SCALING PROPERTIES OF 3-DIMENSIONAL FOAMS

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