Coalescence is a complex phenomenon leading to the merging
of deformable
particles of fluid. The complexity stems largely from the simultaneous
occurrence of phenomena of a different nature (hydrodynamic, electrostatic,
physicochemical) acting at different scales. The stochastic effects
controlling the formation of the liquid bridge between two droplets
of the same liquid, immersed in another nonmiscible liquid, are studied
through a series of molecular dynamics simulations. The case of heptane
droplets in water, relevant to solvent extraction, a key process of
the circular economy, is considered. From this series of simulations,
we have confirmed that the probability function of coalescence of
two identical droplets in contact follows a Poisson distribution.
We moreover propose a criterion for the initiation of coalescence
based on nucleation theory. A complete description of the stochastic
initiation of coalescence is hence provided, opening many perspectives
for the simulation of coalescence in continuous approaches used in
fluid mechanics and chemical engineering. The methodology can be generalized
to droplets of different size and composition, immersed in gas, or
to bubbles, i.e., to other physical problems whose kinetics is influenced
by the molecular scale.