The equilibrium state of 2D foams

The dynamics of two-dimensional cellular networks (foams) is written in terms of coupled rate equations, which describe how the population of s-sided cells is affected by cell disappearance or coalescence and division. In these equations, the effect of the rest of the foam in statistical equilibrium on the disappearing or dividing cell is treated as a local mean field. The rate equations are asymptotically integrable; the equilibrium distribution Ps of cells is essentially unique, driven and controlled by the topological transformations for cells with $s< 6+\sqrt{\mu_2}$. Asymptotic integrability of the equations, and unique distribution, are absent in a global mean-field treatment. Thus, short-ranged topological information is necessary to explain the evolution and stability of foams.