Spreading of a 2D granular analogue of a liquid puddle: Predicting structure through a “granular capillary length”

The structure of an accumulation of granular material, such as a pile of sand, can be characterized by the angle of repose, which is dependent on the balance between gravity and inter-grain friction. In contrast, for the case of a continuous medium, the height of a puddle is dictated by the capillary length which balances gravity and surface tension. Here we present an experiment that allows us to probe the structure of a 2D pile of monodisperse microscopic oil droplets. The droplets are buoyant, adhesive, and friction is negligible. Oil droplets are deposited within a chamber and accumulate at a barrier under the influence of buoyancy. The droplets reach a critical height and spread across the barrier. This process is reminiscent of the spreading of a liquid puddle, even though the pile is granular and 2D in nature. We define a parameter, analogous to the capillary length, which controls the height of the pile and is determined by the balance between buoyant and adhesive forces. These forces can be controlled experimentally to modify the height of the pile. We developed a model that can predict the shape of the pile based on the balance of adhesion and buoyancy.