Symmetry break in the eight bubble compaction

TL;DR

This paper investigates how geometric and mechanical factors influence the three-dimensional packing and symmetry breaking in an eight-bubble foam structure, revealing anisotropic force distributions.

Contribution

It introduces a model combining geometric principles and mechanical constraints to analyze bubble packing and symmetry breaking in foam structures.

Findings

Identifies anisotropic force distribution in bubble interfaces.

Shows geometric optimization aligns with physical stability.

Highlights mechanical cues as key to symmetry breaking.

Abstract

Geometry and mechanics have both a relevant role in determining the three-dimensional packing of 8 bubbles displyaed in a foam structure. We assume that the spatial arrangement of bubbles obeys a geometrical principle maximizing the minimum mutual distance between the bubble centroids. The compacted structure is then obtained by radially packing the bubbles under constraint of volume conservation. We generate a polygonal tiling on the central sphere and peripheral bubbles with both flat and curved interfaces. We verify that the obtained polyhedra is optimal under suitable physical criteria. Finally, we enforce the mechanical balance imposing the constraint of conservation of volume. We find an anisotropy in the distribution of the field of forces: surface tensions of bubble-bubble interfaces with normal oriented in the circumferential direction of bubbles aggregate are larger than the ones with normal unit vector pointing radially out of the aggregate. We suggest that this mechanical cue is key for the symmetry break of this bubbles configuration.