Binding potential and wetting behaviour of binary liquid mixtures on surfaces

We present a theory for the interfacial wetting phase behaviour of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e. the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behaviour, including both liquid-liquid and vapour-liquid phase separation, depending on the nature of the interactions between all the particles of the two different liquids, the temperature and the chemical potentials. Here we show that the interplay between the bulk phase behaviour of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviours, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multi-valued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.