Flow-mediated coupling on projectiles falling in a superlight granular medium

Interesting collective motion emerges when several heavy disks fall in a quasi 2D granular bed of extremely light grains [F. Pacheco-V\'azquez and J.C. Ruiz-Su\'arez, \textit{Nat. Comms.} \textbf{1}, 123 (2010)]. In particular, when two disks impact side by side they initially repel, then they attract each other, until they finally stop. We perform experiments and Discrete Element Soft-Particle simulations to determine the range of action and the origin of these attractive and repulsive flow-mediated forces. Our findings suggest that repulsion results from jamming of grains between intruders while attraction would be due to a ``granular pressure'' drop in the region between intruders caused by a high flow velocity of grains: a Bernoulli-like effect.