Microscopic description of a liquid film on a solid substrate using density functional theory

We examine the wetting properties of planar and spherical substrates using a mean-field density functional theory. Equilibrium density profiles of a fluid close to an attractive wall are obtained by solving an integral equation resulting from the minimization of the grand potential. Using a novel pseudo-arc length continuation scheme, we compute the complete bifurcation diagram of the adsorption as a function of the chemical potential. For a spherical substrate we demonstrate a second unstable branch approaching saturation from the right, absent in the planar case. Our numerical results are in excellent agreement with analytical predictions obtained from a piecewise function approximation in which the density profile is assumed to be everywhere constant except near the wall-liquid and the liquid-gas interfaces. We also show that the sharp-interface approximation, used often to predict wetting behavior on planar substrates, is inadequate to describe wetting on a spherical substrate.