A constitutive model for simple shear of dense frictional suspensions

TL;DR

This paper develops a constitutive model for dense frictional suspensions under shear, capturing shear thickening behaviors and flow states by simulating particle interactions and extending existing rheological theories.

Contribution

It introduces a generalized model that incorporates normal stress responses and maps flow states based on extensive particle simulation data.

Findings

Shear thickening transitions depend on volume fraction and stress.

The model accurately predicts flow curves and shear thickening behavior.

Flow state map delineates regimes of lubricated and frictional contacts.

Abstract

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $\phi$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $\phi$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of shear rate. Recent studies have related shear thickening to a transition between mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over a wide range of the dimensionless parameters $(\phi,\tilde{\sigma}$, and $\mu)$, with $\tilde{\sigma} = \sigma/\sigma_0$ the dimensionless shear stress and $\mu$ the coefficient of interparticle friction: the dimensional stress is $\sigma$, and $\sigma_0 \propto F_0/ a^2$, where $F_0$ is the magnitude of repulsive force at contact and $a$ is the particle radius. The data have been used to populate the model of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev. Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity divergences or \textquotedblleft jamming\textquotedblright\ points at volume fraction $\phi_{\rm J}^0 = \phi_{\rm rcp}$ (random close packing) for the low-stress lubricated state, and at $\phi_{\rm J} (\mu) < \phi_{\rm J}^0$ for any nonzero $\mu$ in the frictional state; a generalization provides the normal stress response as well as the shear stress. A flow state map of this material is developed based on the simulation results.