Drag, lift, and buoyancy forces on a single large particle in dense granular flows

AV Yennemadi and DV Khakhar, PHYSICAL REVIEW FLUIDS, 8, 074301 (2023).

DOI: 10.1103/PhysRevFluids.8.074301

We study size segregation in the limit of a single large particle (intruder) embedded within a flowing granular layer. Using discrete- element-method-based computations, we calculate and characterize the drag, lift, and buoyancy forces experienced by the intruder in two systems: (1) a simple shear flow without gravity and (2) gravity-driven flow down an inclined plane. In agreement with previous studies, the drag force in both systems is seen to follow Stokes' Law with a slightly different constant. However, in contrast with previous work, we report that lift force does not follow the Saffman relation; instead, its variation is captured effectively using a size-corrected Stokes' Law. The buoyancy forces calculated in our work scale in a manner that compares well with previous studies. The computed effective volumes of the intruders were found to be close to previously reported values, and the buoyancy force calculated using this effective volume was found to be significantly lower than our computed buoyancy force, suggesting contributions from other factors. Analysis of the relative velocity and stress in the neighborhood of the intruder shows that the lift force is caused by a net upward collisional stress arising from a higher relative inward velocity in the lower part of the intruder due to a positive slip velocity. The buoyancy force is higher than that predicted by Archimedean buoyancy due to large fluctuations in the pressure near the intruder. A continuum model for the segregation flux is presented based on the computed drag, lift, and buoyancy forces.

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