Force identification of a droplet impacting a flexible superhydrophobic substrate

Understanding and controlling droplet impact on flexible structures such as cantilever beams is critical for various industrial and agricultural applications, yet little is known about the force exerted by a single droplet on the solid surface. Accurate modeling of this force is particularly important for applications such as the design and characterization of micro-electro-mechanical systems (MEMS) and micro energy harvesting systems. This study aims to develop an accurate mathematical model to describe the droplet impact force applied to a superhydrophobic cantilever beam. To achieve this, we first employ computational fluid dynamics to simulate the impact of a water droplet on a superhydrophobic rigid surface, quantifying the dual-peak impact force exerted by the liquid phase on the superhydrophobic surface during the impact. Building on these numerical findings, we propose a novel force model that incorporates structural flexibility and captures the complex nature of the impact force. The proposed model includes both peaks in the dual-peak impact force generated during both the spreading and retracting phases of the droplet impact. The developed model is optimized using the experimentally measured response of the cantilever beam to a droplet impact. For this, the equation of motion of the cantilever is formulated using Euler–Bernoulli beam theory. Comparing the reconstructed and the measured responses of the beam shows the accuracy of the developed model in simulating the actual droplet impact force. Overall, this work deepens the understanding of droplet impact phenomena, provides a foundation for developing accurate droplet impact force models, and helps to improve the design of more efficient energy harvesting systems and MEMS.