Maximum spreading-based method for determining the pre-rebounding sliding length of a water droplet after impact on an inclined superhydrophobic textured surface

Mathematical prediction of liquid droplet sliding along self-cleaning, anti-icing, anti-fouling and water-repellent coatings is critically attractive for research and engineering development. The work deals with the development of a semi-empirical method for estimating the sliding length of a 2.1-mm water droplet before its rebound along inclined (0-85°) superhydrophobic micro-textured surfaces with advancing contact angles of 162-164°. The method is based on energy conservation-based prediction of the maximum spreading diameter of an impacting (0.5-3.2 m/s) water droplet as a time moment preceding its sliding. In the viscous dissipation work equation, the time of maximum droplet spreading is proposed to be considered through the normal ratio of wetting and antiwetting pressures of micro-textured surfaces. The developed method revealed a linear relationship between the sliding length of a droplet and its maximum spreading diameter. It was demonstrated that modeling the wetting of the internal elements of micro-textures is a crucial step in predicting the characteristics of both processes. As a prerequisite for the creation of a semi-empirical method for estimating the sliding length, the difficulties of empirical modeling of this characteristic are reasonably presented and discussed. The validity of the method for predicting the maximum spreading coefficient is substantiated by emphasizing the importance of adhesion work in the physics of spreading. The results of the study demonstrate the effectiveness of using the micro-textured, rough surface with a selected periodicity, contact angle and free surface energy as a practical water-repellent coating. This surface structure has been demonstrated to effectively repel water in real-world applications.