Continuum Model Applied to Granular Analogs of Droplets and Puddles

We investigate the growth of aggregates made of adhesive frictionless oil droplets, piling up against a solid interface. Monodisperse droplets are produced one by one in an aqueous solution and float upward to the top of a liquid cell where they accumulate and form an aggregate at a flat horizontal interface. Initially, the aggregate grows in 3D until its height reaches a critical value. Beyond a critical height, adding more droplets results in the aggregate spreading in 2D along the interface with a constant height. We find that the shape of such aggregates, despite being granular in nature, is well described by a continuum model. The geometry of the aggregates is determined by a balance between droplet buoyancy and adhesion as given by a single parameter, a "granular" capillary length, analogous to the capillary length of a liquid.