Helmholtz and Gibbs free energies of liquid foams

The relative stability of different configurations (i.e. geometries/topologies) of a foam cluster is shown to depend on the choice of constraints, viz. fixed bubble and Plateau border sizes, or fixed bubble and Plateau border pressures. The appropriate thermodynamic potential is the Gibbs free energy, which comprises the (Helmholtz) surface energy plus contributions associated with the bubbles or Plateau borders whose pressure is kept fixed. These energies can be expressed in terms of the sizes and excess pressures in the bubbles. An example is provided which displays the difference between fixing the areas or the pressures for a two-dimensional foam.