A granular material spreading as a liquid: growth dynamics of 3D aggregates of oil droplets

A continuous medium like a puddle has a characteristic critical height set by the capillary length, a balance between gravity and surface tension. In this study, monodisperse frictionless and lightly attractive oil droplets (radius approximately 10 microns) are produced one-by-one in an aqueous solution. Droplets are buoyant and accumulate underneath a glass slide which acts as the top of a liquid cell, forming 3D aggregates. The droplets initially accumulate vertically. As a critical height is reached, the aggregate collapses and spreads horizontally on the glass slide. Despite the aggregates being granular in nature, we find that the equilibrium shape of such aggregates follows the physics of continuous media. Indeed, the height of the aggregate reaches a critical value which is set by a balance between adhesion between the droplets and buoyancy. Both parameters can be tuned in the experiment to vary the geometry of the droplet aggregates. We developed a model that captures the shape of the aggregate with a simple parameter analogous to the capillary length.