Integrating Inertia and Surface Tension Effects in Droplet Coalescence Dynamics

Coalescence of droplets is a fascinating phenomenon observed both in nature and industry, influencing various processes and applications. In nature, the coalescence of sessile droplets can be seen in phenomena such as dew formation on leaves or spider webs. In industry, this phenomenon is applied in processes like spray coating and inkjet printing. When two droplets come into contact, a highly curved liquid bridge forms at the contact point, generating high Laplace pressure that propels the liquid into the bridge and facilitates their merging. Surface tension and viscosity significantly influence this process: higher surface tension increases Laplace pressure and accelerates coalescence, while higher viscosity prolongs the merging process by resisting deformation and flow. Previous studies show that the lubrication approximation can be applied to small, high-viscosity droplets on non-wetting surfaces. However, for larger droplets with lower viscosity, the lubrication equation falls short as inertial effects become significant and must be considered to accurately describe the coalescence dynamics. In this study, by incorporating inertia and surface tension gradients into theoretical models and comparing the results with experimental data, we aim to provide a more comprehensive description of droplet coalescence dynamics across different droplet sizes and liquid properties. This work advances our understanding of the coalescence process and paves the way for further research in this domain.