Probing the Influence of Inertia, Viscosity, and Initial Offset on the Hydrodynamic Interaction of Droplet Pairs in Confined Shear Flow

Understanding the hydrodynamics of droplet collision is vitally important due to the inherent small-scale phenomena and various practical applications. The morphology, course trajectory, and final state of the droplets in such a collision are greatly affected by different physical parameters together with system geometry. Yet the collision behavior of droplet pairs at high density and viscosity ratios remains unexplored and unquantified, and therefore the critical density and viscosity ratios for the collision mode of droplets under geometric parameters were unknown. Through computational analyses, we address the interplay between the density ratio (60 to 800), the viscosity ratio (24 to 60), the initial offset, and the confinement on the coalescence of droplet pairs subjected to a confined shear flow. Simulations have been performed using a free-energy-based lattice Boltzmann method, with the aim of determining new regimes compared to the previous study. The results reveal that the coupling effect of density ratios and viscosity ratios contributes to generating inertia and viscous interaction forces that significantly impact the coalescence consequences. On the other hand, the wall confinement and the initial vertical offset of droplets are shown to play a significant role in either promoting or suppressing the collision mode of interacting droplets. Interestingly, we observe unusual trajectory motion of droplets for an intermediate range of density ratios (i.e., 245-600) near the critical initial offset of droplets. Regions of different collision modes are further presented in terms of phase diagrams, which reveal the critical dependency of droplet behavior on the coupling effect of density ratios, viscosity ratios, initial vertical offset, and confinement. The reported results are expected to provide new insights into the collision of pair droplets under confined shear flows in the effect of various parameters and help elucidate the intrinsic nature and the condition of coalescence.