Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

TL;DR

This paper models the buckling behavior of thin elastic shells, such as crusts on evaporating droplets, revealing how volume constraints induce discontinuous buckling characterized by a snap-through near the boundary.

Contribution

It introduces a numerical model for volume-controlled buckling of spherical shells, highlighting the conditions for discontinuous buckling and providing a scaling theory for critical buckling parameters.

Findings

Discontinuous buckling occurs for thin and large contact angle shells.

Buckling manifests as a single inverted region near the boundary.

Scaling theory accurately predicts buckling volume and inverted region growth.

Abstract

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.