Wettability of reentrant surfaces: a global energy approach

Abstract

In this work we consider two possible wetting states for a droplet when placed on a substrate: the Fakir configuration of a Cassie-Baxter (CB) state with a droplet residing on top of roughness grooves and the Wenzel (W) state characterized by the homogeneous wetting of the surface. We extend a theoretical model based on the global interfacial energies for both states to study the wetting behavior of simple and double reentrant surfaces. Due to the minimization of the energies associated to each wetting state, we predict the thermodynamic wetting state of the droplet for a given surface and obtain its contact angle ${\theta}_C$. We first use this model to find the geometries for pillared, simple and double reentrant surfaces that most enhances ${\theta}_C$ and conclude that the repellent behavior of these surfaces is governed by the relation between the height and width of the reentrances. We compare our results with recent experiments and discuss the limitations of this thermodynamic approach. To address one of these limitations, we implement Monte Carlo simulations of the cellular Potts Model in three dimensions, allowing us to investigate the dependency of the wetting state on the initial state of the droplet. We find that when the droplet is initialized in a CB state, it gets trapped in a local minimum and stays in the repellent behavior irrespective of the theoretical prediction. When the initial state is W, simulations show a good agreement with theory for pillared surfaces, but for reentrant surfaces the agreement only happens in few cases: for most simulated geometries the contact angle reached by the droplet in simulations is higher than ${\theta}_C$ predicted by the model. Moreover, we find that the contact angle of the simulated droplet is higher when placed on the reentrant surfaces than for a pillared surfaces with the same height, width and pillar distance.