Establishing a novel continuum model of static and dynamic contact angles in a superhydrophobic case study: A water droplet on micrometer-sized patterns of a hybrid hydrophobic/-philic surface*

Modeling the static and dynamic contact angles is a grand challenge in studying the wetting and de-wetting of liquids on solid surfaces. We propose a dynamic slip boundary model based on the Young’s equation, and establish a novel, realistic continuum approach to simulate the 3-D contact line dynamics. In this paper, a water droplet interacting with micrometer-sized patterns of a hybrid hydrophobic/-philic surface is presented as a case study to validate our model with experimental measurements. Good agreements have been observed for all cases: (1) static, advancing and receding conditions, and (2) at four different pillar spacings. Moreover, details of the droplet-surface interaction have been studied: (i) penetrations, (ii) sagging, and (iii) local and global contact angles. Our results show that the spurious interfacial velocity, which is small, does not affect the validity of our model. Note that there is no fitting parameters used in this research.