A 2-D analytical model for the wetting behavior of various microtextured surfaces

In this work, a physical model for various microtextured surfaces was proposed to investigate their wettability, and in particular, superhydrophobicity. Using such an analytical model, the thermodynamic states, and specifically, free energy and free energy barriers of the concerned surfaces such as trapezoidal, vertical and inverse trapezoidal surfaces, which were correlated the contact angle and contact angle hysteresis, can be exactly calculated. It was demonstrated based on the theoretical results that the contact angle, which was restricted by sidewall angle of micropillars of these microstructures, was not an independent parameter to affect the wetting behavior, and the re-entrant structures played an important role in the transition from hydrophilicity to superhydrophobicity. Furthermore, the transition criterion was generalized that the sidewall angle should be less than the intrinsic contact angle, and the pillar width and height should be as small as possible, in particular, for the T-shape microstructure. Moreover, it was found that for these transitions, a positive energy barrier could support liquid/vapor interfaces and separate the Wenzel and Cassie state on the hydrophilic substrates. Finally, it was expected that using the present simple and robust model and the corresponding theoretical results, the guidelines for the optimal design of practical superhydrophobic microtextured surfaces could be achieved.