Modeling silo clogging with nonlocal granular rheology

TL;DR

This paper develops and validates a nonlocal continuum model to predict granular flow and clogging in silos, successfully capturing jamming phenomena and flow spreading based on grain size and opening dimensions.

Contribution

It introduces a continuum model that predicts silo clogging and flow behavior, incorporating nonlocal effects and a free-separation criterion, validated against analytical and experimental results.

Findings

Model predicts jamming when opening size is comparable to grain size.

Flow exhibits diffusive spreading influenced by nonlocal parameters.

First continuum model to replicate silo jamming phenomena.

Abstract

Granular flow in a silo demonstrates multiple nonlocal rheological phenomena due to the finite size of grains. We solve the Nonlocal Granular Fluidity (NGF) continuum model in quasi-2D silo geometries and evaluate its ability to predict these nonlocal effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in arXiv:1411.5447, to produce full-field solutions. The implementation is validated against analytical results of the model in the inclined chute geometry, such as the solution for the $H_{\mathrm{stop}}$ curve for size-dependent flow arrest, and the velocity profile as a function of layer height. We then implement the model in the silo geometry and vary the apparent grain size. The model predicts a jamming criterion when the opening competes with the scale of the mean grain size, which agrees with previous experimental studies, marking the first time to our knowledge that silo jamming has been achieved with a continuum model. For larger openings, the flow within the silo obtains a diffusive characteristic whose spread depends on the model's nonlocal amplitude and the mean grain size. The numerical tests are controlled for grid effects and a comparison study of coarse vs refined numerical simulations shows agreement in the pressure field, the shape of the arch in a jammed silo configuration, and the velocity field in a flowing configuration.