On the bounce: capillary rebound of droplets impacting onto a liquid bath #

Radu Cimpeanu, Luke F L Alventosa, Daniel M Harris

11:10 Monday in 4Q04.

Part of the Droplets and impact session.

Abstract #

We consider the canonical problem of a millimetric drop impacting onto a deep bath of the same fluid. Following a comprehensive experimental campaign, measurements of the droplet trajectory are compared directly to the predictions of a quasi-potential model, as well as fully resolved direct numerical simulations of the unsteady multi-phase Navier-Stokes equations. Both theoretical techniques 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 technique. The proposed methodology (Alventosa, Cimpeanu and Harris, JFM 957, 2023) has allowed us to unify and resolve interesting outstanding questions on the rebound dynamics of the multi-fluid system. In particular, we find that increases in gravity or viscosity lead to a decrease in the coefficient of restitution and an increase in the contact time. Furthermore, the inertio-capillary limit defines an upper bound on the possible coefficient of restitution for droplet-bath impact, depending only on the Weber number.