Abstract
The statistics of emulsion lattices — nearly two-dimensional (2D) oil-in-water emulsions — are analyzed using statistica crystallography. Strict mathematical requirements determine the 2D topology, such that random partitioning of space yields a predictable statistical geometry for polygon shapes. For all lattices examined. Aboav's and Lewis's laws are verified; this result is consistent both with the need to fill 2D space and with energy carried not exclusively by pattern boundaries. The aim is synthetic; together, the crystallographic results suggest a universality akin to statistical equations of state which govern emulsions and hence unite their geometric coarsening to other random networks such as froths, magnetic bubbles and acidic monolayers.
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