Ergodicity breaking dynamics of arch collapse

Abstract

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 reinitiation 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.

Nonergodicity in silo unclogging: Broken and unbroken arches

“…Concurrently, numerical simulations performed by Merrigan and coworkers [31] captured quite faithfully the observed features of unclogging. They offered the notion that the stick-slip like dynamics appeared because the arches were exploring a landscape of shapes, each one having its own stability.…”

“…We do not study here the dependencies with perturbation strength and the orifice size; these have been explored, to a limited extent, numerically in Ref. [31].…”

“…Aging is intrinsic to the glassylike behavior of the lowintensity vibration driven unclogging dynamics [30,31]. This time dependency naturally arises from subdiffusive stochastic processes [37,38].…”

“…In this regard, by taking the time series σ (t ) as a stochastic variable, the ergodicity breaking for broken and unbroken arches is revisited. In particular, we investigate the applicability of the CTRW model suggested by the numerical work of Merrigan and coworkers [31].…”

Granular flow from silos with rotating orifice

“…These results led to a fundamental question of the existence of the no-clog regime when exit size is larger than a critical value. In contrast, unclogging transition may involve collective rearrangement of the grains [15] in the packing with a much larger length scale than exit size. Despite a large amount of experimental, theoretical and computational researches in clogging and unclogging in granular flow through bottle neck, quantitative theories that successfully explain these two stochastic transitions are yet to be found.…”