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Foam mechanics: spontaneous rupture of thinning liquid films with Plateau borders

Published online by Cambridge University Press:  10 June 2010

ANTHONY M. ANDERSON ,
LUCIEN N. BRUSH  and
STEPHEN H. DAVIS
ANTHONY M. ANDERSON*
Affiliation:
Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
LUCIEN N. BRUSH
Affiliation:
Department of Materials Science and Engineering, University of Washington, Seattle, WA 98195, USA
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

Spontaneous film rupture from van der Waals instability is investigated in two dimensions. The focus is on pure liquids with clean interfaces. This case is applicable to metallic foams for which surfactants are not available. There are important implications in aqueous foams as well, but the main differences are noted. A thin liquid film between adjacent bubbles in a foam has finite length, curved boundaries (Plateau borders) and a drainage flow from capillary suction that causes it to thin. A full linear stability analysis of this thinning film shows that rupture occurs once the film has thinned to ‘tens’ of nanometres, whereas for a quiescent film with a constant and uniform thickness, rupture occurs when the thickness is ‘hundreds’ of nanometres. Plateau borders and flow are both found to contribute to the stabilization. The drainage flow leads to several distinct qualitative features as well. In particular, unstable disturbances are advected by the flow to the edges of the thin film. As a result, the edges of the film close to the Plateau borders appear more susceptible to rupture than the centre of the film.

JFM classification

Drops and Bubbles: Breakup/coalescence Complex Fluids: Foams Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 63 - 88
Copyright
Copyright © Cambridge University Press 2010

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