# Stable small bubble clusters in two-dimensional foams

## TL;DR

This study combines experiments and simulations to analyze small bubble clusters in 2D foams, revealing how interaction range affects cluster diversity and emphasizing the protocol's impact on cluster formation.

## Contribution

It provides new insights into the role of interaction range and formation protocols in determining bubble cluster configurations in 2D foam systems.

## Key findings

- Short-range attractions increase the diversity of stable bubble clusters.
- Experimental cluster distributions resemble those with long-range interactions.
- Cluster occurrence frequencies are highly protocol-dependent and weakly linked to energy.

## Abstract

Key features of the mechanical response of amorphous particulate materials, such as foams, emulsions, and granular media, to applied stress are determined by the frequency and size of particle rearrangements that occur as the system transitions from one mechanically stable state to another. This work describes coordinated experimental and computational studies of bubble rafts, which are quasi-two dimensional systems of bubbles confined to the air-water interface. We focus on small mechanically stable clusters of four, five, six, and seven bubbles with two different sizes with diameter ratio $\sigma_L/\sigma_S = 1.4$. Focusing on small bubble clusters, which can be viewed as subsystems of a larger system, allows us to investigate the full ensemble of clusters that form, measure the respective frequencies with which the clusters occur, and determine the form of the bubble-bubble interactions. We emphasize several important results. First, for clusters with N > 5 bubbles, we find using discrete element simulations that short-range attractive interactions between bubbles give rise to a larger ensemble of distinct mechanically stable clusters compared to that generated by long-range attractive interactions. The additional clusters in systems with short-range attractions possess larger gaps between pairs of neighboring bubbles on the periphery of the clusters. The ensemble of bubble clusters observed in experiments is similar to the ensemble of clusters with long-range attractive interactions. We also compare the frequency with which each cluster occurs in simulations and experiments. We find that the cluster frequencies are extremely sensitive to the protocol used to generate them and only weakly correlated to the energy of the clusters.