Abstract
We study the crossover from a hexagonal lattice of circular bubbles to a monodisperse hexagonal foam in two dimensions (2D). A long range 1/r3 repulsive interaction (e.g., dipole interaction) is taken into account, and the bubble shape is calculated by numerical solution of the 2D Young−Laplace equation. Unlike short range interaction foams, these foams do not coarsen persistently but reach a local thermodynamic stability at a well-defined bubble size. We find that in (local) thermodynamic equilibrium the bubble shapes depend only on the area fraction of the two phases and not on any material constants; i.e., the bubble shapes of these foams are universal. Experiments with polydisperse dipolar foams in Langmuir monolayers of pentadecanoic acid and myristic acid showed that deformations of the bubbles with respect to the circular shape occur at bubble fractions of ≈70%in good agreement with the calculated monodisperse foams. This area fraction is much smaller than in short range interaction foams.
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