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

TL;DR

This study investigates the surface structure of dry 3D aqueous foams, revealing that while individual bubble behavior deviates, the average area change follows von Neumann's law, with surface foam properties closely resembling 2D foams.

Contribution

It demonstrates that surface foam at a planar boundary exhibits 2D-like statistical properties and that von Neumann's law applies on average despite local deviations.

Findings

Surface foam follows Plateau's laws similar to 2D foams.

Von Neumann's law holds on average for surface bubbles.

Surface foam size and shape distributions are similar to 2D foams, with slight differences.

Abstract

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.