Thermodynamic analysis of superhydrophobicity on three-dimensional hexagonal microcolumn surfaces

Superhydrophobic surfaces are crucial in many applications because of their unique wetting properties. The present study proposes a three-dimensional thermodynamic model, inspired by the morphologies of springtails' skin and mosquitoes' compound eyes in their natural habitats. The model uses thermodynamic principles to analyze the superhydrophobicity of hexagonal columnar microstructures on solid surfaces. From a theoretical standpoint, the variation rules of normalized free energy and normalized free energy barrier with contact angle in two distinct states of wetting were examined. It then calculated the equilibrium contact angle and contact angle hysteresis using the model. The model elucidates the effects of microcolumn height and center distance on free energy and free energy barriers, as well as the transition between composite and non-composite states. Furthermore, it provides the criterion for the transition between the two wetting states in thermodynamic analysis and theoretical equations. Additionally, observations were conducted on the surface of the rough structure. The thermodynamic analysis and theoretical equation calculations of this model facilitate the design of geometric parameters for rough surfaces. The findings provide a reference point for the design of superhydrophobic surfaces with a stable wetting state.