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

When an aqueous drop contacts immiscible oil film, it displays complex interfacial dynamics. Upon contact the spreads onto drop's liquid-air interface, first forming a curvature that drives apparent spreading motion and later fully engulfing drop. We study this flow using both 3-phase Lattice-Boltzmann simulations based on conservative phase field model experiments. Inertially viscously limited dynamics are explored Ohnesorge number $Oh$ as function of $R/H$, ratio between initial radius $R$ film height $H$. Both regimes show $r$ is fairly independent height, scales with time $T$ $r\sim T^{1/2}$ for $Oh\ll 1$ $Oh\gg T^{2/5}$. For we experimentally analogous miscible drop-film coalescence case. Contrary to spreading, however, find late engulfment final interface profiles significantly affected by $H/R$.