Juggling bubbles in square capillaries: an experimental proof of non-pairwise bubble interactions

TL;DR

This study experimentally confirms that bubble interactions in confined foams are non-pairwise, aligning with recent theoretical models, and highlights implications for the mechanical behavior of foams and emulsions.

Contribution

First experimental validation of non-pairwise bubble interactions in confined foams, confirming recent theoretical predictions and providing quantitative agreement with simulations.

Findings

Interactions are non-pairwise and match theoretical models.

Experimental data agrees with Surface Evolver simulations.

Results apply to emulsions beyond foams.

Abstract

.The physical properties of an ensemble of tightly packed particles like bubbles, drops or solid grains are controlled by their interactions. For the case of bubbles and drops it has recently been shown theoretically and computationally that their interactions cannot generally be represented by pair-wise additive potentials, as is commonly done for simulations of soft grain packings. This has important consequences for the mechanical properties of foams and emulsions, especially for strongly deformed bubbles or droplets well above the jamming point. Here we provide the first experimental confirmation of this prediction by quantifying the interactions between bubbles in simple model foams consisting of trains of equal-volume bubbles confined in square capillaries. The obtained interaction laws agree quantitatively with Surface Evolver simulations and are well described by an analytically derived expression based on the recently developed non-pairwise interaction model of H\"ohler et al. [Soft Matter, 2017, 13,(7):1371], based on Morse-Witten theory. While all experiments are done at Bond numbers sufficiently low for the hydrostatic pressure variation across one bubble to be negligible, we provide the full analysis taking into account gravity in the appendix for the interested reader. Even though the article focuses on foams, all results directly apply to the case of emulsions.