Dry three-dimensional bubbles: Growth-rate, scaling state and correlations

The energy and shape of three-dimensional clusters of equal-volume bubbles packed around a central bubble are calculated. The resulting surface areas and bubble pressures provide an improvement upon existing growth laws for three-dimensional bubble clusters. Since a bubble's growth-rate depends mostly on its number of faces, simulations of coarsening can be accelerated by considering bubble topology rather than detailed geometry. The coarsening-induced relaxation of a disordered foam towards a scaling state, in which the normalised bubble volume and face-number distributions remain invariant, can thus be characterised.