Theoretical analysis of droplet transition from Cassie to Wenzel state

Whether droplets transit from the Cassie to the Wenzel state (C–W) on a textured surface is the touchstone that the superhydrophobicity of the surface is still maintained. However, the C–W transition mechanism, especially the spontaneous transition of small droplets, is still not very clear to date. The interface free energy gradient of a small droplet is firstly proposed and derived as the driving force for its C–W evolution in this study based on the energy and gradient analysis. Then the physical and mathematical model of the C–W transition is found after the C–W driving force or transition pressure, the resistance, and the parameters of the meniscus beneath the droplet are formulated. The results show that the micro/nano structural parameters significantly affect the C–W driving force and resistance. The smaller the pillar diameter and pitch, the minor the C–W transition pressure, and the larger the resistance. Consequently, the C–W transition is difficult to be completed for the droplets on nano-textured surfaces. Meanwhile if the posts are too short, the front of the curved liquid–air interface below the droplet will touch the structural substrate easily even though the three phase contact line (TPCL) has not depinned. When the posts are high enough, the TPCL beneath the drop must move firstly before the meniscus can reach the substrate. As a result, the droplet on a textured surface with short pillars is easy to complete its C–W evolution. On the other hand, the smaller the droplet, the easier the C–W shift, since the transition pressure becomes larger, which well explains why an evaporating drop will collapse spontaneously from composite to Wenzel state. Besides, both intrinsic and advancing contact angles affect the C–W transition as well. The greater the two angles, the harder the C–W transition. In the end, the C–W transition parameters and the critical conditions measured in literatures are calculated and compared, and the calculations accord well with the experimental results. (paper)