3D simulations of wet foam coarsening evidence a self similar growth regime

TL;DR

This paper uses 3D simulations to study wet foam coarsening, revealing a self-similar growth regime where bubble size distribution stabilizes and the number of bubbles decreases following a wetness-dependent power law.

Contribution

It introduces a Cellular Potts model simulation of wet foam coarsening in three dimensions, capturing liquid flow and bubble topology changes over a wide range of wetness levels.

Findings

All simulations reach a self-similar growth regime.

Bubble number decreases as a power law with time.

The power law exponent varies with foam wetness.

Abstract

In wet liquid foams, slow diffusion of gas through bubble walls changes bubble pressure, volume and wall curvature. Large bubbles grow at the expenses of smaller ones. The smaller the bubble, the faster it shrinks. As the number of bubbles in a given volume decreases in time, the average bubble size increases: i.e. the foam coarsens. During coarsening, bubbles also move relative to each other, changing bubble topology and shape, while liquid moves within the regions separating the bubbles. Analyzing the combined effects of these mechanisms requires examining a volume with enough bubbles to provide appropriate statistics throughout coarsening. Using a Cellular Potts model, we simulate these mechanisms during the evolution of three-dimensional foams with wetnesses of $\phi=0.00$, $0.05$ and $ 0.20$. We represent the liquid phase as an ensemble of many small fluid particles, which allows us to monitor liquid flow in the region between bubbles. The simulations begin with $2 \times 10^5$ bubbles for $\phi = 0.00$ and $1.25 \times 10^5$ bubbles for $\phi = 0.05$ and $0.20$, allowing us to track the distribution functions for bubble size, topology and growth rate over two and a half decades of volume change. All simulations eventually reach a self-similar growth regime, with the distribution functions time independent and the number of bubbles decreasing with time as a power law whose exponent depends on the wetness.