Stably coalescent stochastic froths

A model of a stochastic froth is introduced in which the rate of random coa lescence of a pair of bubbles depends on an inverse power law of their size s. The main question of interest is whether froths with a large number of b ubbles can grow in a stable fashion; that is, whether under some time-varyi ng change of scale the distributions of rescaled bubble sizes become approx imately stationary. It is shown by way of a law of large numbers for the fr oths that the question can be re-interpreted in terms of a measure flow sol ving a nonlinear Boltzmann equation that represents an idealized determinis tic froth. Froths turn out to be stable in the sense that there are scaling s in which the rescaled measure flow is tight and, for a particular case, s table in the stronger sense that the rescaled how converges to an equilibri um measure. Precise estimates are also given for the degree of tightness of the rescaled measure flows. AMS 1991 Subject Classification: Primary 60K35 Secondary 60K30; 60K40; 60F17.