Mixing and sorting of bidisperse two-dimensional bubbles

P.I.C. Teixeira; F. Graner; M.A. Fortes

doi:doi:10.1140/epje/i2002-10070-8

2022 Impact factor 1.8

Soft Matter and Biological Physics

Eur. Phys. J. E 9, 161-169 (2002)
DOI: 10.1140/epje/i2002-10070-8

Mixing and sorting of bidisperse two-dimensional bubbles

P.I.C. Teixeira^{1, 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

paulo@ist.utl.pt

(Received 1 August 2002 / Published online: 3 December 2002)

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 $\lambda$ ( $\lambda \le 1$ ). 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 $\lambda$ , the minimal configuration for $N\rightarrow \infty$ . 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 $(N,\lambda)$ . As $\lambda$ 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 $\lambda$ .

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