Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging

Abstract

We investigate the flowing behavior of dense suspensions of noncolloidal particles, by coupling macroscopic rheometric experiments and local velocity and concentration measurements through magnetic resonance imaging (MRI) techniques. We find that the flow is localized at low velocities, and that the material is inhomogeneous; the local laws inferred from macroscopic rheometric observations must then be reinterpreted in light of these local observations. We show that the short time response to a velocity step allows dense suspensions to be characterized locally: they have a purely viscous behavior, without any observable influence of granular friction. In the “jammed” zone, there may be a contact network, whereas in the sheared zone there are only hydrodynamic interactions: localization consists of a change in configuration at the grain scale. From the concentration and velocity profiles, we provide for the first time local measurements of the concentration dependence of viscosity, and find a Krieger-Dougherty law η(ϕ)=η0(1−ϕ∕0.605)−2 to apply. Shear-induced migration is almost instantaneous, in contrast to most other observations, and implies that the diffusion coefficients depend strongly on the concentration. We finally propose a simple constitutive law for dense suspensions, based on a purely viscous behavior, that accounts for all the macroscopic and local observations.