Energy Loss for Droplets Bouncing Off Superhydrophobic Surfaces

A water droplet can bounce off superhydrophobic surfaces multiple times before coming to a stop. The energy loss for such droplet rebounds can be quantified by the ratio of the rebound speed U_R and the initial impact speed U_I; i.e., its restitution coefficient e = U_R/U_I. Despite much work in this area, a mechanistic explanation for the energy loss for rebounding droplets is still lacking. Here, we measured e for submillimeter- and millimeter-sized droplets impacting two different superhydrophobic surfaces over a wide range of U_I (4-700 cm s^-1). We proposed simple scaling laws to explain the observed nonmonotonic dependence of e on U_I. In the limit of low U_I, energy loss is dominated by contact-line pinning and e is sensitive to the surface wetting properties, in particular to contact angle hysteresis Δ cos θ of the surface. In contrast, e is dominated by inertial-capillary effects and does not depend on Δ cos θ in the limit of high U_I.