VERTEX INSTABILITIES IN FOAMS AND EMULSIONS

Plateau's rules, which are the basis of most descriptions of foam stru cture, include one which dictates that junctions of more than four Pla teau borders are always unstable. This has been rigorously proved by T aylor for the idealized mathematical model in which the borders are re duced to lines of infinitesimal thickness. Nevertheless we here presen t a mathematical analysis which shows that a symmetric eightfold verte x is metastable, even for arbitrarily thin Plateau borders. This parad oxical result, contrary to conventional wisdom was first suggested by computer simulations and some simple experiments.