  The rebound of droplets impacting a deep fluid bath is studied both
experimentally and theoretically. Millimetric drops are generated using a
piezoelectric droplet-on-demand generator and normally impact a bath of the
same fluid. Measurements of the droplet trajectory and other rebound metrics
are compared directly to the predictions of a linear quasi-potential model, as
well as fully resolved direct numerical simulations (DNS) of the unsteady
Navier-Stokes equations. Both models resolve the time-dependent bath and
droplet shapes in addition to the droplet trajectory. In the quasi-potential
model, the droplet and bath shape are decomposed using orthogonal function
decompositions leading to two sets of coupled damped linear harmonic 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 our parameter regime of interest. Starting from the
inertio-capillary limit in which both gravitational and viscous effects are
negligible, increases in gravity or viscosity lead to a decrease in the
coefficient of restitution and an increase in the contact time. The
inertio-capillary limit defines an upper bound on the possible coefficient of
restitution for droplet-bath impact, depending only on the Weber number. The
quasi-potential model is able to rationalize historical experimental
measurements for the coefficient of restitution, first presented by Jayaratne
and Mason (1964).
