Numerical approach to phase separation in a model emulsion

Abstract
This work explores the dynamical aging processes in a two dimensional system of polydispersed non rigid droplets. We introduce a simplified model that rules the interface dynamics and the coupling between neighboring droplets. This model is based on local microscopic properties of the interfaces and can be seen as a simplified van der Waals binary fluid system in microgravity conditions. An empirical rule for coalescence is used. Given characteristic coupling lengths that determine the microscopic interface potential, we estimate typical coarsening/aging times by numerical simulations for different values of the temperature and follow the time evolution of the number of the droplets. Transient regimes so as relaxing behaviour are discussed. Numerical simulations are based on spatial discrete mesh grids and are performed with a fourth order integration scheme that ensures appropriate total momentum conservation. Despite their longstanding use, much remains to be understood about the mechanisms bringing an initial binary dispersed system to a well separated two phase system. This work aims to help the understanding of such aging mechanisms in dense binary emulsions where theoretical models are still not yet available.