Viscous dissipation during water droplet impact on an oil layer over a water pool

Droplet impact phenomenon is commonly observed in our daily life such as when a raindrop falls into a puddle. Despite its ubiquity, impact of a droplet on another liquid is inherently complex, involving numerous forces. This complexity increases with the introduction of an additional liquid layer. In this study, we investigated the impact of a water droplet on a thin oil layer (~1 mm) deposited on a water pool. We released droplets of different diameters from a consistent height toward oil layers with seven variants of viscosities, ranging from 5 cSt to 500 cSt. As expected, our quantitative measurements revealed that as viscosity increases, the maximum cavity size decreases, indicating that the presence of an oil layer damps impact energy. We found that the damped energy is primarily used to push the oil outward from the impact point. To explain this observation, we developed an analytical model approximating viscous dissipation based on the volume displacement of oil due to impact, defined by the cavity growth rate. However, direct estimation of viscous dissipation was challenging for oil viscosities ν≤200 cSt because the oil layer was too thin to be measured. To address this, we introduced an oil layer volume conservation factor into the model, validating the equation indirectly as the calculated values of this factor matched the experimental range.