Investigations on the impact of a drop onto a small spherical target

This paper reports on experimental and theoretical investigations of the impact of a droplet onto a spherical target. Spatial and temporal variation of film thickness on the target surface is measured. Three distinct temporal phases of the film dynamics are clearly visible from the experimental results, namely the initial drop deformation phase, the inertia dominated phase, and the viscosity dominated phase. Experiments are also conducted to study the effect of droplet Reynolds number and target-to-drop size ratio on the dynamics of the film flow on the surface of the target. It is observed that for a given target-to-drop size ratio, the nondimensional temporal variation of film thickness collapses onto a single curve in the first and second phases. The transition to the viscosity dominated regime occurs earlier for the low Reynolds number cases and residual thickness is also larger. A simplified quasi-one-dimensional approach has been used to model the flow on the spherical target. The theory accounts for the inertial and viscous effects. Gravity and the curvature of the target are also taken into account. An analytical expression for the time-dependent film profile on the sphere is obtained for the inviscid, inertia dominated phase of spreading. Then, the evolution equation for the film thickness near the north pole in the viscosity dominated phase is obtained and solved. Good agreement is observed between the theoretical predictions and the measurements when the values of the drop and target diameters are comparable. No adjustable parameters have been used in the model.