Mixing and sorting of bidisperse two-dimensional bubbles |
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Authors: | PIC Teixeira F Graner MA Fortes |
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Institution: | (1) Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaıde, P-2635-631 Rio de Mouro, Portugal, PT;(2) Departamento de Engenharia de Materiais, e Instituto de Ciência e Engenharia de Materiais e Superfıcies, Instituto Superior Técnico, Avenida Rovisco Pais, P-1049-001 Lisbon, Portugal, PT;(3) CNRS UMR 5588 et Université Grenoble, Laboratoire de Spectrométrie Physique, Boıte Postale 87, F-38402 St. Martin d'Hères Cedex, France, FR |
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Abstract: | 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 λ ( λ≤1). 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 λ, the minimal configuration for N → ∞. 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 (N,λ). As λ 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 λ.
Received 1 August 2002
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ID="a"e-mail: paulo@ist.utl.pt |
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Keywords: | PACS 83 80 Iz Emulsions and foams – 82 70 Rr Aerosols and foams – 02 70 Rr General statistical methods |
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