Normal stress differences in dense suspensions

TL;DR

This study investigates the microscopic origins of normal stress differences in dense suspensions under shear flow, highlighting the roles of hydrodynamic and contact forces and their dependence on particle friction and volume fraction.

Contribution

It reveals the combined effect of hydrodynamic lubrication and frictional contacts as the source of negative first normal stress difference and explores stress anisotropy near jamming.

Findings

Negative $N_1$ arises from hydrodynamic and contact forces.

Positive $N_1$ near jamming involves effects beyond hard-sphere models.

Stress anisotropy vanishes at jamming for frictionless particles but persists with friction.

Abstract

The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_1$, whereas positive values of $N_1$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limit. Furthermore, we found that the stress anisotropy induced by the planarity of the simple shear flow vanishes as the volume fraction approaches the jamming point for frictionless particles, while it remains finite for the case of frictional particles.