Diffuse Interface Modelling of Wetting on Complex Structured Surfaces

Abstract

Wetting on solid surfaces textured with geometries from simple to highly complex structures is of interest from fundamental physics perspective and for potential applications. From the physics point of view, interesting phenomena can be observed, such as hemiwicking, when perfectly wetting liquids propagate through the corrugation of these structured surfaces, and wetting transition, when liquids initially in a suspended state (Cassie-Baxter state) transition to a collapsed state (Wenzel state). In addition, on a microscopic scale where the wettability is dictated by the intermolecular interactions, distinct wetting phenomena can be observed, such as liquid filling and emptying. From the application perspective, wetting on structured surfaces is key to a broad range of technological and industrial applications, from coating and microfluidic to liquid hydrocarbon recovery.

In this thesis, we employ dynamical and quasi-static numerical methods based on diffuse interface model for studying wetting phenomena on structured surfaces. First, we use the Lattice Boltzmann method, which is powerful for studying liquid dynamics. Second, we employ the phase-field energy minimisation method by incorporating distance-dependent solid-liquid interactions to obtain the equilibrium state of the system. Third, we develop a new method based on the phase-field model in the energy minimisation framework, the frozen fluid method, for constructing highly complex geometry structures.

We develop a fully analytical model to predict the propagation coefficients for liquids hemiwicking through square and face-centre/hexagonal arrays of micropillars. This is done by balancing the capillary driving force and a viscous resistive force and solving the Navier-Stokes equation for representative channels. The theoretical predictions for the square array case exhibit excellent agreement with the simulation results for a wide range of geometries and improved accuracy compared to previously proposed models. Furthermore, we demonstrate the applicability of the hydraulic-electric circuit analogy approach in approximating the equivalent channel for face-centred/hexagonal arrays of micropillars.

In the study of liquid filling and emptying on grooved surfaces, we consider short-range and long-range liquid-solid interactions, with the latter including purely attractive and repulsive interactions and those with short-range attraction and long-range repulsion. Comparing the filling and emptying transitions for complete, partial, and pseudo-partial wetting states, we find that the filling and emptying transitions are reversible for the complete wetting case, while significant hysteresis is observed for the partial and pseudo-partial cases. In agreement with previous studies, we show that the critical pressure for the filling transition follows the Kelvin equation for the complete and partial wetting cases. For the pseudo-partial wetting case, we find that the filling transition can display a number of distinct morphological pathways.

Finally, we validate the frozen fluid method through several benchmarking tests, demonstrating its applicability across various solid geometries, including those with flat, curved, and corner features. Subsequently, we utilize the method to investigate the critical pressure of a liquid on superhydrophobic surfaces textured with cylindrical and truncated cone pillars, and mesh geometry. By analyzing the impact of texture parameters, we can optimize superhydrophobic surfaces to enhance their wetting stability.