UNIVERSAL TOPOLOGICAL PROPERTIES OF SHELLS IN SOAP FROTH

An analysis of the shell distribution function of two-dimensional soap froth reveals a universal topological relation on the average number M(j, n) of sides per cell to the number of cells K(j, n) in the jth sh ell of a given center cell with n sides. A plot of M(j, n)K(j, n) vs K (j, n) shows a slope of 5 for j = 1 and a slope of 6 for j greater tha n or equal to 2, for all samples. The results are universal for soap f roths in the scaling state with different preparations, different time s, and different temperatures. A theoretical justification is given ba sed on general topological arguments, which are independently supporte d by experiments.