Two-dimensional spreading of frictionless adhesive oil droplets

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, 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. A granular capillary length, analogous to the capillary length in liquids, 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.

Automated summary

When a pile of sand is poured out of a funnel onto a surface, the friction between the grains allows the pile to grow taller and spread out. In this study, we investigated a similar process using a two-dimensional pile of oil droplets. Unlike sand, the droplets have buoyancy and adhesion, and friction is negligible. As the pile grows, it reaches a critical height at which it spreads out across the boundary. Interestingly, although the behavior is granular, the growth process is similar to that of a continuous liquid. This can be described by a granular capillary length, which determines the critical height of the pile based on the balance between buoyancy and adhesion.