Rheology of dense granular suspensions under extensional flow

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 -> 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. (C) 2018 The Society of Rheology.