Contact line-based model for the Cassie-Wenzel transition of a sessile droplet on the hydrophobic micropillar-structured surfaces

The hydrophobic stability to prevent Cassie-Wenzel (C-W) transition is an important property of superhydrophobic surfaces, which is mainly controlled by the micro/nano structure of surfaces. Based on the contact lines (CLs) around and inside the contact region, we analyzed the applied forces on a static sessile droplet deposited on the hydrophobic micropillar-structured surface. A simplified double-radius fitting method was derived to outline the contour of the droplet, and a force-balance model was gained to describe the critical conditions of the C-W transition. Compared with the classical force-balance models, the theoretical predictions from the proposed model agree much better with the experimental results. A reliable estimation of the critical conditions for the C-W transition during evaporation can be readily formed by integrating the depinning mechanism of the receding CL on the micro-patterned surfaces into our model, which obviously cannot be obtained by the classical force-balance models. The effects of gravity and surface tension in the proposed equilibrium model for the C-W transition reach a compromise. The introduction of surface tension acting on the apparent CL in our model will help to provide appropriate geometric parameters for microstructures on the superhydrophobic surfaces to achieve high hydrophobic stability.