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The Discrete Element Method is widely employed for simulating granular flows, but conventional integration techniques may produce unphysical results for simulations with static friction when particle size ratios exceed R ≈ 3. These inaccuracies arise under certain circumstances because some variables in the velocity-Verlet algorithm are calculated at the half-timestep, while others are computed at the full timestep. To correct this, we develop an improved velocity-Verlet integration algorithm to ensure physically accurate outcomes up to the largest size ratios examined (R = 100). The implementation of this improved synchronized_verlet integration method within the LAMMPS framework is detailed, and its effectiveness is validated through a simple three-particle test case and a more general example of granular flow in mixtures with large size-ratios, for which we provide general guidelines for selecting simulation parameters and accurately modeling inelasticity in large particle size-ratio simulations. 

Lift and drag forces on moving intruders in flowing granular materials are of fundamental interest but have not yet been fully characterized. Drag on an intruder in granular shear flow has been studied almost exclusively for the intruder moving across flow streamlines, and the few studies of the lift explore a relatively limited range of parameters. Here, we use discrete element method simulations to measure the lift force,$$F_{{L}}$$, and the drag force on a spherical intruder in a uniformly sheared bed of smaller spheres for a range of streamwise intruder slip velocities,$$u_{{s}}$$. The streamwise drag matches the previously characterized Stokes-like cross-flow drag. However,$$F_{{L}}$$in granular shear flow acts in the opposite direction to the Saffman lift in a sheared fluid at low$$u_{{s}}$$, reaches a maximum value and then decreases with increasing$$u_{{s}}$$, eventually reversing direction. This non-monotonic response holds over a range of flow conditions, and the$$F_{{L}}$$versus$$u_{{s}}$$data collapse when both quantities are scaled using the particle size, shear rate and overburden pressure. Analogous fluid simulations demonstrate that the flow around the intruder particle is similar in the granular and fluid cases. However, the shear stress on the granular intruder is notably less than that in a fluid shear flow. This difference, combined with a void behind the intruder in granular flow in which the stresses are zero, significantly changes the lift-force-inducing stresses acting on the intruder between the granular and fluid cases. 

Particle segregation in dense flowing size-disperse granular mixtures is driven by gravity and shear, but predicting the associated segregation force due to both effects has remained an unresolved challenge. Here, a model of the combined gravity- and kinematics-induced segregation force on a single intruder particle is integrated with a model of the concentration dependence of the gravity-induced segregation force. The result is a general model of the net particle segregation force in flowing size-bidisperse granular mixtures. Using discrete element method simulations for comparison, the model correctly predicts the segregation force for a variety of mixture concentrations and flow conditions in both idealized and natural shear flows. 

Small particles fall through sheared beds of larger particles in settings ranging from geophysics to industry, but the study of large-to-small size ratios $R$, spanning the trapping threshold $R_t,$has been neglected. In simulations of noncohesive spheres for $R<R_t,$the small-sphere vertical velocity $v_p$first increases with shear rate $\dot{\gamma }$as trapping time decreases, but $v_p$then decreases as velocity fluctuations frustrate downward mobility. For $R>R_t, v_p$is constant at low $\dot{\gamma },$but again decreases at high $\dot{\gamma }$. We model these behaviors and discuss analogies with electron transport in solids. Published by the American Physical Society2024 

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 fluctuation-dominated 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 force-velocity relation) to the inertial regime (quadratic force-velocity 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 first-order 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 gravity-driven segregation of an intruder particle in shear flow simulations. 

Using simulations and a virtual-spring-based approach, we measure the segregation force, $$F_{seg},$$ in size-bidisperse sphere mixtures over a range of concentrations, particle-size ratios and shear rates to develop a semiempirical model for $$F_{seg}$$ that extends its applicability from the well-studied non-interacting intruders regime to finite-concentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the single-intruder 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 controlled-velocity flows where gravity and flow kinematics are varied independently. The scaling law consists of two additive terms: a buoyancy-like gravity-induced 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 kinematics-driven mechanism whereby larger (smaller) intruders are pushed toward higher (lower) shear rate regions. The scaling is validated, without refitting, in wall-driven flows, inclined wall-driven flows, vertical silo flows, and free-surface 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 advection–diffusion–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. 

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 non-segregating particle mixtures by specifying particle size ratio, density ratio, and mixture concentration to achieve the equilibrium condition. Using DEM simulations of quasi-2D bounded heap flow, we show that segregation is significantly reduced for particle mixtures near the equilibrium condition. In addition, the rise-sink transition for a range of particle size and density ratios matches the predictions of the combined size and density segregation model.