumulations of liquid at the bubble vertices, the Plateau borders, and eventually rupture due to van der Waals intermolecular attractions; this drives foam coarsening through the coalescence of neighbouring bubbles. In particular, we demonstrate how gravitational effects strongly modify the shape of the Plateau border interfaces and enhance the drainage flow in the liquid films, driving non-uniform thinning with exponential decay of the minimum film thickness, significantly faster than the power-law thinning predicted when gravitational effects are negligible.

JFM classification

Complex Fluids: Foams Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 1 - 18
Copyright
©2013 Cambridge University Press 

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