## 4 Conclusions  
In this study, the CLSVOF method is employed to examine the behavior of droplet adhesion on the inclined windshield surface under airflow. Droplet sizes and airflow velocities are considered as key factors influencing this phenomenon. Firstly, the study focuses on exploring the variations in the direction and displacement of droplets under different air velocities. Subsequently, based on the outcomes of the numerical simulations, a classification of the droplet motion patterns is established, and the trends in the changes of droplet morphological parameters are analyzed. Finally, the forces acting on the droplets are calculated using relevant equations. The temporal evolution of these forces is investigated, and the primary forces driving droplet movement are compared with other resisting forces. At different airflow velocities, the wind traction force \(F_{wind}\) acting on the droplet changes, leading to distinct modes of droplet motion: accelerated sliding at low wind speeds, equilibrium of forces, and accelerated climbing at high speeds. When the wind speed is low, the gravitational component \(F_{S}\dot{s}\dot{s}\dot{s}\dot{s}\) predominates in the droplet's movement, surpassing the combined effect of other impeding forces, causing the droplet to accelerate downwards along the surface. During this process, the wetting length \(L_{d}\) of the droplet increases, while its height \(H\) decreases slightly. The advancing contact angle \(\theta_{adv}\) increases, and the receding contact angle \(\theta_{mc}\) decreases, resulting in a larger difference in the cosine of the contact angles. As the size of the droplet increases, the variation in morphological parameters becomes more pronounced, and the disparity between the gravitational component \(F_{S}\dot{s}\dot{s}\dot{s}\dot{s}\) and the sum of other hindering forces continues to grow. In the force equilibrium mode, the velocity of the droplet initially increases and then decreases with the rise in air velocity. Throughout the movement, the wetting length \(L_{d}\) of the droplet diminishes while its height \(H\) escalates, resulting in a more compact droplet profile. The advancing contact angle \(\theta_{adv}\) initially rises and then falls, whereas the receding contact angle \(\theta_{mc}\) exhibits the opposite trend. The differences in the cosine values of the contact angle first increase and then decrease, mirroring the variation pattern of the contact angle hysteresis force \(F_{adh}\). When the airflow velocity is high, the droplet accelerates along the surface, primarily driven by wind traction force \(F_{wind}\). As the velocity of the droplet increases, the value of the viscous dissipation force \(F_{\tau}\) also rises. In this mode of motion, the wind traction force \(F_{wind}\) exceeds the combined value of other forces that impede the droplet's movement. During this phase, the droplet's interface experiences intense oscillations, leading to significant fluctuations in both the wetting length \(L_{d}\) and the height \(H\) of the droplet. In addition, the value of \(F_{adh}\) and \(F_{wind}\) also exhibits substantial variations because of droplet oscillation. If the inclination angle of the windshield and the state of the liquid falling change, the behavior of the droplets will also change. Therefore, to understand the droplet motion behavior on the window surface in more detail, further studies are needed based on different droplet falling states and inclination angles of the windshield, which will be the next step in the study. Conceptualization, F.D. and L.X. ; methodology L.X. ; software, X.X. ; validation, X.X. and L.X. ; formal analysis, F.D. ; investigation, X.X. and L.X. ; resources, F.D. ; data curation, X.X. ; writing--original draft preparation, X.X. ; writing--review and editing, X.X. ; visualization, L.X. ; supervision, F.D. ; project administration, F.D. ; funding acquisition, F.D. All authors have read and agreed to the published version of the manuscript.