Apparent contact angle of droplet with polygonal wetting footprint on reentrant microstructure surface

Reentrant microstructures characterized by excellent superhydrophobic property have demonstrated significant potential in liquid–vapor phase-change heat transfer, self-cleaning, and medical protection. Current research about droplet wetting on reentrant microstructure surfaces primarily focuses on the Cassie–Wenzel wetting transition. However, a theoretical prediction of the apparent contact angle on this heterogeneous structure for design guideline is lacking. In this work, microscale three-dimensional (3D) printing is adopted to fabricate T-shape reentrant microstructures to analyze the direction-dependent apparent contact angle of droplet with polygonal wetting footprint. We reveal the step-by-step evolution of polygonal footprint during droplet wetting on the reentrant microstructure via both experiments and lattice Boltzmann simulation. This stepwise wetting evolution is found to be caused by the de-pinning of the droplet contact line due to contacting the neighboring microstructures. We modify the classical double-radius model by considering the rotationally varied wetting radius of the polygonal wetting footprint for better fitting the droplet contour to predict the direction-dependent apparent contact angle. This wetting prediction model is validated by experimental measurement of droplet contact angle on the T-shape reentrant microstructure with varied structure spacing.