Unified 1/2 scaling laws for droplet impact dynamics: From rigid to flexible thin films

Abstract

Droplet impact dynamics on solid surfaces, which are ubiquitously present in aerospace engineering, energy systems, agricultural production, etc., involve complex fluid–structure interactions. Herein, we employ a single-camera high-speed three-dimensional digital image correlation system to quantify the full-field deformations of flexible thin films during droplet impact dynamics. Experimental results revealed that the substrate flexibility not only reduces the maximum spreading diameter by 10% but also modulates rebound dynamics via energy competition between kinetic energy and surface adhesion energy, suggesting that coupled deformation of the solid–fluid interface plays an important role in the dynamic progress. We propose the structure-coupled response number (Sn), a governing dimensionless parameter unifying droplet spreading on both rigid and flexible films, validated by a universal 1/2 scaling law. A theoretical criterion for droplet rebound on hydrophobic flexible thin films is derived and experimentally demonstrated, which achieves the precise control of droplet rebound/non-rebound mode. This work bridges the theories of droplet impact dynamics on rigid and flexible substrates, offering a robust strategy to govern the droplet impact behaviors.