A Generalized Size-Topology Identity for 2-dimensional Dry Foams

Two-dimensional dry foams coarsen according to the von Neumann law as dA/dt ∝ (n-6) where n is the number of sides of a bubble with area A. Such foams reach a self-similar scaling state where area and side-number distributions are stationary. Combining self-similarity with the von Neumann law, we derive a new identity connecting moments of the area distribution with averages of the side-number distribution that are weighted by powers of bubble area. To test this prediction, we collect and analyze high precision image data for a large number of bubbles squashed between parallel acrylic plates and allowed to coarsen into the self-similar scaling state. We find good agreement for moments ranging from two to nineteen. This enables derivation of another identity, which we are now testing, connecting the rate of change of the moments of the area distribution with area-weighted averages of the side-number distribution.