Rheology of dense granular suspensions under extensional flow

TL;DR

This paper investigates how dense granular suspensions behave under extensional and shear flows, revealing universal and deformation-dependent jamming behaviors and extending viscous number rheology to extensional flows.

Contribution

It demonstrates the universal jamming point for frictionless particles and the deformation-dependent jamming for frictional particles, extending viscous number rheology to extensional deformations.

Findings

Frictionless suspensions follow a Newtonian Trouton's ratio up to jamming.

Frictional suspensions exhibit a divergence in Trouton's ratio near a deformation-dependent jamming point.

Viscous number rheology can be extended from shear to extensional flows, especially for frictionless particles.

Abstract

We study granular suspensions under a variety of extensional deformations and simple shear using numerical simulations. The viscosity and Trouton's ratio (the ratio of extensional to shear viscosity) are computed as functions of solids volume fraction $\phi$ close to the limit of zero inertia. Suspensions of frictionless particles follow a Newtonian Trouton's ratio for $\phi$ all the way up to $\phi_0$, a universal jamming point that is independent of deformation type. In contrast, frictional particles lead to a deformation-type-dependent jamming fraction $\phi_m$, which is largest for shear flows. Trouton's ratio consequently starts off Newtonian but diverges as $\phi\to\phi_m$. We explain this discrepancy in suspensions of frictional particles by considering the particle arrangements at jamming. While frictionless particle suspensions have a nearly isotropic microstructure at jamming, friction permits more anisotropic contact chains that allow jamming at lower $\phi$ but introduce protocol dependence. Finally, we provide evidence that viscous number rheology can be extended from shear to extensional deformations, with a particularly successful collapse for frictionless particles. Extensional deformations are an important class of rheometric flow in suspensions, relevant to paste processing, granulation and high performance materials.