Modeling the Dynamic Contact Angle and the Pinning Effect of Water Droplets in Shear Flow

Understanding the behavior of water droplets has become increasingly important for automotive products as the industry moves toward electrification in recent years. Particularly, predicting the pinning effect, where water droplets remain stationary against external forces by changing their contact angle or surface tension, is crucial for assessing drainage behavior. Hoffman and Kistler proposed dynamic contact angle models based on the capillary number (<i>Ca</i>) to predict droplet motion. However, since the <i>Ca</i> number includes the contact line speed, it is difficult to predict the pinning effect by way of dynamic contact angle equations formulated by the <i>Ca</i> number. This study aims to predict the pinning effect by analyzing the balance of forces acting on the water droplets. Through experimental observations of the contact angles of water droplets under shear flow and numerical simulations to evaluate the drag force acting on the droplets under the same conditions, we derived a relationship between the drag force and the dynamic contact angle. Furthermore, this relationship was implemented in commercial computational fluid dynamics (CFD) software, and its effectiveness was validated by comparing predicted critical airflow velocities with experimental results. These results demonstrate that the numerical simulation method, which accounts for the balance of forces on the droplets, effectively predicts the pinning effect.