Apollonian emulsions

Sylvie Kwok (1) , Robert Botet (2) , Abdulwahed Shglabow (1) , Bernard Cabane (3, 1)

1 LCMD - Laboratoire Colloïdes et Matériaux Divisés
2 LPS - Laboratoire de Physique des Solides
3 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

We have discovered the existence of extremely 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. 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 a week. The packing structure of the droplets were 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 spheric-ity. 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 the elastic energy associated with interactions of neighboring droplets.

Domaines: Matière Molle [cond-mat.soft]

Sylvie Kwok, Robert Botet, Abdulwahed Shglabow, Bernard Cabane. Apollonian emulsions. EPL - Europhysics Letters, 2020, 130 (3), pp.38001. ⟨10.1209/0295-5075/130/38001⟩. ⟨hal-02863574⟩