Wetting on Micropatterned Surfaces: Partial Penetration in the Cassie State and Wenzel Deviation Theoretically Explained

Abstract

A liquid droplet on a micropatterned substrate equalizes into either the Cassie–Baxter (also called Cassie for short) or the Wenzel state. This paper investigates the wetting phenomena on ideal micropatterned surfaces consisting of straight micropillars at different pillar dimensions and spacings (the word “ideal” refers to being chemically homogeneous and free of submicron-scale roughness all over the micropatterned surface). Two modeling approaches are used: (1) a thermodynamic approach analyzing the Gibbs energy of the droplet–solid–gas system and (2) a computational fluid dynamics (CFD) approach studying the three-dimensional dynamic wetting process to validate the results of the first approach. The thermodynamic approach incorporates three creative submodels proposed in this paper: (i) a sagging model explaining the pillar edge effect, (ii) a touchdown model transitioning the droplet’s partial penetrating condition toward its full penetrating condition, i.e., the Wenzel state, and (iii) a liquid-volume model dynamically computing the liquid volume between the pillar valleys while in the partial penetrating condition or in the Wenzel state. The results of the thermodynamic approach reveal (1) a small energy barrier between the Cassie and Wenzel states, (2) no partial penetration and sagging of the liquid in the Cassie state on the ideal straight micropillared surface, and (3) that the apparent contact angle in the most stable Wenzel state can be 5° or more lower than the prediction of the Wenzel equation when the pillar height is equal or greater than 75 μm. To the best of our knowledge, this paper presents the theoretical explanation of this Wenzel deviation on micropatterned surfaces for the first time in the literature. Utilizing the state-of-the-art continuum model developed by the authors in previous studies, the CFD approach investigates the same wetting conditions and confirms the same findings.

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