Rheology and dynamical heterogeneity in frictionless beads at jamming density

TL;DR

This study uses numerical simulations to analyze the rheological behavior and dynamical heterogeneity of frictionless particles near the jamming point, revealing power-law relationships between shear stress, relaxation time, and correlation length.

Contribution

It provides new quantitative estimates of critical exponents governing rheology and dynamical heterogeneity in frictionless bead systems at jamming density.

Findings

Shear stress scales as a power law with shear rate, with an exponent of approximately 1/δ_S=0.64.

Relaxation time diverges as a power law with shear rate, with an exponent of about 0.27.

Correlation length increases following a power law with shear rate, with an exponent near 0.23.

Abstract

We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dot\gamma$ is realized. The system behaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to $\dot\gamma^{1/\delta_S}$, where $1/\delta_S=0.64(2)$. It is also found that the relaxation time $\tau$ and the correlation length $\xi$ of the velocity increase obeying power laws: $\tau\sim\dot\gamma^{-\beta}$ and $\xi\sim\dot\gamma^{-\alpha}$, where $\beta=0.27(3)$ and $\alpha=0.23(3)$.