AUTHOR=Chieco Anthony T. , Sethna James P. , Durian Douglas J. 

TITLE=Average evolution and size-topology relations for coarsening 2d dry foams

JOURNAL=Frontiers in Soft Matter

VOLUME=2

YEAR=2022

URL=https://www.frontiersin.org/journals/soft-matter/articles/10.3389/frsfm.2022.941811

DOI=10.3389/frsfm.2022.941811

ISSN=2813-0499

ABSTRACT=<p>Two-dimensional dry foams coarsen according to the von Neumann law as <italic>dA</italic>/<italic>dt</italic> ∝ (<italic>n</italic> − 6) where <italic>n</italic> is the number of sides of a bubble with area <italic>A</italic>. 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 time derivatives of moments of the bubble area distribution and a relation connecting area moments with averages of the side-number distribution that are weighted by powers of bubble area. To test these predictions, 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 2–20.</p>