2018 Impact factor 1.686
Soft Matter and Biological Physics
Eur. Phys. J. E 9, 447-452 (2002)
DOI: 10.1140/epje/i2002-10102-5

Lower bounds for the surface energy of two-dimensional foams

P.I.C. Teixeira1, 2, F. Graner3 and M.A. Fortes2

1  Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal
2  Departamento de Engenharia de Materiais e Instituto de Ciência e Engenharia de Materiais e Superfícies, Instituto Superior Técnico, Avenida Rovisco Pais, P-1049-001 Lisbon, Portugal
3  CNRS UMR 5588 et Université Grenoble I, Laboratoire de Spectrométrie Physique, Boîte Postale 87, F-38402 St. Martin d'Hères Cedex, France

paulo@ist.utl.pt

(Received 5 November 2002 / Published online: 28 January 2003)

Abstract
Amongst the two-dimensional cellular patterns that fill a plane, dry foams at stable equilibrium typify a particular subset for which the total perimeter P of cell boundaries (i.e., films between bubbles) has a local minimum. For a given set of bubble areas Ai ( $i=1,\ldots,N$), P can be written in the form $P=R(\sum_{i=1}^N\sqrt{A_i})/2$, where R is topology dependent. We seek the set of areas Ai and the cluster topology that minimise R, and propose lower bounds for R that set lower bounds for the surface energy of i) individual bubbles, with circular edges meeting at $2\pi/3$ angles at vertices (Plateau cells), and ii) infinite periodic bubble clusters.

PACS
83.80.Iz - Emulsions and foams.
82.70.Rr - Aerosols and foams.
02.70.Rr - General statistical methods.

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