Z-cone model for the energy of an ordered foam

Abstract

We develop the Z-Cone Model, in terms of which the energy of a foam may be estimated. It is directly applicable to an ordered structure in which every bubble has Z identical neighbours. The energy (i.e. surface area) may be analytically related to liquid fraction. It has the correct asymptotic form in the limits of dry and wet foam, with prefactors dependent on Z. In particular, the variation of energy with deformation in the wet limit is consistent with the anomalous behaviour found by Morse and Witten [Europhysics Letters, 1993, 22, 549] and Lacasse et al. [Physical Review E, 54, 5436], with a prefactor Z/2.