Complete wetting near an edge of a rectangular-shaped substrate

TL;DR

This paper investigates the behavior of fluid wetting near a rectangular substrate edge, revealing how the interface height scales with chemical potential and substrate size, supported by theoretical and numerical analysis.

Contribution

It introduces a detailed analysis of complete wetting near a substrate edge using interfacial Hamiltonian and density functional theories, highlighting the dependence of interface height on molecular forces and substrate size.

Findings

The interface height near the edge scales as 578 46 478 with chemical potential.

For large finite substrates, the interface height deviation scales as L^{-1}.

Numerical DFT results support the theoretical predictions.

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.