Ergodicity breaking dynamics of arch collapse

Gravity driven flows such as in hoppers and silos are susceptible to clogging due to the formation of arches at the exit whose failure is the key to re-initiation of flow. In vibrated hoppers, clog durations exhibit a broad distribution, which poses a challenge for devising efficient unclogging protocols. Using numerical simulations, we demonstrate that the dynamics of arch shapes preceding failure can be modeled as a continuous time random walk (CTRW) with a broad distribution of waiting times, which breaks ergodicity. Treating arch failure as a first passage process of this random walk, we argue that the distribution of unclogging times is determined by this waiting time distribution. We hypothesize that this is a generic feature of unclogging, and that specific characteristics, such as hopper geometry, and mechanical properties of the grains modify the waiting time distribution.