Structure and coarsening at the surface of a dry three-dimensional aqueous foam

摘要

We utilize total-internal reflection to isolate the two-dimensional surface foam formed at the planar boundarynof a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau’snlaws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state wherenstatistical distributions appear independent of time, except for an overall scale factor. There we find that statisticalnmeasures of side number distributions, size-topology correlations, and bubble shapes are all very similar to thosenfor two-dimensional foams. However, the size number distribution is slightly broader, and the shapes are slightlynmore elongated. A more obvious difference is that T2 processes now include the creation of surface bubbles,ndue to rearrangement in the bulk, and von Neumann’s law is dramatically violated for individual bubbles. Butnnevertheless, our most striking finding is that von Neumann’s law appears to holds on average, namely, thenaverage rate of area change for surface bubbles appears to be proportional to the number of sides minus six, butnwith individual bubbles showing a wide distribution of deviations from this average behavior.