Intermittency and Velocity Fluctuations in Hopper Flows Prone to Clogging

We study experimentally the dynamics of granular media in a discharging hopper. In such flows, there often appears to be a critical outlet size Dc such that the flow never clogs for D > Dc. We report on the time-averaged velocity distributions, as well as temporal intermittency in the ensemble-averaged velocity of grains in a viewing window, for both D < Dc and D > Dc, near and far from the outlet. We characterize the velocity distributions by the standard deviation and the skewness of the distribution of vertical velocities. We propose a measure for intermittency based on the two-sample Kolmogorov-Smirnov DKS statistic for the velocity distributions as a function of time. We find that there is no discontinuity or kink in these various measures as a function of hole size. This result supports the proposition that there is no well-defined Dc and that clogging is always possible. Furthermore, the intermittency time scale of the flow is set by the speed of the grains at the hopper exit. This latter finding is consistent with a model of clogging as the independent sampling for stable configurations at the exit with a rate set by the exiting grain speed [C. C. Thomas and D. J. Durian, Phys. Rev. Lett. 114, 178001 (2015)].