Cell topology during coarsening of simulated three-dimensional dry liquid foams

Cell topology provides a deep insight into the structure of dry liquid foams. This paper analyses the cell topology of simulated 3-dimensional monodisperse dry liquid foams through the process of coarsening, where gas slowly diffuses through the cell interfaces. The coarsened foams are polydisperse, yet show a difference in cell types to annealed, low energy foams of comparable polydispersity. These two types of foams are analysed using average face degree of the cells and a measure of combinatorial roundedness, a new concept from combinatorial topology. We see that the spectrum of cell types changes drastically through the evolution of the foam via coarsening, from cells with a face degree between 12 and 14, with many 4-, 5-, and 6-side faces, to a combination of very large cells with many faces alongside a high frequency of tetrahedra and other cells with low face degree. These results demonstrate the insight that topological methods can give into foams and other complex structures.