Jamming of Granular Flow in a Two-Dimensional Hopper

We seek an understanding of the physics of jamming in flow from a hopper. Using spatio-temporal video data for photoelastic disks (mean diameter $d$) flowing through a two-dimensional hopper (opening size $D$.), we have found experimental support for the hypothesis that the probability of flow surviving until time $t$ without jamming has the form $P_s(t) = \exp (-t/\tau)$. The important physics is encapsulated in $\tau$, and how that depends on the ratio $D/d$. Estimates of $\tau$ vary as a power-law or an exponential in $D/d$ for a jamming model and an arch formation model. Through particle tracking we conclude that jamming requires both a high packing fraction and a stable force chain arch at the outlet. Work in progress is yielding data for $\tau$ vs. the hopper angle as well as $D/d$.