Molecular simulations of droplet coalescence in oil/water/surfactant systems
We report a molecular simulation study of the mechanism by which droplets covered with a surfactant monolayer coalesce. We study a model system where the rate-limiting step in coalescence is the rupture of the surfactant film. Our simulations allow us to focus on the stages at the core of the coalescence process: the initial rupture of the two surfactant monolayers, the rearrangement of the surfactant molecules to form a channel connecting the two droplets, and the expansion of the radius of the resulting channel. For our numerical study, we made use of the dissipative particle dynamics method. We used a coarse-grained description of the oil, water, and surfactant molecules. The rupture of the surfactant film is a rare event on the molecular time scale. To enhance the sampling of the rupture of the surfactant film, we used forward flux sampling (FFS). FFS not only allows us to estimate coalescence rates, it also provides insight into the molecular structure and free energy of the "transition" state. For an oil-water-oil film without surfactant, the rupture rate decreases exponentially with increasing film thickness. The critical state is different in thin and thick films: Thin films break following a large enough thickness fluctuation. Thicker films break only after a sufficiently large hole fluctuation-they can heal. Next, we designed surfactant molecules with positive, zero, and negative natural curvatures. For a water film between two surfactant-covered oil droplets, the rupture rate is highest when the surfactant has a negative natural curvature, lowest when it has zero natural curvature, and lying in between when it has a positive natural curvature. This nonmonotonic variation with curvature stems from two effects: First, the surfactants with a large absolute value of the natural curvature have lower interfacial tension and bending rigidity. This promotes the interfacial fluctuations required to nucleate a channel. Second, the sign of the natural curvature determines whether there is a critical channel radius at which the channel free energy has a maximum. The latter is in agreement with the hole-nucleation theory of Kabalnov and Wennerström [Langmuir 12, 276 (1996)]. Our simulations seriously overestimate the relative stability of surfactant free emulsions. We argue that this is due to the fact that our model does not allow for nanobubble formation and capillary evaporation-processes that are presumably of key importance in the coalescence of surfactant-free emulsions.