Simulation of droplet bouncing on flexible substrate in 2D and 3D with WC-TL SPH method

Abstract

Droplet impacts on super-hydrophobic surfaces play an important role in many fields. Previous studies have focused on rigid substrates and ignored the effect of substrate deformation. Simulating droplet impacts on a flexible substrate is a challenge to numerical methods due to the coupling of free surface, elasticity, large deformation and surface tension. In this study, a fully meshfree model of fluid–solid interaction is developed based on the smoothed particle hydrodynamics (SPH) method. The liquid droplet is modeled by the weakly compressible (WC) SPH method, and the flexible substrate is modeled by the total Lagrangian (TL) SPH method. Liquid surface tension is modeled by the continuum surface force (CSF) method through reconstructing the free surface of the droplet. The surface geometry reconstruction process is given for both 2D and 3D cases, enabling the model to simulate the bouncing of droplets in both 2D and 3D cases. Furthermore, in order to reduce the computational cost of 3D simulation, the TL-SPH model combined with shell theory established the TL-SPH-shell model, thus achieving the simulation of 3D droplet impact on thin plates. For verification and testing, the established WC-TL SPH model is used to simulate the process of droplet impact on various substrates, including fixed-fixed and curved beams, micro-pillar substrates, and cantilever beams. The results show that the spreading, retraction and bouncing processes of the droplets interact with the deformation and recovery of the flexible substrate, accompanied by large deformation and dynamic characteristics, which can be effectively simulated by the model.