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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: [email protected]
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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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References

Anderson, A. M., Brush, L. N. & Davis, S. H. 2010 Foam mechanics: spontaneous rupture of thinning liquid films with Plateau borders. J. Fluid Mech. 658, 63–88.CrossRefGoogle Scholar
Banhart, J. 2001 Manufacture, characterisation and application of cellular metals and metal foams. Prog. Mater. Sci. 46 (6), 559–632.Google Scholar
Bashforth, F. & Adams, J. C. 1883 An Attempt to Test the Theories of Capillary Action: By Comparing the Theoretical and Measured Forms of Drops of Fluid. Cambridge University Press.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.Google Scholar
Breward, C. J. W. & Howell, P. D. 2002 The drainage of a foam lamella. J. Fluid Mech. 458, 379–406.Google Scholar
Brush, L. N. & Davis, S. H. 2005 A new law of thinning in foam dynamics. J. Fluid Mech. 534, 227–236.Google Scholar
Debrégeas, G., De Gennes, P. G. & Brochard-Wyart, F. 1998 The life and death of ‘bare’ viscous bubbles. Science 279, 1704–1707.Google Scholar
Erneux, T. & Davis, S. H. 1993 Nonlinear rupture of free films. Phys. Fluids A-Fluid 5, 1117.Google Scholar
Hamaker, H. C. 1937 The Londonvan der Waals attraction between spherical particles. Physica 4, 1058–1072.Google Scholar
Ida, M. P. & Miksis, M. J. 1998 The dynamics of thin films I: general theory. SIAM J. Appl. Maths 456–473.Google Scholar
Koehler, S. A., Hilgenfeldt, S. & Stone, H. A. 1999 Liquid flow through aqueous foams: the node-dominated foam drainage equation. Phys. Rev. Lett. 82, 4232–4235.Google Scholar
Koehler, S. A., Hilgenfeldt, S., Weeks, E. R. & Stone, H. A. 2002 Drainage of single Plateau borders: direct observation of rigid and mobile interfaces. Phys. Rev. E 66, 040601.CrossRefGoogle ScholarPubMed
Mysels, K. J., Frankel, S. & Shinoda, K. 1959 Soap Films: Studies of Their Thinning and a Bibliography, vol. 230, pp. 91–106. Pergamon.Google Scholar
Naire, S., Braun, R. J. & Snow, S. A. 2000 An insoluble surfactant model for a vertical draining free film. J. Colloid Interface Sci. 230, 91–106.Google Scholar
Pigeonneau, F. & Sellier, A. 2011 Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface. Phys. Fluids 23, 92–102.Google Scholar
Plateau, J. A. F. 1873 Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires. Gauthier Villars.Google Scholar
Schultz, W. W. & Davis, S. H. 1982 One-dimensional liquid fibres. J. Rheol. 26, 331–345.Google Scholar
Schwartz, L. W. & Princen, H. M. 1987 A theory of extensional viscosity for flowing foams and concentrated emulsions. J. Colloid Interface Sci. 118, 201–211.Google Scholar
Schwartz, L. W. & Roy, R. V. 1999 Modelling draining flow in mobile and immobile soap films. J. Colloid Interface Sci. 218, 309–323.Google Scholar
Stewart, P. S. & Davis, S. H. 2012 Dynamics and stability of metallic foams: network modelling. J. Rheol. 56 (3), 543–574.Google Scholar
Stewart, P. S. & Davis, S. H. 2013 Self-similar coalescence of clean foams. J. Fluid Mech. 722 (3), 645–664.CrossRefGoogle Scholar
Verbist, G., Weaire, D. & Kraynik, A. M. 1996 The foam drainage equation. J. Phys.: Condens. Matter 8, 3715–3731.Google Scholar
Vrij, A. 1966 Possible mechanism for the spontaneous rupture of thin, free liquid films. Discuss. Faraday Soc. 42, 23–33.Google Scholar
Weaire, D. & Hutzler, S. 1999 The Physics of Foams. Oxford University Press.Google Scholar