Soft wetting: Modified Cassie-Baxter equation for soft superhydrophobic surfaces

Abstract

The classic Cassie-Baxter equation has been used for decades to describe the equilibrium contact angle of a droplet on a partially wetted, rough substrate and inspired numerous follow-up explorations in wetting. However, the Cassie-Baxter equation itself and its various modified forms apply mainly to rigid surfaces, where the distortion of structures under the surface tension force has not been considered. Encouraged by the trend that many natural surfaces and various modern devices are flexible, here, we study how flexibility of surface structures affects the surface wettability, namely, the equilibrium contact angle of a water droplet. Substrates decorated with soft pillar arrays are fabricated and the equilibrium contact angles of water droplets are measured by substrate vibration. We found a deviation between the measured equilibrium contact angles and those predicted by the classic Cassie-Baxter equation, and the deviation is more pronounced for softer pillars. By incorporating the elastic energy in the deflected pillars along the droplet perimeter into the droplet-structure interfacial system, we develop a modified Cassie-Baxter equation for droplets on soft pillar arrays.