Describing Droplet Motion on Surface-Textured Ratchet Tracks with an Inverted Double Pendulum Model

We describe the motion of a droplet on textured ratchet track using nonlinear resonator model. A is composed semicircular pillar array that induces net surface tension local gradient placed it. When vertical vibration applied, hysteresis overcome, and moves toward lower energy barrier; however, due to repetitive structure texture, it keeps moving until end track. The depends amplitude frequency oscillation, this dependence nonlinear. Therefore, finding fully analytic solution represent not trivial. Consequently, remains poorly understood. In study, we elaborate utility double pendulum as basis for modeling surfaces inducing asymmetric force. Similar motion, resonators, such pendulum, are simple, yet systems. Moreover, an inverted has key characteristics two-phase peak which also observed in motion. use various data-processing methods highlight similarity between these two systems both qualitatively quantitatively. After establishing comparison, propose model utilizes mounted cart successfully simulate This methodology will lead development accurate droplet-motion approach, believe be useful understand dynamics more deeply.