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arXiv · 0810.5724

Spherical Foams in Flat Space

Carl D. Modes·Randall D. Kamien
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Abstract

Regular tesselations of space are characterized through their Schlafli symbols {p,q,r}, where each cell has regular p-gonal sides, q meeting at each vertex, and r meeting on each edge. Regular tesselations with symbols {p,3,3} all satisfy Plateau's laws for equilibrium foams. For general p, however, these regular tesselations do not embed in Euclidean space, but require a uniform background curvature. We study a class of regular foams on S^3 which, through conformal, stereographic projection to R^3 define irregular cells consistent with Plateau's laws. We analytically characterize a broad classes of bulk foam bubbles, and extend and explain recent observations on foam structure and shape distribution. Our approach also allows us to comment on foam stability by identifying a weak local maximum of A^(3/2)/V at the maximally symmetric tetrahedral bubble that participates in T2 rearrangements.

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Carl D. Modes, Randall D. Kamien. 2008-10-31. Spherical Foams in Flat Space. https://doi.org/10.1039/c3sm51585k

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