Brownian Dynamics of Emulsion Film Formation and Droplet Coalescence

We analyze the evolution of the thickness and radius of a thin liquid film formed during the collision of two deformable emulsion Brownian droplets. These variables exhibit fluctuations due to thermal disturbances from the continuous liquid phase. As a result, the system probes a random trajectory in the configuration space until it reaches a critical film thickness, at which point the droplets coalesce. Therefore, the film is modeled as a disk with thickness and radius 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, inter-facial 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.