Generalized models for advancing and receding contact angles of fakir droplets on pillared and pored surfaces

Understanding how surface properties determine the mobility of a fakir droplet on patterned surfaces, which is typically characterized by advancing and receding contact angles, is important in the design of superhydrophobic surfaces for tailored applications. However, most analytical models of the contact angles are limited to a specific motion direction and surface type, e.g., receding on a pillared surface. Although it was suggested that the contact angles should be determined by the local configuration and dynamics of the droplet boundary, their link remains vague due to the lack of detailed visualizations. In this study, the contact line dynamics of a fakir droplet in both advancing and receding motions on not only micropillared but also micropored surfaces are visualized in reflection interference contrast microscopy along with the contact angle measurement. Based on the energy change induced by the displacement of a contact line and the deformation of a liquid-gas interface in between contact lines, theoretical models of the contact angles to encompass the two different motion directions and surface types are formulated. Moreover, further generalized models are established to serve as effective analytical models to predict the contact angles only based on the given structure dimensions and the inherent surface hydrophobicity.