Modified Kelvin equations for capillary condensation in narrow and wide grooves

TL;DR

This paper introduces a modified Kelvin equation to accurately predict capillary condensation in grooves, accounting for edge effects and groove width, supported by density functional theory calculations.

Contribution

It develops a modified Kelvin equation incorporating an edge contact angle to describe capillary condensation in grooves of varying width and depth.

Findings

Modified Kelvin equation accurately predicts transition pressures.

Edge contact angle depends on groove depth and corner menisci formation.

Transition behavior varies with contact angle and groove width.

Abstract

We consider the location and order of capillary condensation transitions occurring in deep grooves of width $L$ and depth $D$. For walls that are completely wet by liquid (contact angle $\theta=0$) the transition is continuous and its location is not sensitive to the depth of the groove. However for walls which are partially wet by liquid, where the transition is first-order, we show that the pressure at which it occurs is determined by a modified Kelvin equation characterized by an edge contact angle $\theta_E$ describing the shape of the meniscus formed at the top of the groove. The dependence of $\theta_E$ on the groove depth $D$ relies, in turn, on whether corner menisci are formed at the bottom of the groove in the low density gas-like phase. While for macroscopically wide grooves these are always present when $\theta<45\degree$ we argue that their formation is inhibited in narrow grooves. This has a number of implications including that the local pining of the meniscus and location of the condensation transition is different depending on whether the contact angle is greater or less than a universal value $\theta^*\approx 31\degree$. Our arguments are supported by detailed microscopic density functional theory calculations which show that the modified Kelvin equation remains highly accurate even when $L$ and $D$ are of the order of tens of molecular diameters.