Star-triangle equivalence in two-dimensional soap froths

Abstract

In two-dimensional foams at equilibrium, triangular bubbles can be freely exchanged with threefold stars, three edges ending at a central vertex. This theorem is deduced here from Moukarzel's duality. Moreover, to probe the method, a few related properties are established: under slow gas diffusion, cell extinction is a continuous process for triangles but not for other types of bubble. In general, the gas flow results in different configurations in the presence of a triangle from those in the presence of a star.