Efficient mesh-free modeling of liquid droplet impact on elastic surfaces

The impact of liquid droplets on flexible substrates is a common phenomenon in applications, such as plant leaves repelling raindrops and piezoelectric sensors harvest droplet energy. It involves the coupling of free surface flow, elasticity and surface/interface with large deformations that are difficult to simulate using traditional numerical methods. In this study, a novel fluid–flexible structure interaction model is established based on the smoothed particle hydrodynamics (SPH) method. The droplet is described by a weakly compressible (WC) SPH formulation, and the flexible substrate is described by the total Lagrangian (TL) SPH formulation and Mindlin–Reissner shell theory using one layer of particles. Surface tension and wetting effects are simulated by an additional negative pressure term that creates attractive forces among fluid particles, and appropriate kernel functions are selected to eliminate stress instability owing to droplet spreading and retraction. The proposed model is applied to simulate the dynamic process of the droplet impact on hydrophilic and super-hydrophobic cantilever thin plates. The interaction of the droplet and thin plate is investigated under various conditions including stiffness, Weber number, and wettability. Predicted phenomena such as the springboard effect, droplet morphology, plate deformation, and vibration are consistent with experimental observations. The modeling strategy using the TL-SPH shell formulation and free surface WC-SPH formulation showed improved computational efficiency for 3D simulations. Nonlinear behaviors such as droplet spreading, splashing, and large deflection of the substrate, can be effectively reproduced, which demonstrates the potential of SPH in simulating such problem.