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

摘要

The contribution to the free energy for a film of liquid of thickness $h$ ona solid surface, due to the interactions between the solid-liquid andliquid-gas interfaces is given by the binding potential, $g(h)$. The preciseform of $g(h)$ determines whether or not the liquid wets the surface. Note thatdifferentiating $g(h)$ gives the Derjaguin or disjoining pressure. We develop amicroscopic density functional theory (DFT) based method for calculating$g(h)$, allowing us to relate the form of $g(h)$ to the nature of the molecularinteractions in the system. We present results based on using a simple latticegas model, to demonstrate the procedure. In order to describe the static anddynamic behaviour of non-uniform liquid films and drops on surfaces, amesoscopic free energy based on $g(h)$ is often used. We calculate suchequilibrium film height profiles and also directly calculate using DFT thecorresponding density profiles for liquid drops on surfaces. Comparingquantities such as the contact angle and also the shape of the drops, we findgood 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 thefluid molecules and those between the fluid and wall. We find that truncatingcan have a significant effect on $g(h)$ and the associated wetting behaviour ofthe fluid.