Pre-empting Plateau: the nature of topological transitions in foam

Abstract

When the area of a face in a dry foam approaches zero in some quasistatic processes, Plateau's rules dictate that there must be an instability. This is more subtle than generally supposed. We argue that it is generally pre-empted, that is, the instability arises before an unstable multiple vertex is formed. Experiments and calculations which simulate Plateau's wire frame experiments support this view.