Influence of the fluid structure on the binding potential: comparing liquid drop profiles from density functional theory with results from mesoscopic theory

For a film of liquid on a solid surface, the binding potential $g(h)$ gives the free energy as a function of the film thickness $h$ and also the closely related structural disjoining pressure $\Pi = - \partial g / \partial h$. The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of $g(h)$. Here, the method we developed in [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures $g(h)$ decays in an oscillatory fashion with increasing $h$, leading to highly structured terraced liquid droplets.