Spreading of a 2D granular analogue of a liquid puddle: predicting the structure and dynamics through a continuum model

When sand flows out of a funnel onto a surface, a three dimensional pile that is stabilized by friction grows taller as it spreads. Here we investigate an idealized two dimensional analogue: spreading of a pile of monodisperse oil droplets at a boundary. In our system the droplets are buoyant, adhesive, and in contrast to sand, here friction is negligible. The buoyant droplets are added to the pile one-at-a-time. As the aggregate grows, it reaches a critical height and the 2D pile spreads out across the barrier. We find that, while granularity is important, the growth process is reminiscent of a continuum liquid. We define a ``granular capillary length'', analogous to the capillary length in liquids, which sets the critical height of the aggregate through a balance of buoyancy and adhesion. At a coarse-grained level, the granular capillary length is capable of describing both steady-state characteristics and dynamic properties of the system, while at a granular level repeated collapsing events play a critical role in the formation of the pile.