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Issue 10, 2020
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Apollonian packing in polydisperse emulsions

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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 organise themselves according to Apollonian packing rules. These polydisperse HIPEs are formed by emulsifying oil dropwise in a surfactant-poor aqueous continuous phase. After stirring has ceased, their droplet size distributions begin to evolve spontaneously and continuously through coalescence towards well-defined power laws with the Apollonian exponent. Small-angle X-ray Scattering performed on aged HIPEs demonstrate that the droplet packing structure agrees with that of a numerically simulated random Apollonian packing. We argue that when such concentrated emulsions are allowed to evolve, the coalescing droplets must obey volume and sphericity conservation. This leads to a mechanism that differs from typical coalescence in dilute emulsions.

Graphical abstract: Apollonian packing in polydisperse emulsions

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Article information


Submitted
31 Aug 2019
Accepted
17 Feb 2020
First published
18 Feb 2020

Soft Matter, 2020,16, 2426-2430
Article type
Communication

Apollonian packing in polydisperse emulsions

S. Kwok, R. Botet, L. Sharpnack and B. Cabane, Soft Matter, 2020, 16, 2426 DOI: 10.1039/C9SM01772K

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