Effect of friction in a toy model of granular compaction

TL;DR

This paper introduces a toy model for granular compaction incorporating friction and arch resistance, revealing two distinct regimes of compaction dynamics separated by a critical friction threshold.

Contribution

The study presents a novel toy model that captures realistic granular compaction behaviors, emphasizing the role of friction and identifying a critical threshold separating different regimes.

Findings

Identified a critical slipping threshold Wc* dividing two compaction regimes.

Below Wc*, system properties are independent of friction; above Wc*, properties follow Janssen theory.

Demonstrated different dynamics: slow compaction with paralyzed regions and inverse logarithmic behavior.

Abstract

We proposed a toy model of granular compaction which includes some resistance due to granular arches. In this model, the solid/solid friction of contacting grains is a key parameter and a slipping threshold Wc is defined. Realistic compaction behaviors have been obtained. Two regimes separated by a critical point Wc* of the slipping threshold have been emphasized : (i) a slow compaction with lots of paralyzed regions, and (ii) an inverse logarithmic dynamics with a power law scaling of grain mobility. Below the critical point Wc*, the physical properties of this frozen system become independent of Wc. Above the critical point Wc*, i.e. for low friction values, the packing properties behave as described by the classical Janssen theory for silos.