## 3 Results and Discussion
### Dynamic Force Analysis
#### 3.5.1 Impact of Droplet Sizes  
Figure 16 illustrates the variations in force experienced by droplets of sizes \(D\) = 3 mm, \(D\) = 3.5 mm, and \(D\) = 4 mm under the airflow of U = 3 m/s. The evolution of the droplet contact angle hysteresis force \(F_{adv}\), a significant factor impeding droplet movement, is  
Figure 15: Variations of contact angle cosine for droplets with initial spherical diameter \(D\) of 3 mm, 3.5 mm and 4 mm in different air velocities: (**a**) U = 3 m/s; (**b**) U = 7 m/s. depicted in Figure 16a. According to Equation (20), the primary determinants are the differences in cosine values of the advancing and receding contact angles \(cos\theta_{rec}-cos\theta_{adv}\), and the wetting length \(L_{d}\). As the droplet size increases, the wetting length \(L_{d}\) also increases. The analysis of the cosine values of the contact angles in Figure 15a reveals that an increase in the advancing contact angle \(\theta_{adv}\), and a decrease in the receding contact angle \(\theta_{rec}\), which lead to a rise in the value of \(cos\theta_{rec}-cos\theta_{adv}\) over time. Moreover, as the droplet size enlarges, the initial fluctuation effect during droplet movement becomes more pronounced. Consequently, with the passage of time and increase in droplet size, the value of \(F_{adh}\) escalates, and the initial fluctuations in droplet movement become more evident. Under the influence of airflow, the wind traction force \(F_{wind}\) exerted on the droplet is illustrated in Figure 16b. The figure indicates that, at low airflow speeds, \(F_{wind}\) is generally modest, but its magnitude escalates with droplet size increases. According to Equation (23), \(F_{wind}\) is primarily influenced by the airflow velocity and the projected area S of the droplet. At the same airflow speed, an increase in the wetting length \(L_{d}\) of the droplet during its movement leads to a slight decrease in its the projected area, resulting in a decrease in the \(F_{wind}\). The viscous dissipation force \(F_{\tau}\) of the droplet, determined by the internal velocity gradient, is depicted in Figure 16c. The figure shows that, with the progression of time and enlargement of droplet size, the rate of increase of the viscous dissipation force \(F_{\tau}\) initially rises and then diminishes, because the magnitude of the viscous dissipation force \(F_{\tau}\) is mainly influenced by the volume of the droplet and the speed of its movement. As the droplet size expands, its volume increase. In the airflow of U = 3 m/s, the droplet accelerates its slide along the surface, resulting in a continuous increase in its speed. Figure 16: Evolution of the force magnitude on droplets of different sizes over time at U = 3 m/s: (**a**) contact angle hysteresis force \(F_{adh}\); (**b**) wind traction force \(F_{wind}\); (**c**) viscous dissipation force \(F_{\tau}\). According to the analysis in Section 3.3, at the velocity of U = 3 m/s, the droplet undergoes accelerated sliding motion, with its gravitational component \(F_{g}\)_sina_ serving as the primary force propelling the motion. In contrast, the contact angle hysteresis force \(F_{adh}\), viscous dissipation force \(F_{\tau}\), and wind traction force \(F_{wind}\) act as impediments. To illustrate the variations in forces acting on the droplets, Figure 17 displays a bar chart comparing the magnitude of the droplet's gravitational component force \(F_{g}\)_sina_ with the sum of the other inhibitory forces at t = 150 ms. The force values are annotated on the bars. As depicted in the graph, the contact angle hysteresis force \(F_{adh}\) emerges as the most substantial force obstructing the droplet's motion. During the accelerated sliding phase, the droplet's gravitational component force marginally exceeds the aggregate of the contact angle hysteresis force \(F_{adh}\), viscous dissipation force \(F_{\tau}\), and wind traction force \(F_{wind}\), aligning with the findings in Section 3.3.