Experimentally Testing a Generalized Coarsening Model for Individual Bubbles in Quasi-Two-Dimensional Wet Foams

Abstract

We present high-precision data for the time evolution of bubble area $A(t)$ and circularity shape parameter $C(t)$ for quasi-2d foams consisting of bubbles squashed between parallel plates. In order to fully compare with predictions by Roth et al. [Phys. Rev. E 87 2013] and Schimming et al. [Phys. Rev. E 96 2017], foam wetness is systematically varied by controlling the height of the sample above a liquid reservoir which in turn controls the radius $r$ of the inflation of the Plateau borders. For very dry foams, where the borders are very small, classic von Neumann behavior is observed where a bubble's growth rate depends only on its number $n$ of sides. For wet foams, the inflated borders impede gas exchange and cause deviations from von Neumann's law that are found to be in accord with the generalized coarsening equation. In particular, the overall growth rate varies linearly with the film height, which decrease as surface Plateau borders inflate. And, more interestingly, the deviation from $dA/dt\propto (n-6)$ von Neumann behavior grows in proportion to $nCr/\sqrt{A}$. This is highlighted definitively by data for six-sided bubbles, which are forbidden to grow or shrink except for the existence of this term. And it is tested quantitatively by variation of all four relevant quantities: $n$, $C$, $r$, and $A$