## 3 Results and Discussion  
### Experiment and Model Validation  
During the study, we developed an experimental setup to capture the movement of adhesive droplets on a tilted surface within airflow environment, as illustrated in Figure 7. A high-speed video camera equipped with an image processing system was utilized to record the details of droplet motion under the airflow, while an LED light source provided illumination for the experiments. Airflow was generated using a centrifugal fan, with the wind speed regulated by a wind speed adjustment device. The air passed through a 100 cm long rectifier equipped with damping screens to ensure the stable airflow. The hydrophilic glass substrate had a tilt angle of 30 degrees, identical to tilt \(\alpha\) in the 3D model.  
To ensure the accuracy and reliability of the experimental data, we conducted at least three replicated experiments for each airflow velocity to assess the behavior of the droplets and minimize experimental error. Figure 8 illustrates the dynamic behavior of droplets in airflow environments with velocities of U = 3 m/s, 6 m/s, and 10 m/s, using droplets with a spherical diameter of \(D\) = 3 mm. The initial state of droplet movement is marked as t = 0 ms, with the red arrow indicating the direction of droplet movement along the tilted surface.  
Figure 6: Results of droplet spreading factors under different minimum grid sizes.  
Figure 7: Schematic diagram of the experimental setup.  
As shown in the Figure 8, at U = 3 m/s, the droplet retains its spherical cap shape in the initial state. Over time, the droplets travel greater distances along the surface and increase in velocity. At U = 6 m/s, the droplet initially moves down the surface, but its contour changes significantly during movement, resulting in an increase in droplet height \(H\) and a decrease in wetting length \(L_{d}\). Additionally, the distance the droplet travels decreases significantly between t = 100 ms and 150 ms. At U = 10 m/s, the high airflow velocity prevents the droplet from maintaining a symmetric spherical cap shape in the initial state, causing the droplet to accelerate upwards along the inclined plane.  
In addition, this section also compares the profiles of droplets and the displacement of the contact line under airflow conditions of U = 6 m/s between experimental observations and simulation results to validate the accuracy of the simulation. The distances between the contact lines in both experimental and numerical simulations were analyzed using the contact angle plug-in of ImageJ 1.8.0 software, with each measurement repeated five times for enhanced precision.  
Figure 9 presents a comparison between the profiles of droplets in numerical simulations and experimental observations over various time intervals. Figure 9 depicts the movement distances of the advancing and receding contact lines. The average error between the numerical simulation results and the experimental measurements of the contact angle is found to be less than 5%, which falls within the acceptable range of engineering error. This demonstrates the reliability of the numerical model, as evidenced by the consistent agreement between the experimental data and the numerical results.  
Figure 8: Schematic diagram of droplet with spherical diameter \(D\) = 3 mm along the inclined windshield surface at different airflow speeds: (**a**) U = 3 m/s; (**b**) U = 6 m/s; (**c**) U = 10 m/s.