EQUILIBRIUM AND EVOLUTION OF FROTHS UNDER TOPOLOGICAL CONSTRAINTS

The effects of geometrical and topological constraints on the evolution and equilibrium properties of froths have been evaluated by a statistical mechanics approach. The constraints are a constant total volume occupied by a cellular system and a constant mean number of neighbours per cell. The energy of the system has been associated with the extension of the interfaces between cells. The calculation has been simplified by assuming that the volume, the surface and the number of neighbours of a cell depend upon only one parameter: the cell size. It has been found that, at high temperatures, the entropic term associated with the topological constraint leads to a stable equilibrium state. A rough estimation of such a temperature for soap froth, has given the 'unphysical' value T-c similar or equal to 10(16) K. At 'normal' temperatures, the system evolves, increasing the mean cell size and decreasing the number of cells. It has been found that the constraints force the system to evolve through self-similar configurations; at a rate of growth proportional to the spread of the size distribution.