Microscopic theory for the rheology of jammed soft suspensions

TL;DR

This paper introduces a microscopic-based constitutive model for the rheology of jammed soft suspensions, capturing key features like yield stress and stress relaxation behaviors through derived tensorial equations.

Contribution

It presents a novel microscopic derivation of a nonlinear tensorial rheological model for jammed soft suspensions, linking particle dynamics to macroscopic stress responses.

Findings

Qualitatively reproduces yield stresses in shear and normal stresses.

Captures stress relaxation after preshear with dependence on preshear strength.

Provides a framework connecting microscopic parameters to macroscopic rheology.

Abstract

We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a non-linear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.