## 3 Results and Discussion
### Dynamic Force Analysis
#### 3.5.2 Impact of Air Velocities  
Figure 18 illustrates the variations in force experienced by the droplet with a spherical diameter of \(D\) = 3 mm under airflow velocities of U = 3 m/s, 7 m/s, and 10 m/s. The evolution of the contact angle hysteresis force \(F_{adh}\) is depicted in Figure 18a. At U = 3 m/s, during the accelerated sliding phase, the value of \(cos\theta_{rec}-cos\theta_{adv}\) increases, leading to a corresponding increase in over time. At U = 7 m/s, the droplet undergoes initial acceleration followed by a halt, with the value of \(cos\theta_{rec}-cos\theta_{adv}\) first rising and then falling, mirroring the trend in \(F_{adh}\). At U = 10 m/s, the droplet accelerates upward, due to the impact of the airflow, and the droplet's shape undergoes significant alterations initially, causing fluctuations in the value of \(cos\theta_{rec}-cos\theta_{adv}\). However, as the upward trajectory of the droplet stabilizes, the value of \(F_{adh}\) also stabilizes. Figure 18b shows the wind traction force \(F_{wind}\) of the droplet at different airflow velocities. It is evident that, as the airflow velocity escalates, the value of \(F_{wind}\) also increases. At higher wind speeds, the instability in the droplet's projected area S leads to fluctuations in the value of \(F_{wind}\). Figure 18c presents the magnitude of the viscous dissipation force \(F_{\tau}\) acting on the droplet. Given that the volume of the droplet remains constant, the value of \(F_{\tau}\) aligns with the trend in the droplet's speed. With the increase in airflow velocity, the droplet's motion mode transitions from accelerated sliding to a state of force equilibrium, and eventually to accelerated climbing. In the accelerated sliding mode, the speed of the droplet progressively increases. In the force equilibrium mode, the speed initially rises and then decreases. In the accelerated climbing mode, the speed of the droplet consistently increases, with the direction opposite to that observed in the accelerated sliding mode.  
Figure 17: Comparison of the dominant force and the sum of hindering forces.  
As the airflow velocity changes, the dominant force influencing the droplet also changes. Figure 19 presents a bar chart comparing the dominant force with the sum of other hindering forces at different airflow velocities. The chart reveals that, at U = 3 m/s and U = 7 m/s, the gravitational component \(F_{S}\dot{s}\dot{s}\) serves as the principal force driving the droplet. With an increase in airflow velocity, the total of other hindering forces also rises, nearing the value of \(F_{S}\dot{s}\dot{s}\dot{s}\dot{s}\). However, at U = 10 m/s, the leading force in the droplet shifts to \(F_{wind}\), and the magnitude of \(F_{wind}\) surpasses the aggregate of other forces, propelling the droplet to accelerate upward in alignment with the airflow direction.  
Figure 19: Comparison of the dominant force and the sum of hindering forces.  
Figure 18: Evolution of the force magnitude on droplets of \(D\) = 3 mm over time at different velocities: (**a**) contact angle hysteresis force \(F_{\mathrm{{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{ \it{   }}}}}}}}}}}}}}}\); (**b**) wind traction force \(F_{\mathrm{{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{ \it{{\it{{   }}}}}}}}}}}}}}}}\); (**c**) viscous dissipation force \(F_{\mathrm{r}}\).