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

Motivated by observing 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 the externally pressurized shells case. Scaling theory for shallow shells is shown to approximate well the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force. (letter to the editor)