Applications and extensions of the Z-cone model for the energy of a foam

• Published in: Colloids and surfaces. A, Physicochemical and engineering aspects Vol. 473; pp. 115 - 122
• Main Authors: Whyte, David, Murtagh, Robert, Weaire, Denis, Hutzler, Stefan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 20.05.2015
• Subjects: Emulsions; Foams; Minimal surfaces; Foams; Minimal surfaces; Emulsions
• ISSN: 0927-7757; 1873-4359
• DOI: 10.1016/j.colsurfa.2014.12.041

A bubble in an ordered foam can be split into sections: one for each neighbour. We approximate these sections as spherical cones and obtain an analytic form for the energy as a function of deformation, and use this to obtain a liquid fraction profile for a foam under gravity. [Display omitted] •We compute an effective Hookean spring constant as a function of contact number for bubble–bubble interactions.•We use the analytic Z-cone model to obtain a liquid fraction profile for a foam under gravity.•We extend the Z-cone model to allow the computation of energies for bubbles of differing sizes. We present an extended analysis of the Z-cone model for the estimation of the energy of an ordered foam. In particular, we show that it results in an interaction potential with an exponent consistent with those previously reported, as well as an equilibrium liquid fraction profile under gravity consistent with those experimentally observed in ordered foams. We also extend the model to deal with curved interfaces, as a first step to modelling ordered bidisperse foams.