Flows in hoppers and silos are susceptible to clogging due to the formation of arches at the exit. The failure of these arches is the key to re-initiation of flow, yet the physical mechanism of failure is not well understood. Experiments on vibrated hoppers exhibit a broad distribution of the duration of clogs. Using numerical simulations of a hopper in two dimensions, we show that arches become trapped in locally stable shapes that are explored dynamically under vibrations. The shape dynamics, preceding failure, break ergodicity and can be modeled as a continuous-time random walk with a broad distribution of waiting, or trapping, times. We argue that arch failure occurs as a result of this random walk crossing a stability boundary, which is a first-passage process that naturally gives rise to a broad distribution of unclogging times. This work was done in collaboration with Carl Merrigan and Prof. Chakraborty from Brandeis and Prof. Tewari from UMass Amherst.

Merrigan, Carl, Sumit Kumar Birwa, Shubha Tewari, and Bulbul Chakraborty. "Ergodicity breaking dynamics of arch collapse." Physical Review E (Rapid Communication) 97, no. 4 (2018): 040901.

LAMMPS-based numerical simulations were used to understand how the flowrate varies with opening size and wall friction. In contrast to scaling predictions, our data suggest that the height of the free-fall arch (used in scaling) does not vary with opening size for higher wall frictions. This work is in collaboration with Neil Shah and Prof. Tewari of UMass Amherst and Prof. Easwar of Smith College.

The observed velocities of particles near the opening are used to extrapolate their starting positions had they been in free fall. In contrast to scaling predictions, our data suggest that the height of this free-fall arch does not vary with opening size for higher wall frictions. Analysis of the packing fraction at the opening also suggests that wall friction does not play a key role in controlling packing fraction at the opening.

Shah, Neil, Sumit Kumar Birwa, Brenda Carballo-Ramirez, Nalini Easwar and Shubha Tewari. ”Effect of wall friction on 2D hopper flowrate.” under preparation to submit in Granular Matter.