Schematic drawing of the early stages of droplet coalescence. When two surfactant-covered droplets coalesce, the two monolayers must merge. In order for droplets to merge, the surfactants must reorient and rearrange to form a channel. Expansion of the channel radius completes the coalescence process.
The simulation system is a “zoom in” on two oil droplets in water. The chemical potential of the water film is fixed so as to mimic the equilibrium with the bulk water reservoir.
Schematic illustration of the surfactants used in this study. The light gray particles are hydrophilic/head beads and the dark gray particles hydrophobic/tail beads . The surfactants are labeled , , and , to reflect that they have negative, zero, and positive natural curvatures, respectively.
(Color) Three trajectories connecting states and for the system with . The vertical lines are the interfaces employed in the FFS scheme.
Film-rupture rates in an oil-water-oil film, without surfactant, as a function of film thickness.
The critical value of the reaction coordinate vs film thickness . When is positive, it denotes a critical channel radius; when it is negative, it denotes the critical local film thickness as defined in Appendix A. The solid line is a fit to the four lowest -values. The dashed line is a continuation of the solid line with slope as predicted by the channel nucleation theory (see text).
The rate of reaching the stage described by in the film rupture process. The final rupture rate is where levels out.
(Color) Snapshots of the critical configuration for . The green dots in (b), (c), and (d) denote the thinnest point in the film. (a) Oil, plane. (b) Surfactant, plane. Only bonds are drawn. (c) Surfactant, plane. Only bonds are drawn. (d) Water, plane. The beads are drawn with a radius of to show the film thinning. (According to the definition of there is no hole.)
(Color) Snapshots of the critical configuration for . The green area in (d) and (f) is the area of the hole, according to the definition of . (a) Oil, plane. (b) Surfactant, plane. Only bonds are drawn. (c) Water, plane. (d) Surfactant, plane. Only bonds are drawn. (e) Water, plane. The beads are drawn with a radius of to show the film thinning around the hole.
(Color) A zoom-in on snapshots of the critical configuration for . Only the bonds are drawn. (a) plane. (b) plane. The red circle in (b) encircles the cluster of hydrophobic tails that are oriented towards each other and make up the channel.
Surface tension, bending rigidity, film-rupture rates, and the critical reaction coordinate for an oil-water-oil film at . The surface tension values are normalized by the bare oil/water surface tension, . is given in DPD units. The surfactants are shown in Fig. 3.
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