Dynamic Behavior of Droplets Impacting on Superhydrophobic Substrates under Vibrational Fields

The phenomenon of droplets impacting solid surfaces under a vibrating field is commonly observed in various production and application processes across industries such as manufacturing, agriculture, and energy. This study examines the dynamic behavior of a free-falling droplet impacting a vibrating superhydrophobic substrate using high-speed photography. The effects of the initial phase angle (φ), Weber number (We), and vibration frequency (f) on the droplet's morphological evolution and energy dissipation during the impact process are analyzed. Based on the experiments, the maximum spreading diameter and maximum rebound height of the droplets were systematically analyzed under varying initial phase angles, Weber numbers, and vibration frequencies. This analysis revealed the mechanism behind the generation of daughter droplets and enabled the quantification of the Weber number and initial phase angle ranges that result in their formation. Meanwhile, the relationship between the dimensionless spreading coefficient and dimensionless time under varying vibration frequencies and initial phase angles was established, highlighting the effects of vibration frequency and initial phase angle on the spreading and retraction processes during droplet impact. Additionally, an energy analysis of the droplet impact on a vibrating substrate was performed to develop a theoretical mathematical model for predicting the maximum spreading diameter. The prediction error was found to be within 1% when compared to the experimental results.