The Statistical Mechanics of Clogging

Abstract

The gravity-driven flow of grains from a hole in a hopper is an iconic granular phenomenon. It differs from fluid flow in that rate is independent of fill height, and more spectacularly so in that it can suddenly and unexpectedly clog. Basic questions about this process remain unanswered: how does the susceptibility to clogging increase with increasing hole size, and is there a well-defined clogging transition above which the system never clogs? What distinguishes flow microstates that lead to clogging from those that don't? Why are some clogs stable, but some spontaneously break? These problems extend beyond jamming, as they involve driving, boundaries, and gradients in state variables. Earlier work showed that grain positions are the key microscopic degrees of freedom. As a next step, we tracked grains in the vicinity of the outlet for a sufficiently large number of clogging events (>50k) to enable classification by a support-vector machine. The resulting accuracy is limited, but its interpretable structure functions reveal that cornerstones -more so than keystones- play a crucial role in clog formation. We also introduce a phenomenological model where the flow rate is modeled with a Langevin-type equation with multiplicative noise, where clogging is an absorbing state. By coupling flow rate to a hidden mode, we successfully model the observed non-exponential distribution of lifetimes for metastable clogs.