Engulfment of a drop on solids coated by thin and thick fluid films

We investigate the dynamics of an aqueous droplet as it becomes engulfed by an oil film coating a solid substrate. This process is simulated by the conservative phase-field equation and pressure-velocity formulation using the lattice Boltzmann method, which capture the interface dynamics and the flow momentum for the ternary flow system. Through numerical simulations, we characterize how the droplet engulfment dynamics is affected by the thickness of the fluid film coating the substrate as a function of the Ohnesorge number. The simulation results imply that when the fluid film thickness is four times or more than four times of the droplet radius, the influence of fluid film thickness can be neglected. Different regimes are identified and described by scaling analysis.