Equilibrium and stability of two-dimensional pinned drops

TL;DR

This paper analyzes the equilibrium and stability of two-dimensional pinned drops on sharp edges, revealing how stability depends on drop size and the Bond number, with implications for superhydrophobic surfaces.

Contribution

It provides a detailed analysis of the stability limits of pinned drops, considering the effects of size and Bond number, which was not thoroughly explored before.

Findings

Smaller fixed-volume drops are more stable.

Open drops become less stable as their Bond number decreases.

Stability depends critically on the drop size and contact angle pinning conditions.

Abstract

Superhydrophobicity relies on the stability of drops's interfaces pinned on sharp edges to sustain non-wetting (Cassie-Baxter) equilibrium states. Gibbs already pointed out that equilibrium is possible as long as the pinning angle at the edge falls between the equilibrium contact angles corresponding to the flanks of the edge. However, the lack of stability can restrict further the realizable equilibrium configurations. To find these limits we analyze here the equilibrium and stability of two-dimensional drops bounded by interfaces pinned on mathematically sharp edges. We are specifically interested on how the drop's stability depends on its size, which is measured with the Bond number $Bo = (\mathcal{W}_d/\ell_c)^2$, defined as the ratio of the drop's characteristic length scale $\mathcal{W}_d$ to the capillary length $\ell_c = \sqrt{\sigma/\rho g}$. Drops with a fixed volume become more stable as they shrink in size. On the contrary, open drops, i.e. capable of exchanging mass with a reservoir, are less stable as their associated Bond number decreases.