Mixing and sorting of bidisperse two-dimensional bubblesP.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, Laboratoire de Spectrométrie Physique, Boîte Postale 87, F-38402 St. Martin d'Hères Cedex, France
(Received 1 August 2002 / Published online: 3 December 2002)
We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area ( ). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of , the minimal configuration for . For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in "phase-separated" clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair . As is varied, this alternates between a circular cluster of one of the mixed tilings, and "partial wetting" of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area .
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