Growing length and time scales in a suspension of athermal particles

TL;DR

This paper investigates how relaxation time and correlation length diverge near the jamming transition in a suspension of athermal particles, revealing critical scaling behavior and power-law decay of shear stress.

Contribution

It introduces a simulation study quantifying the divergence of relaxation time and correlation length with a new critical exponent near jamming.

Findings

Relaxation time and correlation length diverge algebraically at jamming.

The dynamic critical exponent is estimated as approximately 4.6.

Shear stress decays as a power law at the jamming point.

Abstract

We simulate a relaxation process of non-brownian particles in a sheared viscous medium; the small shear strain is initially applied to a system, which then undergoes relaxation. The relaxation time and the correlation length are estimated as functions of density, which algebraically diverge at the jamming density. This implies that the relaxation time can be scaled by the correlation length using the dynamic critical exponent, which is estimated as 4.6(2). It is also found that shear stress undergoes power-law decay at the jamming density, which is reminiscent of critical slowing down.