A catastrophe phenomenon produced by impact of drop trains

The impact of drop trains is widespread in industrial and agricultural applications, as well as in nature, making it crucial to investigate. In this study, the impact of drop trains on solid surfaces is experimentally investigated using a high-speed camera. A catastrophe phenomenon that had previously been overlooked is discovered: with the successive impact of drop trains, the impact result undergoes a discontinuous catastrophe, from a thin film impact generating the crown splash to a thick film impact generating the Worthington jet. The thickness of the thin film is less than 0.23 times the impact drop's diameter, while the thickness of the thick film ranges from 0.52 to 1.05 times the impact drop's diameter. The reason for the catastrophe is revealed from a phenomenological perspective. The number of impact drops and the impact Weber number are important factors determining the occurrence of catastrophe, and the critical number of impact drops for the catastrophe is linearly and positively correlated with the impact Weber number. Based on the cusp catastrophe theory, a catastrophe threshold model for drop train impact is established. This model is able to predict the threshold for the occurrence of catastrophe and provide a method for identifying the thin film stage, the thick film stage, and the transient catastrophe stage between these two stages. The catastrophe threshold model achieves the identification accuracy of 83.48%, 91.72%, and 77.50% for the total measured data, the thin film stage, and the thick film stage, respectively, indicating its good performance.