Statistical Mechanics of a Thin Film on a Solid Substrate

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.