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

Abstract

This paper examines the dynamics of saturated vapor in a corner formed by two walls. It is shown that, if the angle φ between the walls is sufficiently small, the vapor becomes unstable and spontaneous condensation occurs near the corner, giving rise to an ever-growing liquid meniscus. The diffuse-interface model and the lubrication approximation are used to demonstrate that the condensation occurs if and only if φ + 2θ < π, where θ is the angle between the meniscus free boundary and the walls. This criterion has a simple physical explanation: if it holds, the meniscus surface is concave -hence, the so-called Kelvin effect causes condensation. If the near-vertex region of the corner is smoothed, the instability can be triggered off only by a finite-size perturbation, with enough liquid to cover a certain proportion of the smoothed aria by a (microscopically thin) liquid film.