Based on the three-dimensional thermodynamic model, the wettability of a superhydrophobic solid surface with a circular truncated cone microstructure has been investigated. The relationship between the microstructure of the circular truncated cone surface and superhydrophobic property is established by introducing the tension of the three-phase contact line in the composite state. The results show that the base angle and base spacing of the circular truncated cone have great influence on the wetting transition of composite and non-composite states. The theoretical expressions of the critical transition criteria are also given. The accuracy of the theoretical results is verified by comparing the theoretical prediction with the existing experimental data in the literature. The model established in this paper provides a theoretical basis and a reference for the optimal geometric parameters for studying the wettability of advanced superhydrophobic materials by using engineering microstructures.

Superhydrophobic surfaces have attracted great interest due to their self-cleaning, dust-proofing and friction-reducing properties. Related papers have proposed methods and theoretical bases for preparing these surfaces in order to achieve excellent superhydrophobicity. However, the influence of the roughness of the solid surface structure on its superhydrophobicity requires further in-depth thermodynamic analysis. In this paper, three-dimensional (3D) cylinder microtextured surface models are selected based on thermodynamic analysis. On this basis, a simulation diagram of the three-phase contact line of a circular cylinder section in a 3D model is presented. The effects of the intrinsic contact angle and geometrical parameters of the cylinder microtexture on free energy and the free energy barrier, as well as contact angle hysteresis, are theoretically investigated. The obtained results reveal the necessity of the transition between the non-composite state and composite state. The transition criteria between the non-composite and composite wetting states are obtained from the perspective of thermodynamic analysis and theoretical equations. The calculated results are basically consistent with the theoretical calculations and experimental results. This method provides theoretical guidance for the design of superhydrophobic surfaces.