Complete wetting near an edge of a rectangular-shaped substrate

Abstract

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 ℓE 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 δℓE(L) ∼ L−1 in the limit of large L. Both predictions are supported by numerical solutions of the DFT.