Capillary condensation of saturated vapor in a corner formed by two intersecting walls

TL;DR

This paper investigates the conditions under which vapor condenses spontaneously in the corner of two intersecting walls, demonstrating that a critical angle and contact angle determine the onset of capillary condensation and meniscus growth.

Contribution

The study introduces a criterion for capillary condensation in corners based on the angle and contact angle, using a diffuse-interface model and lubrication approximation.

Findings

Condensation occurs if the sum of the corner angle and twice the contact angle is less than pi.

The meniscus volume grows linearly with time once it exceeds a certain thickness.

Smoothed corners require finite perturbations to trigger condensation.

Abstract

The dynamics of saturated vapor between two intersecting walls is examined. It is shown that, if the angle $\phi$ between the walls is sufficiently small, the vapor becomes unstable, and spontaneous condensation occurs in the corner, similar to the so-called capillary condensation of vapor into a porous medium. As a result, an ever-growing liquid meniscus develops near the corner. The diffuse-interface model and the lubrication approximation are used to demonstrate that the meniscus grows if and only if $\phi+2\theta<\pi$, where $\theta$ is the contact angle corresponding to the fluid/solid combination under consideration. This criterion has a simple physical explanation: if it holds, the meniscus surface is concave -- hence, the Kelvin effect causes condensation. Once the thickness of the condensate exceeds by an order of magnitude the characteristic interfacial thickness, the volume of the meniscus starts to grow linearly with time. If the near-vertex region of the corner is smoothed, the instability can be triggered off only by finite-size perturbations, such that include enough liquid to cover the smoothed aria by a microscopically-thin liquid film.