Nontrivial rheological exponents in sheared yield stress fluids

TL;DR

This paper investigates the physical origins of non-trivial rheological exponents in sheared yield stress fluids, proposing a mean-field model with mechanical noise and validating it through numerical simulations.

Contribution

It introduces a mean-field model incorporating stress diffusion and rate-dependent parameters to explain non-trivial rheological exponents, supported by numerical tests.

Findings

Dependence of shear modulus or relaxation time on shear rate alters rheological exponents.

Mean-field predictions remain robust despite structural disorder and partial stress relaxation.

Numerical simulations support the proposed mechanism for non-trivial exponents.

Abstract

In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.