Vertex instabilities in foams and emulsions

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Abstract
Plateau's rules, which are the basis of most descriptions of foam structure, include one which dictates that junctions of more than four Plateau borders are always unstable. This has been rigorously proved by Taylor for the idealized mathematical model in which the borders are reduced to lines of infinitesimal thickness. Nevertheless we here present a mathematical analysis which shows that a symmetric eightfold vertex is metastable, even for arbitrarily thin Plateau borders. This paradoxical result, contrary to conventional wisdom, was first suggested by computer simulations and some simple experiments.

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