Scaling properties of three-dimensional foams

We obtain the scaling states of three-dimensional soap foams by using equilibrium statistical mechanics techniques. We consider a phase space where each bubble is characterized by its center of mass position, volume, surface and number of faces. A Gibbs entropy function is then defined and, as done in standard statistical mechanics, we obtain the probability density function defined in the phase space by maximizing the entropy subject to convenient constraints. The froth is supposed to completely fill the available volume and we consider energy terms accounting for surface tension and the thermal energy of the gas inside the bubbles. We find that the volume distribution presents an exponential decay with cell size and the correlation between cell volume and number of faces fits very well the available numerical data. Additional distribution functions and average values are also in good agreement with numerical simulations.