Study on the wetting transition of a liquid droplet sitting on a square-array cosine wave-like patterned surface

A liquid droplet deposited on a hydrophobic surface with a square-array cosine wave-like pattern is simulated by using the Surface Evolver to study on the Cassie-Wenzel wetting transition. All the metastable states of a liquid drop with a fixed drop volume on the model surface are determined at different surface roughnesses. The maximum/minimum contact angles among the metastable states at each surface roughness correspond to the advancing/receding contact angles. It is interesting to find out that when the surface roughness is slightly smaller than the transition roughness (between the Wenzel and Cassie states) the drop under the condition of the advancing and receding contact angle would exhibit the Cassie and Wenzel state, respectively. Both experimental and simulation results demonstrate that a liquid droplet of a fixed volume on patterned substrates may exhibit either the Wenzel state or the Cassie state at a certain surface roughness. An increase in the surface roughness may induce the wetting transition from the Wenzel state to the Cassie state to occur. The slip-jump behavior of an advancing contact line with increasing drop volume at different viewing angles is carefully discussed to demonstrate the distorted three-phase contact line. Effect of surface roughness and drop size on liquid penetration into groove of the model surface is discussed.