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Apollonian emulsions - coalescence in high internal-phase-ratio emulsions

Abstract : We studied oil-in-water high internal-phase-ratio emulsions (HIPEs) at internal volume fraction phi = 0.95, stabilized by non-ionic surfactant, hexaethylene glycol monododecyl ether (C12E6). By varying C12E6 concentration, we obtained two distinct types of HIPEs that we qualified as “solid” or “liquid”. Surfactant-rich HIPEs formulated with >8%C12E6 in the continuous phase are of the “solid” variety: their droplets are distorted into polyhedrons separated by thin films of continuous phase. These films confer an “elastic solid” property on the HIPEs, which display shear-thinning flow beyond their yield stress at high strain rates. By reducing surfactant concentration to below 3%C12E6, we allowed coalescence and obtained a new HIPE structure: oil droplets retaining their spherical shapes, filling space with an extremely polydisperse population. Their diameter distribution, n(a), obeyed a power law: n(a)~a^(-(df+1)). df is the fractal dimension of the set of droplets and was consistently 2.48-2.50 after a week of emulsion evolution, a similar value to that of a Random Apollonian Packing (RAP) of spheres. We confirmed by X-ray Scattering that oil droplets in these surfactant-poor HIPEs are indeed a RAP. This is the first recorded instance of an Apollonian packing fabricated in real physical systems in 2200 years. Apollonian emulsions flow spontaneously like a viscous Newtonian liquid, a behaviour previously unknown in emulsions beyond phi = 0.6. They also have exceptional metastability, remaining emulsified up to a year, even though droplet sizes grow through on-going coalescence. We found that overall surface area increased with time in Apollonian HIPEs, indicating a different evolutionary mechanism from coalescence in dilute emulsions. Through numerical simulation, we determined that two coalescing droplets in an Apollonian emulsion fragment into multiple smaller spherical droplets to optimally fill voids in the vicinity while maintaining minimal elastic energy in the system by avoiding droplet deformation. We named this mechanism “coalescence-fragmentation”, made possible because surfactant molecules evicted during coalescence cannot be evacuated into the very limited amount of continuous phase without causing a steep rise in chemical potential. We found that it is lower in free energy costs to create small spherical droplets than to allow larger droplets to deform one another. Thus, we postulated that an Apollonian packing may be a local thermodynamic minimum.
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Submitted on : Thursday, September 3, 2020 - 11:26:09 AM
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  • HAL Id : tel-02929171, version 1


Yii-Wenn Sylvie Kwok. Apollonian emulsions - coalescence in high internal-phase-ratio emulsions. Chemical Physics [physics.chem-ph]. Université Paris sciences et lettres, 2019. English. ⟨NNT : 2019PSLET028⟩. ⟨tel-02929171⟩



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