Calculation of apparent contact angle for sessile droplets on structured hydrophobic surfaces based on dynamic of contact line during droplet formation

The sessile-droplet method is widely used to characterize surface wettability, however, the measured apparent contact angle (APCA) is usually a non-unique value between the advancing and receding contact angles, which seems hardly to be predicted by the classical Cassie-Baxter model. Thus, a reliable calculation model for APCAs of sessile droplets on structured hydrophobic surfaces is needed to guide the structural design of functional hydrophobic surfaces. Focusing on the force and motion analysis of the contact line during the formation process of sessile droplets, a theoretical model was developed to calculate the APCA of the droplet on hydrophobic surfaces featured with square micropillar arrays. The present model considers the synergistic effect of the droplet shape and the contact-line pinning on the APCA. Compared with the Cassie-Baxter model, the APCAs calculated by the proposed model agree better with the experimental data. This study shows that APCA is generally more susceptible to advancing contact angle, which is not significantly different on structured hydrophobic surfaces with different dimensions, resulting in the inability of APCA to accurately characterize surface wettability. As a complement, receding-contact-angle and adhesion-force measurements, which can reflect the effects of structural dimensions, are recommended to be adopted to characterize surface wettability.