Coarsening foams robustly reach a self-similar growth regime

Dry liquid foams coarsen like other diphasic systems governed by interfacial energy: gas slowly diffuses across liquid films, resulting in large bubbles growing at the expense of smaller ones which eventually shrink and disappear. A foam scatters light very effectively, preventing direct optical observation of bubble sizes and shapes in large foams. Using high speed x-ray tomography, we have produced 4D movies (i.e., 3D + time) of up to 30,000 bubbles. After a transient regime, the successive images look alike, except that the average bubble size increases as the square root of time: This scaling state is the long sought self-similar growth regime. The bubble size and face-number distributions in this regime are compared with experimental distributions for grains in crystals and with numerical simulations of foams.