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arXiv · 1908.07881

Apollonian Packing in Polydisperse Emulsions

Sylvie Kwok·Robert Botet·Lewis Sharpnack·Bernard Cabane
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Abstract

We have discovered the existence of polydisperse High Internal-Phase-Ratio Emulsions (HIPE) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organize themselves in the available space according to Apollonian packing rules. These polydisperse HIPE are formed during emulsification of surfactant-poor compositions of oil-surfactant-water two-phase systems. Their droplet size-distributions evolve spontaneously towards power laws with the Apollonian exponent. Small-Angle X-Ray Scattering performed on aged HIPEs demonstrated that the droplet packing structure coincided with that of a numerically simulated Random Apollonian Packing. We argue that these peculiar, space-filling assemblies are a result of coalescence and fragmentation processes obeying simple geometrical rules of conserving total volume and minimizing surface area.

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Sylvie Kwok, Robert Botet, Lewis Sharpnack, Bernard Cabane. 2019-08-21. Apollonian Packing in Polydisperse Emulsions. https://doi.org/10.1039/c9sm01772k

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