Apollonian packing in polydisperse emulsions. Issue 10 (26th February 2020) - Kwok, Sylvie; Botet, Robert; Sharpnack, Lewis; Cabane, Bernard
Abstract : Random Apollonian packing of extremely polydisperse oil droplets created through coalescence-fragmentation in high internal-phase-ratio emulsions (HIPE). 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.