Mixing and sorting of bidisperse two-dimensional bubbles.
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< or =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-->infinity. 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.
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Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal. paulo@ist.utl.pt
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Fortes
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