Mechanics of Shape Shifting Droplets

Liquid droplets of oil emulsions in water have been observed to spontaneously deform into polyhedral shapes as the system is cooled down. Spherical droplets undergo faceting and other shape transitions at temperatures where the interface monolayer freezes into a hexagonal crystal while the bulk oil and water remain liquid. While a planar interface could be tiled perfectly by a hexagonal lattice, a sphere is topologically constrained to accommodate defects, which induce deforming local stresses. We seek to understand the mechanism driving the volume-conserving deformations by modelling the droplets as 2D elastic surfaces. By looking at the interplay of the elastic energy, surface tension and buoyancy, we have been able to gain insight into the temperature-dependent behaviour of the droplets. Our analysis has led to the study of the size scaling properties of defect-induced stress and its coupling to the curvature of the surface. We have found this coupling to be key in explaining the mechanics behind the shape transformations.