Apparent contact angle of curved and structured surfaces

Abstract

The apparent contact angle is typically used to quantify the wettability on rough or structured surfaces. In particular, the prediction of the apparent contact angle is essential to design and control the surface wettability on structured surfaces. Researchers have questioned the validity of Wenzel and Cassie–Baxter equations regarding utilizing solid material of interfacial contact area instead of that at the triple contact line to calculate the apparent contact angle. In this study, we devised a new method to predict the apparent contact angle on a structured surface by utilizing the properties of actual contact angle derived from the “transversality condition.” The transversality condition shows that when a liquid is in equilibrium on a smooth curved solid surface, the actual contact angle equals the Young’s contact angle (disregarding influence of line tension). By treating the structured surface as a curved surface, the equilibrium condition was applied to calculate the apparent contact angle on both smooth and non-smooth structured surfaces. Experiments were conducted on surfaces with both concentric and parallel V-shaped grooves, which served to verify our conclusion. The proposed model demonstrates that the apparent contact angle is only influenced by the material at the triple contact line and remains independent of the contact area, a principle that is, however, violated by the Wenzel and Cassie equations. Furthermore, the model facilitates exploration of the manner in which different shapes of micro–nano structures with the same roughness factor impact the apparent contact angle, a phenomenon that the Wenzel equation fails to explain. According to various authors and the experimental results in this study, the Wenzel equation was deemed inadequate for calculating the apparent contact angle on most structured surfaces. The proposed method for accurately predicting the apparent contact angle holds potential to offer scientific guidance in the development of structured surfaces with precisely controlled wettability. This has a broad range of applications in fields such as microfluidics, biography, engineering.