A model for approximately stretched-exponential relaxation with continuously varying stretching exponents

TL;DR

This paper demonstrates that relaxation in a sheared suspension model can be effectively described by a stretched-exponential function with a strain-dependent exponent, revealing a continuous variation in relaxation behavior.

Contribution

It introduces a model showing how relaxation in sheared suspensions can be approximated by a stretched exponential with a variable exponent depending on strain amplitude.

Findings

Relaxation follows a stretched exponential with 0.25 < β < 1.

The exponent β varies with strain amplitude.

The model's relaxation form aligns with numerical simulations.

Abstract

Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/\tau)^{\beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort\'e et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $\beta$ that depends on the strain amplitude: $0.25 < \beta < 1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.