Rising dynamics and lift effect in dense segregating granular flows

Abstract

In order to explore the rising dynamics and the existence of a lift effect in dense segregating granular flows, we perform two-dimensional discrete numerical simulations in the case of single free intruders and bi-disperse granular mixtures. In both configurations, we do not observe a measurable lift force acting on the larger grains. The large force fluctuations acting on the bigger grains reduce to the weight of the latter, following the mere action-reaction principle. This suggests that the rising dynamics is driven by the force fluctuations, coupled with the properties of the surrounding granular bed itself. We propose the strong asymmetry displayed by granular bed resistance to downward (plunging) and upward (withdrawing) motion, as reported in detail by Hill et al. [“Scaling vertical drag forces in granular media,” Europhys. Lett. 72(1), 137–143 (2005)], as a key ingredient for segregation. Accordingly, moving an object toward the free surface is about 10 times easier than moving an object toward the rigid bottom. This asymmetry allows for an effective upward motion when large grains are submitted to upward force fluctuations, without being counterweighted by sinking episodes when large grains are submitted to downward force fluctuations. In addition to gravity, the existence of two different boundary conditions formed by the free surface and the rigid bottom explains this difference of resistance to motion. In this respect, the mechanism allowing size segregation in dense granular flows would be the same as that allowing legged locomotion in sand [Li et al., “A terradynamics of legged locomotion on granular media,” Science 339, 1408–1412 (2013)].In order to explore the rising dynamics and the existence of a lift effect in dense segregating granular flows, we perform two-dimensional discrete numerical simulations in the case of single free intruders and bi-disperse granular mixtures. In both configurations, we do not observe a measurable lift force acting on the larger grains. The large force fluctuations acting on the bigger grains reduce to the weight of the latter, following the mere action-reaction principle. This suggests that the rising dynamics is driven by the force fluctuations, coupled with the properties of the surrounding granular bed itself. We propose the strong asymmetry displayed by granular bed resistance to downward (plunging) and upward (withdrawing) motion, as reported in detail by Hill et al. [“Scaling vertical drag forces in granular media,” Europhys. Lett. 72(1), 137–143 (2005)], as a key ingredient for segregation. Accordingly, moving an object toward the free surface is about 10 times easier than moving an object toward th...