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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.