Continuum model applied to granular analogues 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 upwards to the top of a liquid cell where they accumulate and form an aggregate at a flat horizontal interface. The horizontal spreading of aggregates along the interface results from sudden discrete avalanches. 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. The continuum model presented well explains the average growth rate of the aggregates, while the avalanches, which result in discrete growth steps, are a signature of the underlying granular nature of the aggregates.