Edge contact angle and modified Kelvin equation for condensation in open pores

TL;DR

This paper develops a modified Kelvin equation to describe capillary condensation in finite open pores, introducing an edge contact angle that accounts for finite size effects and matches microscopic simulations.

Contribution

It introduces a new macroscopic model with an edge contact angle for finite pores, validated by microscopic density functional theory simulations.

Findings

Edge contact angle is larger than the equilibrium contact angle in finite pores.

Modified Kelvin equation accurately predicts condensation pressure in small pores below the wetting temperature.

The model's predictions agree well with microscopic simulations for small to moderate pore sizes.

Abstract

We consider capillary condensation transitions occurring in open slits of width $L$ and finite height $H$ immersed in a reservoir of vapour. In this case the pressure at which condensation occurs is closer to saturation compared to that occurring in an infinite slit ($H=\infty$) due to the presence of two menisci which are pinned near the open ends. Using macroscopic arguments we derive a modified Kelvin equation for the pressure, $p_{cc}(L;H)$, at which condensation occurs and show that the two menisci are characterised by an edge contact angle $\theta_e$ which is always larger than the equilibrium contact angle $\theta$, only equal to it in the limit of macroscopic $H$. For walls which are completely wet ($\theta=0$) the edge contact angle depends only on the aspect ratio of the capillary and is well described by $\theta_e\approx \sqrt{\pi L/2H}$ for large $H$. Similar results apply for condensation in cylindrical pores of finite length. We have tested these predictions against numerical results obtained using a microscopic density functional model where the presence of an edge contact angle characterising the shape of the menisci is clearly visible from the density profiles. Below the wetting temperature $T_w$ we find very good agreement for slit pores of widths of just a few tens of molecular diameters while above $T_w$ the modified Kelvin equation only becomes accurate for much larger systems.