Underdamped dynamics of a droplet deposited onto a fluid bath*

The deposition of droplets on a fluid interface is studied both experimentally and theoretically. Millimetric drops impact a deep bath of the same fluid and are generated using a custom syringe pump connected to a vertically-oriented needle. Measurements of the droplet trajectory are compared directly to the predictions of a quasi-potential model, as well as fully resolved unsteady Navier-Stokes direct numerical simulations. Both models resolve the time-dependent bath interface shape, droplet trajectory, and droplet deformation. In the quasi-potential model, the droplet and bath shape are decomposed using orthogonal function decompositions leading to a set of coupled damped linear oscillator equations solved using an implicit numerical method. The underdamped dynamics of the drop are directly coupled to the response of the bath through a single-point kinematic match condition which we demonstrate to be an effective and efficient model in certain parameter regimes.  Specific scenarios where the oscillations of the droplet and bath play a significant role in the overall dynamics will be highlighted. Ongoing and future work will be discussed.