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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.Free, publiclyaccessible full text available October 10, 2023

Using simulations and a virtualspringbased approach, we measure the segregation force, $F_{seg},$ in sizebidisperse sphere mixtures over a range of concentrations, particlesize ratios and shear rates to develop a semiempirical model for $F_{seg}$ that extends its applicability from the wellstudied noninteracting intruders regime to finiteconcentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the singleintruder assumption applies and provides an accurate description of the pressure partitioning between species.

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.

Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due to the opposing effects of the two segregation mechanisms. Using discrete element method (DEM) simulations of combined size and density segregation we show that the segregation velocity is well described by a model that depends linearly on the local shear rate and quadratically on the species concentration for free surface flows. Concentration profiles predicted by incorporating this segregation velocity model into a continuum advectionâ€“diffusionâ€“segregation transport model match DEM simulation results well for a wide range of particle size and density ratios. Most surprisingly, the DEM simulations and the segregation velocity model both show that the segregation direction for a range of size and density ratios depends on the local species concentration. This leads to a methodology to determine the combination of particle size ratio, density ratio and particle concentration for which a bidisperse mixture will not segregate.

Aguirre, M.A. ; Luding, S. ; Pugnaloni, L.A. ; Soto, R. (Ed.)Particle segregation in geophysical and industrial granular flows is typically driven by gravity and shear. While gravityinduced segregation is relatively well understood, shearinduced segregation is not. In particular, what controls segregation in the absence of gravity and the interplay between shearand gravitydriven segregation remain unclear. Here, we explore the shearinduced segregation force on an intruder particle in controlledvelocity granular flows where the shear profile is systematically varied. The shearinduced segregation force is found to be proportional to the shear rate gradient, which effectively pushes the large intruder from lower to higher shear rate regions. A scaling law is developed for the segregation force that is accurate over a wide range of overburden pressures and shear rates, and hence inertial numbers.

Aguirre, M.A. ; Luding, S. ; Pugnaloni, L.A. ; Soto, R. (Ed.)In dense flowing bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the two segregation mechanisms either enhance (large/light and small/heavy) or oppose (large/heavy and small/light) each other. In the latter case, an equilibrium condition exists in which the two mechanisms balance and the particles no longer segregate. This leads to a methodology to design nonsegregating particle mixtures by specifying particle size ratio, density ratio, and mixture concentration to achieve the equilibrium condition. Using DEM simulations of quasi2D bounded heap flow, we show that segregation is significantly reduced for particle mixtures near the equilibrium condition. In addition, the risesink transition for a range of particle size and density ratios matches the predictions of the combined size and density segregation model.