The Geometry of Bubbles and Foams [chapter]

John M. Sullivan
1999 Foams and Emulsions  
We consider mathematical models of bubbles, foams and froths, as collections of surfaces which minimize area under volume constraints. The resulting surfaces have constant mean curvature and an invariant notion of equilibrium forces. The possible singularities are described by Plateau's rules; this means that combinatorially a foam is dual to some triangulation of space. We examine certain restrictions on the combinatorics of triangulations and some useful ways to construct triangulations.
more » ... ly, we examine particular structures, like the family of tetrahedrally close-packed structures. These include the one used by Weaire and Phelan in their counterexample to the Kelvin conjecture, and they all seem useful for generating good equal-volume foams.
doi:10.1007/978-94-015-9157-7_23 fatcat:rrxr2ryyfzeq3amdqjeve7ifui