Stable small bubble clusters in two-dimensional foams

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 σ L /σ 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.

The hydra string method: a novel means to explore potential energy surfaces and its application to granular materials

“…In doing so, we presented systemic approach to tailor the various system specific parameters of the HSM to arbitrary systems and demonstrated this approach on an example soft-sphere granular system. The results of the above numerical experiments may be very different for other systems with different potential functions, such as a pairwise Lennard-Jones potential between particles, commonly used in bubbles [35] and as a model for molecules/atoms in chemistry [36]. This broad applicability is one of the major assets of this method.…”

The Hydra String Method: A Novel Means to Explore Potential Energy Surfaces and its Application to Granular Materials

“…In doing so, we presented a systemic approach to tailor the various system specific parameters of the HSM to arbitrary systems and demonstrated this approach on an example soft-sphere granular system. The results of the above numerical experiments may be very different for other systems with different potential functions, such as a pairwise Lennard-Jones potential between particles which is commonly used in bubbles [22] and as a model for molecules/atoms in chemistry [23]. This broad applicability is one of the major assets of this method.…”