Slow and fast particles in shear-driven jamming: critical behavior

TL;DR

This study uses simulations to analyze shear-driven jamming in two dimensions, revealing two distinct particle processes that influence the velocity distribution and shear viscosity near the jamming transition, highlighting a decoupling of correlations and viscosity.

Contribution

It identifies and characterizes two separate physical processes in shear-driven jamming, linking them to different terms in the shear viscosity divergence and providing a new understanding of the critical behavior.

Findings

Velocity distribution comprises slow and fast particle processes.

Shear viscosity divergence is dominated by the fast process, with corrections from the slow process.

Particle correlations and shear viscosity are controlled by different particle sets.

Abstract

We do extensive simulations of a simple model of shear-driven jamming in two dimensions to analyze the velocity distribution at different densities $\phi$ around the jamming density $\phi_J$ and at different low shear strain rates, $\dot\gamma$. We then find that the velocity distribution is made up of two parts which are related to two different physical processes which we call the slow process and the fast process as they are dominated by the slower and the faster particles, respectively. Earlier scaling analyses have shown that the shear viscosity $\eta$, which diverges as the jamming density is approached from below, consists of two different terms and we present strong evidence that these terms are related to the two different processes: the leading divergence is due to the fast process whereas the correction-to-scaling term is due to the slow process. The analysis of the slow process is possible thanks to the observation that the velocity distribution for different $\dot\gamma$ and $\phi$ at and around the shear-driven jamming transition, has a peak at low velocities and that the distribution has a constant shape up to and slightly above this peak. We then find that it is possible to express the contribution to the shear viscosity due to the slow process in terms of height and position of the peak in the velocity distribution and find that this contribution matches the correction-to-scaling term, determined through a standard critical scaling analysis. A further observation is that the collective particle motion is dominated by the slow process. In contrast to the usual picture in critical phenomena with a direct link between the diverging correlation length and a diverging order parameter, we find that correlations and shear viscosity decouple since they are controlled by different sets of particles and that shear-driven jamming is thus an unusual kind of critical phenomenon.