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The Geometry of Bubbles and Foams

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Foams and Emulsions

Part of the book series: NATO ASI Series ((NSSE,volume 354))

Abstract

We consider mathematical models of bubbles, foams and froths, as collections of surfaces which minimize area under volume constraints. The resulting surfaces have constant mean curvature and an invariant notion of equilibrium forces. The possible singularities are described by Plateau’s rules; this means that combinatorially a foam is dual to some triangulation of space. We examine certain restrictions on the combinatorics of triangulations and some useful ways to construct triangulations. Finally, we examine particular structures, like the family of tetrahedrally close-packed structures. These include the one used by Weaire and Phelan in their counterexample to the Kelvin conjecture, and they all seem useful for generating good equal-volume foams.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL, USA, 61801-2975

    John M. Sullivan

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  1. John M. Sullivan
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Editor information

Editors and Affiliations

  1. Laboratoire de Physique des Solides, Université de Paris-Sud, Orsay, France

    J. F. Sadoc

  2. Institut de Physique, Université Louis Pasteur, Strasbourg, France

    N. Rivier

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© 1999 Springer Science+Business Media Dordrecht

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Sullivan, J.M. (1999). The Geometry of Bubbles and Foams. In: Sadoc, J.F., Rivier, N. (eds) Foams and Emulsions. NATO ASI Series, vol 354. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9157-7_23

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  • DOI: https://doi.org/10.1007/978-94-015-9157-7_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5180-6

  • Online ISBN: 978-94-015-9157-7

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