Density fluctuations and correlations of confined fluids

The density fluctuations about the equilibrium structure of fluids confined by parallel planar walls are analyzed for the cases of identical and symmetrically opposed fields at the walls. We determine the stability matrix (of the second derivatives of the free energy functional with respect to the density) for conditions both above and below the wetting transition temperature Tw of the semi-infinite system and corroborate in all cases that the equilibrium configurations are stable. We identify the fluctuations close to the walls and in the middle of the slab and discuss their effect when the wall separation L diverges. For competing walls above Tw the localized fluctuation with lowest eigenvalue describes the displacements of the incipient wetting films that become unimpeded interfacial translations for L→∞. Below Tw the fluctuations with lowest eigenvalue correspond to stiffer deformations extended across the slab. For identical walls above Tw coexisting states display incipient prewetting films and the lowest eigenvalue describes the nature of their growth as L increases. We also calculate the pair correlation function for the inhomogeneous states and, for symmetrically opposed walls, we obtain standard Ornstein–Zernike (OZ) behavior at the walls, but find significant deviations from this law at the interface-like region in the middle of the slab. To model fluids with short-ranged forces we use a ferromagnetic Ising-type Hamiltonian in mean-field approximation.