Structure and coarsening at the surface of a dry three-dimensional aqueous foam
We utilize total-internal reflection to isolate the two-dimensional `surface foam' formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state where statistical distributions are independent of time, except for an overall scale factor. There we find that statistical measures of side number distributions, size-topology correlations, and bubble shapes, are all very similar to those for two-dimensional foams. However the size number distribution is slightly broader and the shapes are slightly more elongated. A more obvious difference is that T2 processes now include the creation of surface bubbles, due to rearrangement in the bulk. And von Neumann's law is dramatically violated for individual bubbles. But nevertheless, our most striking finding is that von Neumann's law appears to holds on average. Namely the average rate of area change for surface bubbles appears to be proportional to the number of sides minus six, but with individual bubbles showing a distribution of deviations from this average behavior.