(270b) Drag on a Sphere in Granular Shear Flows

Granular flows consisting of multiple particle species tend to segregate due to differences in particle size, density, or other physical properties. Accurate modeling of the segregation process often requires the knowledge of the effective inter-species drag resulting from particle contacts as different particle species percolate through each other. However, a full picture of the granular drag remains unclear even for the simplest scenario where a single intruder particle migrates in a sheared granular bed. Here, we use discrete element method simulations to explore the drag on a spherical intruder in a uniform-shear granular flow in the absence of gravity. The intruder is displaced by an external force perpendicular to the shear, resulting in an effectively constant intruder velocity (i.e., the effective drag force exerted on the intruder by bed particle contacts counterbalances the applied force). For broadly varied applied forces, intruder properties (size and density ratios), and flow conditions (shear rates and overburden pressures, hence inertial numbers), we find a striking similarity between intruder drag in a granular flow and drag on a sphere in a viscous fluid; that is, the drag coefficient C_d and the intruder Reynolds number Re_i follows a Stokesian form, C_d=8c/Re_i, for Re_i spanning five orders of magnitude, where c lies approximately between 1 and 3, noting that c=3 corresponds to Stokes drag on a sphere in a viscous fluid. Furthermore, an empirical expression is developed to capture the secondary dependence of c on the inertial number and the intruder size and density ratios. Finally, we show that the modified Stokes’ drag model leads to a terminal velocity-like formulation for the segregation velocity of intruder particles, matching extensive simulations of gravity-driven segregation in granular flows. This material is based upon work supported by the National Science Foundation under Grant No. CBET-1929265.