Viscous dissipation upon water droplet impact on an oil layer atop water pool

The impact of a droplet onto another liquid is already a complex problem in which many forces are involved, but the problem becomes even more complex when an additional liquid layer is introduced. In this study, we report our investigation of the impact of water droplet on a thin oil layer ( similar to 1 mm) atop water pool. As expected, the oil layer acts as a damper to the impact kinetic energy of the droplet, and the damping is greater as the viscosity of oil increases. We find that the damped energy is associated with the drainage of oil outward from the thin oil layer at the point of impact, i.e., viscous dissipation. To rationalize this observation, we introduce an analytical model that approximates the amount of viscous dissipation based on the volume displacement of oil by impact, defined by the cavity growth rate. Here, we introduce a parameter called the oil layer volume conservation factor and validate the equation indirectly, as the calculated values of this factor fall within the range of experimental values.