Average Evolution and Size-Topology Relations for Coarsening 2d Dry Foams

Abstract

Two-dimensional dry foams coarsen according to the von Neumann law as $dA/dt\propto (n-6)$ 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 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 two to twenty.

8 pages, 7 figures

References in corpus (3)

• Bubble statistics and coarsening dynamics for quasi-two dimensional foams with increasing liquid content
• Border-Crossing Model for the Diffusive Coarsening of Two-Dimensional and Quasi-Two-Dimensional Wet Foams
• Experimentally Testing a Generalized Coarsening Model for Individual Bubbles in Quasi-Two-Dimensional Wet Foams

Cited by in corpus (1)

• A simply solvable model capturing the approach to statistical self-similarity for the diffusive coarsening of bubbles, droplets, and grains