Cohesion mediated layering in sheared grains

TL;DR

This paper investigates pattern formation in sheared granular mixtures, revealing that cohesive grains form layered structures driven by phase separation-like mechanisms, with a theoretical model closely matching simulation results.

Contribution

It introduces a phase separation-inspired free energy model to explain cohesion-driven layering in sheared grains, validated by discrete simulations.

Findings

Cohesive grains form percolating layers at higher cohesion and concentration.

Average agglomerate size and stress collapse onto a single curve with $c_oC$.

The free energy model accurately reproduces observed layering patterns.

Abstract

We consider pattern formation in a sheared dense mixture of cohesive and non-cohesive grains. Our findings show that cohesive grains, which would typically form distributed agglomerates, instead segregate into percolating stripes or layers when the cohesive grain concentration ($c_o$) and cohesion strength ($C$) increase -- in a way that the average agglomerate size and the average normal stress collapse onto a single curve when plotted against $c_oC$. Our central proposal is that the development of interfaces between cohesive and non-cohesive grains is akin to phase separation in binary molecular mixtures driven by an effective free energy, although we are dealing with a non-equilibrium system; we setup the segregation flux such that the effect of this free energy is activated only upon application of the external driving. By constructing the segregation flux proportional to the gradient of the variational derivative of the free energy, we closely reproduce the layering in the steady-state limit. We find a robust correspondence between the parameter $c_o C$ in the discrete simulations and the parameters in the free energy.