Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Abstract

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.