Complete wetting near an edge of a rectangular-shaped substrate

We consider fluid adsorption near a rectangular edge of a solid substrate that interacts with the fluid atoms via long range (dispersion) forces. The curved geometry of the liquid-vapour interface dictates that the local height of the interface above the edge E must remain finite at any subcritical temperature, even when a macroscopically thick film is formed far from the edge. Using an interfacial Hamiltonian theory and a more microscopic fundamental measure density functional theory (DFT), we study the complete wetting near a single edge and show that , as the chemical potential departure from the bulk coexistence δμ = μs(T) − μ tends to zero. The exponent depends on the range of the molecular forces and in particular for three-dimensional systems with van der Waals forces. We further show that for a substrate model that is characterised by a finite linear dimension L, the height of the interface deviates from the one at the infinite substrate as δ E(L) L−1 in the limit of large L. Both predictions are supported by numerical solutions of the DFT.