Numerical simulation of coalescence of micron-submicron sized droplets and thin films

Dynamics of droplet merging emerges with an utmost significance in many scientific areas and its effects ranges vastly from agriculture to engineering. Understanding the underlying physics of coalescence of droplets is, therefore, crucial to have control over its effects in complex systems which they are included. In this study, time dependent coalescence dynamics of fully wetting cylindrical droplets is investigated extensively. Droplets are created utilizing the Young-Laplace equation, and the dynamics of the temporal development and the merger of two liquid droplets is studied through the solution of the governing unsteady Reynolds equation, obtained with lubrication assumption. The governing Reynolds equation is a 4th order non-linear partial differential equation for film thickness and it is solved using a time step marching algorithm in conjunction with an implicit formulation of the spatial domain solved iteratively to account for the non-linear terms.