Influence of temperature on wettability of micro hierarchical rough surfaces: A three-dimensional thermodynamic model

Inspired by the micrometer-scale hierarchical microstructures on the surface of cicada wings, this paper presents a three-dimensional thermodynamic analytical model to comprehensively analyze the superhydrophobicity of rough surfaces with micro-hierarchical structures. Emphasis is placed on the variation of normalized free energy and free energy barrier as a function of apparent contact angle for different wettability states. The effect of temperature-dependent intrinsic contact angle on the intertransition between different wettability states is explored. Additionally, the model allows obtaining the equilibrium contact angle and contact angle hysteresis through corresponding calculations. Importantly, the present model elucidates the influence of the height of the micropillar of the paraboloid on the intertransition between different wettability states at a specific temperature. The geometrical parameters of a droplet in a certain environment, when it is in the final stable wettability state, can be designed based on this model. By conducting a thorough investigation into the effect of temperature on the contact angle of rough surfaces with micro-hierarchical structures, this study offers a fresh perspective for understanding the wettability behavior of droplets at the micrometer scale. Moreover, it provides a theoretical basis for designing rough surfaces with micro-hierarchical structures for application in various environments.