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.
Cite
@article{arxiv.1908.07881,
title = {Apollonian Packing in Polydisperse Emulsions},
author = {Sylvie Kwok and Robert Botet and Lewis Sharpnack and Bernard Cabane},
journal= {arXiv preprint arXiv:1908.07881},
year = {2020}
}