  We study the behavior of very thin liquid films wetting homogeneous planar
and spherical substrates. In order to describe a simple fluid at very small
scales, we employ a classical density functional theory (DFT). Here, we model a
fluid with a local density approximation (LDA) for its hard-sphere contribution
and assume that the intermolecular attractive forces are long-range. In
particular, we first introduce the basic concept of DFT, and then present
computations for fluid films on planar and spherically symmetric walls. We
present equilibrium density profiles and adsorption isotherms. We also compare
our results to predictions from a sharp-interface approximation (SIA) and
suggest a piecewise function approximation (PFA), which assumes that the
density profile at the wall-liquid and the liquid-vapor interfaces varies
smoothly.
