Abstract
We calculate using force analysis the jamming probability of mixed disks that movedownwards under gravity in a two-dimensional hopper. Jamming happens when disks forman arc across the hopper opening and we determine the stability of the forcesacting at different arc points. To test the accuracy of our technique, we performedhopper experiments (side-wall separation: 0.2 cm) using disks (average thickness:0.198 ± 0.02 cm) at variousd/R values whered is the hopper openingdimension and R isthe disk radius. For N identical disks, the jamming probability is a sigmoidal function ofN. We measured thejamming probability at d/R = 2.97, 3.48, 4.0, 4.3 and 4.97, and verified the presence of three possible flow regimes: (1) jam-free continuous flow forN less thanthe onset Nd, (2) transitory flow where the probability increases withN forNd≤N≤Nu and (3) anN-independent jammedstate for N greater thanthe saturation threshold Nu. Good agreement is found between theory and experiments. The existence of three flow regimes is confirmedfor all d/R valueswith the Nu valueincreasing with d/R—the 2D hopper is more robust against jamming when relatively smallhomogeneous disks are used. We also experimented with mixtures ofN largeand n small disks and confirmed that jamming becomes more likely with increasingN for aconstant n (and vice versa) until the maximum jamming probability is attained.
Published Version
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