  Evaporating droplets of polymer or colloid solution may produce a glassy
crust at the liquid-vapour interface, which subsequently deforms as an elastic
shell. For sessile droplets, the known radial outward flow of solvent is
expected to generate crusts that are thicker near the pinned contact line than
the apex. Here we investigate, by non-linear quasi-static simulation and
scaling analysis, the deformation mode and stability properties of elastic caps
with a non-uniform thickness profile. By suitably scaling the mean thickness
and the contact angle between crust and substrate, we find data collapse onto a
master curve for both buckling pressure and deformation mode, thus allowing us
to predict when the deformed shape is a dimple, mexican hat, and so on. This
master curve is parameterised by a dimensionless measure of the non-uniformity
of the shell. We also speculate on how overlapping timescales for gelation and
deformation may alter our findings.
