Mathematical modelling of liquids on surfaces

This thesis investigates the wetting behaviour of liquids on solid surfaces both in and out of equilibrium using two different general approaches from statistical mechanics. These are based on generalised lattice-gas models. Properties such as wettability and the contact angle are determined by the attraction strength parameters between the particles and with the solid surface. The wetting behaviour of liquids is characterised by the binding or interface potential, which we calculate. The two approaches used are kinetic Monte Carlo (KMC) and density functional theory (DFT). The time evolution in our KMC model involves two processes: (1) single-particle moves, which incorporates into the model particle diffusion over the surface and within the droplets, evaporation and condensation, i.e., the exchange of particles between droplets and the surrounding vapour; (2) larger-scale collective moves, which model advective hydrodynamic fluid motion, which are determined by considering the dynamics predicted by a thin-film equation. We calculate the thermodynamic quantities such as the contact angle using various methods and make a comparison between results from the different approaches. We present results for droplets joining, spreading, sliding under gravity, dewetting, the effects of evaporation, the interplay of diffusive and advective dynamics, and how all this behaviour depends on the temperature and other parameters. In addition, we consider the interfacial phase behaviour of binary liquid mixtures. We develop a DFT based method for calculating the binding potential as a function of the local adsorption of each species at the interface. This function characterises the interfacial phase behaviour of the mixture. Moreover, we show that in certain cases it can be multivalued.