Hydrodynamic collision and deformation of compound droplet pairs in confined shear flow

In this study, we numerically investigate the collision dynamics of core-shell compound droplet pairs under confined shear flow conditions. We focus on three collision modes: pass-over, coalescence, and reverse-back motions, analyzing their motion trajectories and morphological evolution. Notably, the coalescence mode exhibits significant dynamic behavior during evolution. However, the coalescence behavior of compound droplet pairs, as well as the impact of geometric parameters, including the initial vertical offset of droplets and the degree of confinement, on their dynamic behaviors, remains largely unexplored and unquantified. Our simulation results reveal that core droplets have little effect on the trajectory of droplet pairs during their pass-over and reverse-back motions, yet they significantly affect the dynamics in the coalescence mode. Additionally, we have addressed how the interplay between the core-shell size ratio, initial offset, and wall confinement affects the transition between collision modes, morphology, trajectory, and final state of the droplet pairs. Our findings show that an increase in the core-shell size ratios restricts the deformability of the shell droplets. Furthermore, in the coalescence mode, larger core droplets coalesce more rapidly due to spatial adjustment, expediting the stabilization of the newly formed compound droplet. While the size of the core droplets does not alter the transition boundary from coalescence to reverse-back mode based on initial vertical offset, they significantly influence the transition from coalescence to pass-over mode. Moreover, by analyzing confinement as another crucial geometric factor, we demonstrate the coupling effects of confinement and initial vertical offset on the transition between different collision modes.