Dynamics of spontaneous emulsification

Abstract

We present a model for spontaneous emulsification resulting from a transiently negative interfacial tension between water and oil regions, which may be achieved under conditions of strong adsorption of surfactant molecules to the interface. While our approach builds on a linear stability analysis, it addresses the essential non-linear coupling of surface growth to the diffusion flux of surfactants to the interface. We consider a large drop of oil of radius R embedded in a dilute surfactant solution and predict that undulations develop with a characteristic wavelength λ*, which at long times t obeys λ*∼t1/3. This suggests that the size of the droplets created spontaneously at the interface scales as ξo1/3, where ξo is a diffusion length which is comparable to R under steady state diffusion conditions. We discuss the regimes of applicability of our results to various experimental systems.