Drop rebound at low Weber number

Abstract

We study the rebound of drops impacting non-wetting substrates at low Weber number $We$ through experiment, direct numerical simulation, and reduced-order modeling. Submillimeter-sized drops are normally impacted onto glass slides coated with a thin viscous film that allows them to rebound without contact line formation. Experiments are performed with various drop viscosities, sizes, and impact velocities, and we directly measure metrics pertinent to spreading, retraction, and rebound using high-speed imaging. We complement experiments with direct numerical simulation and a fully predictive reduced-order model that applies natural geometric and kinematic constraints to simulate the drop shape and dynamics using a spectral method. At low $We$, drop rebound is characterized by a weaker dependence of the coefficient of restitution on $We$ than in the more commonly studied high-$We$ regime, with nearly $We$-independent rebound in the inertio-capillary limit, and an increasing contact time as $We$ decreases. Drops with higher viscosity or size interact with the substrate longer, have a lower coefficient of restitution, and stop bouncing sooner, in good quantitative agreement with our reduced-order model. In the inertio-capillary limit, low $We$ rebound has nearly symmetric spreading and retraction phases and a coefficient of restitution near unity. Increasing $We$ or viscosity breaks this symmetry, coinciding with a drop in the coefficient of restitution and an increased dependence on $We$. Lastly, the maximum drop deformation and spreading are related through energy arguments, providing a comprehensive framework for drop impact and rebound at low $We$.