Universality in the buckling behavior of drying suspension drops

Fast evaporation of particle-suspension drops results in complex morphologies of the final dried granules. Understanding the morphological transformations is important to industrial processes such as spray drying where droplets of particulate suspensions are dried at a fast rate to produce granules of thermally sensitive materials. The transformation of an initial spherical shell to complex morphologies of the final dried granule has been attributed to the buckling of particle-packed shells. Here, we demonstrate a universal scaling law for buckling that depends on the particle size, hardness, particle packing and size of drying drop. The critical transition for buckling is set by a dimensionless number that measures the competition between the compressive stress generated by capillary forces and the elastic strength of the packing. The same dimensionless number is also responsible for cracking of drying colloidal films, suggesting a universality in the mechanical behaviour of particle packings saturated with a solvent. These results should enable design of hierarchically structured, buckle-free granules with varying porosity, surface composition and internal structure.