Study of inertial coalescence of droplets on a solid substrate using lattice Boltzmann modeling

Whenever two liquid drops contact, they coalesce to form a single droplet to minimize the surface energy. It is a fundamental process and has a wide range of applications in droplet condensation, microfluidic devices, inkjet printing, and powder metallurgy. Earlier studies were focussed on the coalescence of free droplets. However, in many applications, e.g., dropwise condensation, coalescing drops are in contact with a solid surface. Besides, the coalescence dynamics of sessile drops on a surface deviates significantly from that of free drops. In the present work, we focus on the early-stage coalescence of drops on a solid substrate in the inertial regime. We use a pseudo-potential lattice Boltzmann method to simulate coalescence of equal size droplets and the coalescence of unequal size droplets. Our simulation results show that for a surface with contact angle below 90°, bridge height grows with time and follow h∼t^2/3. We also show that the rescaled bridge profile at different times collapses into a single curve. We supplement our LBM simulation results with scaling analysis.