The profile, apparent contact angle (ACA), contact angle hysteresis (CAH), and wetting state transmission energy barrier (WSTEB) are important static and dynamic properties of a large-volume droplet on the hierarchical surface. Understanding them can provide us with important insights into functional surfaces and promote the application in corresponding areas. In this paper, we establish three theoretical models (models 1-3) and the corresponding numerical methods, which were obtained by the free energy minimization and the nonlinear optimization algorithm, to predict the profile, ACA, CAH, and WSTEB of a large-volume droplet on the horizontal regular dual-rough surface. In consideration of the gravity, the energy barrier on the contact circle, the dual heterogeneous structures and their roughness on the surface, the models are more universal and accurate than the previous models. It showed that the predictions of the models were in good agreement with the results from the experiment or literature. The models are promising to become novel design approaches of functional surfaces, which are frequently applied in microfluidic chips, water self-catchment system, and dropwise condensation heat transfer system.
Double-roughness surfaces can be used to mimic lotus surfaces. The apparent contact angles (ACAs) of droplets on these surfaces were first calculated by Herminghaus. Then Patankar utilized the pillar model to improve the Herminghaus approach and put forward the formulas for ACAs calculation of the homogeneous double-roughness surfaces where the dual-scale structures and the bases were the same wettable materials. In this paper, we propose a numerical calculation method of ACAs on the heterogeneous double-roughness surfaces where the dual-scale structures and the bases are made of different wettable materials. This numerical calculation method has successfully enhanced the Herminghaus approach. It is promising to become a novel design approach of heterogeneous superhydrophobic surfaces, which are frequently applied in technical fields of self-cleaning, anti-icing, antifogging, and enhancing condensation heat transfer.
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