title: Lower bounds for the surface energy of two-dimensional foams.
abstract: Amongst the two-dimensional cellular patterns that fill a plane, dry foams at stable equilibrium typify a particular subset for which the total perimeter P of cell boundaries ( i.e., films between bubbles) has a local minimum. For a given set of bubble areas Ai (i=1,..., N), P can be written in the form P=R(SigmaN(i=1) square root Ai)/2, where R is topology dependent. We seek the set of areas Ai and the cluster topology that minimise R, and propose lower bounds for R that set lower bounds for the surface energy of i) individual bubbles, with circular edges meeting at 2pi/3 angles at vertices (Plateau cells), and ii) infinite periodic bubble clusters.
authors.affiliation: Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal. paulo@ist.utl.pt
authors.forename: P I C
authors.initials: PI
authors.lastname: Teixeira
authors.forename: F
authors.initials: F
authors.lastname: Graner
authors.forename: M A
authors.initials: MA
authors.lastname: Fortes