Volume 130, Number 3, May 2020
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||05 June 2020|
1 Laboratoire Colloïdes et Matériaux Divisés - Chemistry, Biology and Innovation (CBI) UMR8231, ESPCI Paris, CNRS, PSL Research University - 10 rue Vauquelin, 75005 Paris, France
2 Laboratoire de Physique des Solides, CNRS UMR8502, Université Paris- Saclay - 91405 Orsay, France
Received: 14 January 2020
Accepted: 23 May 2020
We have discovered the existence of extremely polydisperse High Internal-Phase-Ratio Emulsions (HIPEs) 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. Such Apollonian emulsions are obtained from dispersing oil dropwise in water in the presence of very little surfactant, and allowing them to evolve at rest for at least a week. The packing structure of the droplets was confirmed through size distribution measurements that evolved spontaneously towards power laws with the known Apollonian exponents, as well as comparison of the structure factors of aged HIPEs measured by Small-Angle X-ray Scattering with that of a numerically simulated Random Apollonian Packing. Thanks to the perfect sphericity of the droplets, Apollonian emulsions were found to display Newtonian flow even at such extremely high volume fraction. We argue that these fascinating space-filling assemblies of spherical droplets are a result of coalescence and fragmentation processes obeying simple geometrical rules of conserving total volume and sphericity, and minimizing the elastic energy associated with interactions of neighbouring droplets.
PACS: 89.75.Fb – Structures and organization in complex systems / 82.70.Kj – Emulsions and suspensions / 47.55.dk – Surfactant effects
© EPLA, 2020
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