Vertical velocity of a small sphere in a sheared granular bed

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 Rt, has been neglected. In simulations of noncohesive spheres for R<Rt, the small-sphere vertical velocity vp first increases with shear rate γ˙ as trapping time decreases, but vp then decreases as velocity fluctuations frustrate downward mobility. For R>Rt, vp is constant at low γ˙, but again decreases at high γ˙. We model these behaviors and discuss analogies with electron transport in solids.