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Soft Matter and Biological Physics


Eur. Phys. J. E 7, 123-127 (2002)
DOI: 10.1140/epje/i200101168

Uniqueness, stability and Hessian eigenvalues for two-dimensional bubble clusters

D. Weaire1, S.J. Cox1 and F. Graner2

1  Department of Physics, Trinity College, Dublin 2, Ireland
2  Laboratoire de Spectrométrie Physique, Boîte Postale 87, F-38402 St. Martin d'Hères Cedex, France

simon.cox@tcd.ie

(Received 8 November 2001)

Abstract
A recent conjecture on two-dimensional foams suggested that for fixed topology with given bubble areas there is a unique state of stable equilibrium. We present counter-examples, consisting of a ring of bubbles around a central one, which refute this conjecture. The discussion centres on a novel form of instability which causes symmetric clusters to become distorted. The stability of these bubble clusters is examined in terms of the Hessian of the energy.

PACS
82.70.Rr - Aerosols and foams.
46.32.+x - Static buckling and instability.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002