Drag on a sphere in granular shear flows

Drag in granular media has significant implications for granular rheology, particle segregation, impact and penetration, and even robotic locomotion. Extensive research has focused on the drag force on intruders in static or vibrofluidized granular beds, but the fundamental characteristics and scaling laws for particle drag in flowing granular materials remain largely unknown. Here, we use discrete element method simulations to study the drag force on a driven intruder particle in an otherwise size- and density-monodisperse granular shear flow, in the absence of gravity. For a wide range of applied intruder forces and flow conditions (shear rate and overburden pressure), the intruder particle velocity is constant (i.e., the drag force exerted by its neighbouring particles counterbalances the applied driving force) and the drag force is proportional to the velocity. The linear force-velocity relation can be cast into a modified Stokes' drag model with a drag coefficient dependent on the intruder size and density, as well as the flow inertial number. Intriguingly, changing the direction of the applied force with respect to the shear flow also affects the drag coefficient, which is attributed to the anisotropic contact force orientation and drag-induced lift effects in granular shear flows. Finally, our drag model accurately predicts the dependence of the segregation velocity on particle size and density ratios, as observed previously in gravity-driven granular segregation studies.