Scaling Laws of Droplet Coalescence: Theory and Numerical Simulation

When two Newtonian liquid droplets are brought into contact on a solid substrate, a highly curved meniscus neck is established between the two which transforms the bihemispherically shaped fluid domain to a hemispherically shaped domain. The rate at which such topological transformation, called coalescence phenomenon, evolves results from a competition between the inertial force which resists the transformation, the interfacial force which promotes the rate, and the viscous force which arrests it. Depending on the behaviour of these forces, different scaling laws describing the neck growth can be observed, predicted theoretically, and proved numerically. The twofold objective of the present contribution is to propose a simple theoretical framework which leads to an Ordinary Differential Equation, the solution of which predicts the different scaling laws in various limits, and to validate these theoretical predictions numerically by modelling the phenomenon in the commercial Finite Element software COMSOL Multiphysics.