Phase-field model to predict the wettability of micro-structured surfaces

Interest in wetting phenomena has significantly increased over the past few decades, both in industry and academia: the existence in nature of biological systems with special wetting properties has led to investigate their potential technological applications, stimulating the creation of bio-inspired surfaces equipped with specific combinations of chemical composition and surface structures. The dynamics of phenomena involving liquid droplets in contact with solid substrates is governed by processes that are still unclear, especially when there are non-smooth or chemically heterogeneous surfaces; many approaches have been developed over the years with the aim of explaining and overcoming some of the unsolved problems, but currently there is no all-encompassing theory. Several studies have hypothesized and experimentally verified the existence of multiple possible wetting states for a textured surface, including some metastable configurations; however, the number of factors that contribute to defining the equilibrium shape of a droplet on a micro-structured surface is high, so wettability may be difficult to assess a priori. For these reasons, it would be useful to develop a method to predict the behavior of a droplet depending on the micro-structures with which it interacts; the use of numerical simulations for this purpose is complicated by the movement of the interface. The first part of this thesis is dedicated to a description of some laws that underlie the statics of wetting, with the analysis of models commonly used to explain the different equilibrium configurations of a droplet in contact with a non-smooth solid surface. Afterward, an overview of the equations governing the dynamics of wetting phenomena is presented, along with some of the approaches that can be adopted to numerically study problems involving moving interfaces, and the related boundary conditions; particular attention is paid to a diffuse-interface method based on the Cahn-Hilliard equation. Then, a phase-field model is developed through the software COMSOL Multiphysics, which allows to numerically simulate the contact between a drop of liquid and a solid substrate: firstly a smooth surface is used, in order to assess the physical consistency of the simulations, identify the suitable model parameters and establish the analysis protocol for the results. Later, a micro-structured surface is introduced into the model, and the macroscopic contact angle obtained at different boundary conditions imposed on the solid wall is evaluated; finally, the micro-structure geometry and droplet initial conditions are modified in order to estimate their influence on the system behavior. Simulation results are also compared with what is assumed by the theoretical models.