(276e) Percolation of a Fine Particle in a Sheared Granular Bed

Granular size segregation is a phenomenon commonly encountered in various natural and industrial settings. While this problem has been extensively studied for large to small particle size ratio R<3 and above the geometric trapping threshold, R>R_t=6.464 (free sifting), segregation for intermediate R values, particularly in flowing granular beds, remains unclear. Here we investigate the percolation of a fine spherical particle in a sheared-large-particle bed with constant shear rate, γ, under gravity for 2<R<7, which includes both the trapping and passing regimes observed in the static bed. At low γ, where the flow inertial number I<0.01, corresponding to quasi-static flow, a fine particle is never permanently trapped even for R<R_t due to the shear-driven temporal and spatial variation of the bed structure. In this regime, the percolation velocity v_p increases with γ for R<R_t but remains constant for R>R_t. We propose a probabilistic model that considers R, γ, particle size, gravity, and bed structure that accurately predicts v_p in this regime. However, at higher shear rates (0.01<I<1), the model breaks down as v_p decreases with increasing γ for all R due to the increasing granular temperature. As I approaches 1, the decrease of v_p slows, and v_p tends toward a non-zero value for all R. Additionally, a higher restitution coefficient leads to smaller v_p for all cases, consistent with results for a completely static bed of large particles. Funded by NSF Grant No. CBET-2203703.