Dynamics of miscible and immiscible droplet impacts on a sessile water droplet

This study uses a combination of high-speed imaging and volume-of-fluid simulations to investigate the dynamics of low-velocity collisions between liquid droplets and a sessile water droplet on a moderately hydrophobic substrate. Four liquids with different miscibility and interfacial properties—ethanol, ethyl acetate, carbon disulfide, and water—are examined under identical impact conditions. The observed post-impact behaviors of liquids were markedly different, including variations in oscillation persistence, coalescence time, and rebound dynamics. A Black–Nichols (BN) diagram is presented as a compact gain–phase representation of the droplet impact response. This framework reveals distinct dynamical signatures associated with the liquids: miscible liquids exhibit rapid damping and negative phase shifts, while immiscible liquids display extended gain plateaus and persistent oscillations due to interfacial energy storage. The oscillation frequency remains nearly invariant across liquids, indicating a geometrically constrained capillary–inertial mode. However, damping characteristics depend strongly on interfacial transport processes. The BN slope scales with the interfacial relaxation time and collapses with the interfacial Péclet number, establishing a direct link between the transient sessile droplet's deformation response in a gain–delay representation and molecular diffusion. Off-center impacts further highlight the role of interfacial shear and mixing through asymmetric spreading and interface evolution. These results demonstrate that the dynamics of droplet collisions cannot be fully described by classical dimensionless numbers alone, but rather require the incorporation of molecular transport properties. The proposed BN-based framework is a powerful tool for analyzing multiphase interactions in applications such as microfluidics, coating, and interfacial engineering.