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 ${\ell }_E$ 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 ${\ell }_E(0)-{\ell }_E(\delta \mu )\sim \delta {\mu }^{{\beta }_E^{co}}$, as the chemical potential departure from the bulk coexistence $\delta \mu ={\mu }_s(T)-\mu$ tends to zero. The exponent ${\beta }_E^{co}$ depends on the range of the molecular forces and in particular ${\beta }_E^{co}=2/3$ 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 $\delta {\ell }_E(L)\sim L^{-1}$ in the limit of large $L$. Both predictions are supported by numerical solutions of the DFT.

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Cited by in corpus (1)

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