Stability of the non-wetting state in a droplet impinging on surfaces with multiple holes

The hydrophobicity of low-energy surfaces is frequently enhanced by masking with micro-structures. However, wetting transition from the Cassie state (total non-wetting state) to the Wenzel state (total wetting state), which often occurs under external factors, such as impingement and vibration, is known to weaken the water repellency, namely, the hydrophobicity of these textured surfaces. The present work numerically examines the stability of the total non-wetting state on the multi-hole surface (MHS) and multi-pillar surface (MPS). The results show that the multi-hole structures not only enhance the hydrophobicity of a surface but also suppress the so-called Cassie-to-Wenzel wetting transition seen on the MPS. On the MHS, the stable air pocket in the holes prevents the three-phase contact line (TPCL) from depinning, thereby stabilizing the total non-wetting state for an impinging droplet. Furthermore, transition to the total wetting state is not found, even under a large We condition due to the corresponding pressure increase in the air pocket. A theoretical model for predicting the maximum spreading factor of an impinging droplet is constructed, which considers the air cavity in the center of the droplet and the energy loss of the TPCL depinning on structures.