Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using discrete element method simulations, we show that segregation of a single particle intruder can be described in a unified manner across different flow configurations. A scaling relation for the net segregation force is obtained by measuring forces on an intruder particle in controlledvelocity flows where gravity and flow kinematics are varied independently. The scaling law consists of two additive terms: a buoyancylike gravityinduced pressure gradient term and a shear rate gradient term, both of which depend on the particle size ratio. The shear rate gradient term reflects a kinematicsdriven mechanism whereby larger (smaller) intruders are pushed toward higher (lower) shear rate regions. The scaling is validated, without refitting, in walldriven flows, inclined walldriven flows, vertical silo flows, and freesurface flows down inclines. Comparing the segregation force with the intruder weight results in predictions of the segregation direction that match experimental and computational results for various flow configurations.
This content will become publicly available on October 10, 2023
Drag force in granular shear flows: regimes, scaling laws and implications for segregation
The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuationdominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear forcevelocity relation) to the inertial regime (quadratic forcevelocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this firstorder description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravitydriven segregation of an intruder particle in shear flow simulations.
 Award ID(s):
 1929265
 Publication Date:
 NSFPAR ID:
 10358658
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 948
 ISSN:
 00221120
 Sponsoring Org:
 National Science Foundation
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