Can one predict a drop contact angle?

The study of wetting phenomena is of great interest due to the multifaceted technological applications of hydrophobic and hydrophilic surfaces. The theoretical approaches proposed by Wenzel and later by Cassie and Baxter to describe the behavior of a droplet of water on a rough solid are extensively used and continuously updated to characterize the apparent contact angle of a droplet. However, the equilibrium hypothesis implied in these models means that they are not always predictive of experimental contact angles due to the strong metastabilities typically occurring in the wetting of heterogeneous surfaces. A predictive scheme for contact angles is thus urgently needed both to characterize a surface by contact angle measurements and to design super-hydrophobic and -oleophobic surfaces with the desired properties, for example, contact angle hysteresis. In this work, a combination of Monte Carlo simulation and the string method is employed to calculate the free energy profile of a liquid droplet deposited on a pillared surface. For the analyzed surfaces, it is shown that there is only one minimum of the free energy that corresponds to the superhydrophobic wetting state while the wet state can present multiple minima. Furthermore, when the surface roughness decreases the amount of local minima observed in the free energy profile increases. The presented approach clarifies the origin of contact angle hysteresis providing quantitative tools for understanding and controlling wetting at structured surfaces.