Z-cone model for the energy of an ordered foam

We develop the Z -Cone Model, in terms of which the energy of a foam may be estimated. It is directly applicable to an ordered structure in which every bubble has Z identical neighbours. The energy ( i.e. surface area) may be analytically related to liquid fraction. It has the correct asymptotic for...

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Published inSoft matter Vol. 1; no. 36; pp. 713 - 718
Main Authors Hutzler, Stefan, Murtagh, Robert P, Whyte, David, Tobin, Steven T, Weaire, Denis
Format Journal Article
LanguageEnglish
Published England 28.09.2014
Subjects
Asymptotic properties
Bubbles
Deformation
Drying
Foams
Liquids
Mathematical analysis
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Summary:We develop the Z -Cone Model, in terms of which the energy of a foam may be estimated. It is directly applicable to an ordered structure in which every bubble has Z identical neighbours. The energy ( i.e. surface area) may be analytically related to liquid fraction. It has the correct asymptotic form in the limits of dry and wet foam, with prefactors dependent on Z . In particular, the variation of energy with deformation in the wet limit is consistent with the anomalous behaviour found by Morse and Witten [ Europhysics Letters , 1993, 22 , 549] and Lacasse et al. [ Physical Review E , 54 , 5436], with a prefactor Z /2. We present a new analytical model for the energy of a foam as a function of liquid fraction, which shows the correct asymptotic forms in the wet and dry limits.
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ISSN:1744-683X
1744-6848
DOI:10.1039/c4sm00774c