First normal stress difference and crystallization in a dense sheared granular fluid

TL;DR

This study investigates the first normal stress difference and microstructure in dense sheared granular fluids using simulations, revealing a sign change in normal stress difference linked to microstructural reorganization and shear-induced crystallization.

Contribution

It demonstrates that collisional anisotropies, not velocity fluctuation anisotropy, dominate normal stress differences in dense granular flows and links microstructure changes to stress behavior.

Findings

Normal stress difference remains positive in dilute flows

Sign reversal of normal stress difference occurs at high density

Shear-induced crystallization signals fluid-solid coexistence

Abstract

The first normal stress difference (${\mathcal N}_1$) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in {\it dilute} granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behaviour in the {\it dense} limit. As in the elastic hard-sphere fluids, ${\mathcal N}_1$ remains {\it positive} (if the stress is defined in the {\it compressive} sense) for dilute and moderately dense flows, but becomes {\it negative} above a critical density, depending on the restitution coefficient. This sign-reversal of ${\mathcal N}_1$ occurs due to the {\it microstructural} reorganization of the particles, which can be correlated with a preferred value of the {\it average} collision angle $\theta_{av}=\pi/4 \pm \pi/2$ in the direction opposing the shear. We also report on the shear-induced {\it crystal}-formation, signalling the onset of fluid-solid coexistence in dense granular fluids. Different approaches to take into account the normal stress differences are discussed in the framework of the relaxation-type rheological models.