Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling

TL;DR

This paper develops a density functional theory approach to calculate the binding potential for liquid films on surfaces, compares it with mesoscopic models, and analyzes how force truncation affects wetting behavior.

Contribution

It introduces a microscopic DFT method to compute the binding potential and relates molecular interactions to wetting phenomena, validated against mesoscopic models.

Findings

Good agreement between DFT and mesoscopic profiles.

Truncating dispersion forces significantly impacts wetting behavior.

The form of g(h) is sensitive to interaction range truncation.

Abstract

The contribution to the free energy for a film of liquid of thickness $h$ on a solid surface, due to the interactions between the solid-liquid and liquid-gas interfaces is given by the binding potential, $g(h)$. The precise form of $g(h)$ determines whether or not the liquid wets the surface. Note that differentiating $g(h)$ gives the Derjaguin or disjoining pressure. We develop a microscopic density functional theory (DFT) based method for calculating $g(h)$, allowing us to relate the form of $g(h)$ to the nature of the molecular interactions in the system. We present results based on using a simple lattice gas model, to demonstrate the procedure. In order to describe the static and dynamic behaviour of non-uniform liquid films and drops on surfaces, a mesoscopic free energy based on $g(h)$ is often used. We calculate such equilibrium film height profiles and also directly calculate using DFT the corresponding density profiles for liquid drops on surfaces. Comparing quantities such as the contact angle and also the shape of the drops, we find good agreement between the two methods. We also study in detail the effect on $g(h)$ of truncating the range of the dispersion forces, both those between the fluid molecules and those between the fluid and wall. We find that truncating can have a significant effect on $g(h)$ and the associated wetting behaviour of the fluid.