Brownian dynamics of emulsion film formation and droplet coalescence

We analyze the evolution in thickness and radius of the film formed during the collision of two deformable emulsion Brownian droplets. These variables exhibit random fluctuations due to thermal disturbances from the continuous liquid phase. As a result, the system probes a random trajectory in the configurational space until it reaches a critical film thickness, at which point the droplets coalesce. Therefore, the film is modeled as a disk with thicknesses and radi that can fluctuate. Our analysis is based on a Langevin-Brownian dynamics approach, which accounts for the thermodynamic and hydrodynamic interactions in the lubrication approximation. We examine the effect of parameters such as droplet size, interfacial mobility, and electrolyte concentration on the coalescence of small Brownian droplets. The results suggest that the coalescence times depend on a complex interplay between the thermodynamic and hydrodynamic interactions.