Growth laws and self-similar growth regimes of coarsening two-dimensional foams: Transition from dry to wet limits

TL;DR

This paper investigates the topology and growth dynamics of two-dimensional coarsening foams across liquid fractions, proposing a unified growth law that bridges dry and wet limits, validated by simulations.

Contribution

It introduces a new growth law incorporating bubble-bubble and bubble-Plateau border interfaces, applicable across all liquid fractions, and demonstrates self-similar growth regimes.

Findings

The proposed growth law accurately predicts bubble growth rates.

Self-similar growth regimes are observed at all liquid fractions.

The model interpolates between dry and wet foam limits.

Abstract

We study the topology and geometry of two dimensional coarsening foams with arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law, and the wet limit described by Marqusee equation, the relevant bubble characteristics are the Plateau border radius and a new variable, the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau borders interfaces. The resulting prediction is successfully tested, without adjustable parameter, using extensive bidimensional Potts model simulations. Simulations also show that a selfsimilar growth regime is observed at any liquid fraction and determine how the average size growth exponent, side number distribution and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals and other domains with coarsening driven by curvature.