Regular three-dimensional bubble clusters: shape, packing and growth-rate
Simon Cox, Francois Graner
TL;DR
This paper investigates the shape, packing, and growth dynamics of three-dimensional bubble clusters, providing improved models for their energy, shape, and pressure, and exploring the maximum number of bubbles that can surround a central bubble.
Contribution
It introduces refined calculations for bubble cluster energy and shape, and extends the kissing problem to deformable bubbles in 3D.
Findings
Derived new formulas for surface area and pressure in bubble clusters
Improved growth laws for three-dimensional bubble packings
Analyzed maximum packing numbers for deformable bubbles
Abstract
We consider three-dimensional clusters of identical bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for three-dimensional bubble clusters. We discuss the possible number of bubbles that can be packed around a central one: the ``kissing problem'', here adapted to deformable objects.
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