Origin of the long-ranged attraction or repulsion between intruders in a confined granular medium

Zuriguel et al. ( Phys. Rev. Lett. , vol. 95, 2005 a , 258002) and Pacheco-Vázquez and Ruiz-Suárez ( Nat. Commun. , vol. 1, 2010, p. 123) demonstrated that there exists a long-ranged force between intruders placed at a certain distance from each other in granular flow. The origin of these long-ranged forces, induced collectively by the grains, has not been fully understood. In our work, we provide a unified explanation for the origin of both attraction and repulsion between two intruders in terms of the building up of force chains and their subsequent buckling. The surface and shear zone of the other intruder makes a significant contribution to the strength or buckling of the force chains. Bernoulli’s effect used in earlier studies predicts the nature of these forces, viz. , attraction or repulsion, correctly but is not well supported as observed in our study. The time-averaged flow fields around the intruders also support our explanation for the origin as evidenced by the burst in kinetic energy and granular temperature. The model proposed in this work predicts the qualitative trend of the sideways force with the separation between the intruders by combining Bernoulli’s equation with a minimum contact criterion of force chains. There exists an equilibrium at which the intruders neither attract nor repel each other and a certain separation distance where maximum attraction occurs between the two intruders. The effects of the static pressure, the velocity of the moving intruders and the friction coefficient on the attraction or repulsion force between the intruders have also been explored in our system.