## 3 Results and Discussion
### Changes in Droplet Morphology Parameters  
Based on the above analysis, it has been concluded that, under different air velocities, the adhering droplets on the inclined surface can be divided into three motion modes: accelerated decline, force equilibrium, and accelerated climb. In this section, the surface wettability and surface properties of droplets under different motion modes are described by investigating the droplet wetting length \(L_{d}\), droplet height \(H\), and the cosine number of advancing contact angle \(\theta_{adv}\) and receding contact angle \(\theta_{rec}\) on the inclined surface. Figure 14 compares the values of wetting length \(L_{d}\) and droplet height H in different motion modes for the adherent droplets with spherical diameter \(D\) of 3 mm, 3.5 mm, and 4 mm on a 30\({}^{\circ}\) windshield in the air velocity of U = 3 m/s, 7 m/s and 10 m/s based on the simulation results in the previous section. From Figure 14a,b, at the velocity of U = 3 m/s, the droplet is in an accelerated downward motion at this time. The gravitational component force \(F_{g}sin\alpha\) dominates the droplet motion. Therefore, the value of wetting length \(L_{d}\) will be affected by the dominant force at the beginning, and then increased, while the value of droplet height \(H\) will decrease. As the size of the droplet increases, the inertial force of the droplet strengthens, leading to a more pronounced increase in \(L_{d}\) and decrease in \(H\). The forces gradually stabilize the droplet during the continuous acceleration of the decline. Therefore, the droplet morphology also reflects the trend of \(L_{d}\) and \(H\) changes first and then stabilizes. However, due to the existence of constant output wind force and the inertial force, it will lead to the oscillation at the droplet interface, and the value of \(L_{d}\) and \(H\) have smaller fluctuations under this trend. At wind speed U = 7 m/s, wind traction force \(F_{wind}\) increases significantly. From Figure 14c,d, unlike the case of U = 3 m/s, the value of \(L_{d}\), which initially adheres to the inclined surface and remains stable, decreases significantly, and the value of \(H\) increases significantly, showing a \"compact\" droplet pattern. At this time, the droplet forces have not yet reached equilibrium, so in the subsequent motion process the force equilibrium will be reached through the change in \(L_{d}\) and \(H\). With time changes, the value of \(L_{d}\) increases and tends to be stable, but the value of \(H\) still fluctuates up and down, and gradually stabilizes after 120 ms. From the overall tendency, the stable value of \(L_{d}\) decreases and the value of \(H\) increases compared with the initial value. Figure 13: Schematic diagrams of droplet contours and motion on the windshield at air velocity \(U\) of 8–12 m/s: (**a**) \(D\) = 3 mm; (**b**) \(D\) = 3.5 mm; (**c**) \(D\) = 4 mm; (The arrow direction corresponds to the direction of droplet motion, and the contours correspond to the time step: 0 s–50 ms–100 ms–150 ms). At higher wind speeds U = 10 m/s, at this time wind traction force \(F_{wind}\) becomes completely the dominant force in the droplet motion. From Figure 14e,f, it can be seen that, the higher the wind speed, the more likely the droplets will experience violent interfacial oscillations. Therefore, raindrops experience sharp changes in both droplet wetting length and droplet height. Figure 14: Diagrams of droplet wetting length \(L_{d}\) and droplet height \(H\) with initial spherical diameters \(D\) of 3 mm, 3.5 mm and 4 mm in different air velocities: (**a,b**) U = 3 m/s; (**c,d**) U = 7 m/s; (**e,f**) U = 10 m/s. \(L_{d}\) and droplet height \(H\) values during the climb along the inclined plane, and this change increases as the size of the droplet increases. At the moment of initial motion, the droplets are more \"compact\" than at U = 7 m/s due to the influence of larger airflow force, and the number and amplitude of fluctuations in the \(L_{d}\) and \(H\) values are much higher.