Amorphous glassy materials of diverse nature-concentrated emulsions, granular materials, pastes, molecular glasses-display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many applications. A general feature of such systems, well documented yet not really understood, is the strongly nonlinear nature of the flow rule relating stresses and strain rates. Here we use a microfluidic velocimetry technique to characterize the flow of thin layers of concentrated emulsions, confined in gaps of different thicknesses by surfaces of different roughnesses. We find evidence for finite-size effects in the flow behaviour and the absence of an intrinsic local flow rule. In contrast to the classical nonlinearities of the rheological behaviour of amorphous materials, we show that a rather simple non-local flow rule can account for all the velocity profiles. This non-locality of the dynamics is quantified by a length, characteristic of cooperativity within the flow at these scales, that is unobservable in the liquid state (lower emulsion concentrations) and that increases with concentration in the jammed state. Beyond its practical importance for applications involving thin layers (for example, coatings), these non-locality and cooperativity effects have parallels in the behaviour of other glassy, jammed and granular systems, suggesting a possible fundamental universality.

The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

We study the rheology of cornstarch suspensions, a non-Brownian particle system that exhibits shear thickening. From magnetic resonance imaging velocimetry and classical rheology it follows that as a function of the applied stress the suspension is first solid (yield stress), then liquid, and then solid again when it shear thickens. For the onset of thickening we find that the smaller the gap of the shear cell, the lower the shear rate at which thickening occurs. Shear thickening can then be interpreted as the consequence of dilatancy: the system under flow wants to dilate but instead undergoes a jamming transition because it is confined, as confirmed by measurement of the dilation of the suspension as a function of the shear rate.

SynopsisWe investigate the flowing behavior of dense suspensions of non-colloidal particles, by coupling macroscopic rheometric experiments and local velocity and concentration measurements through 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 the light of these local observations. We show that the short time response to a velocity step allows to characterize dense suspensions locally: they have a purely viscous behavior, without any observable influence of friction. In the jammed zone, there may be a contact network, whereas in the sheared zone there are only hydrodynamic interactions: localization consists in a change in configuration at the grain scale. From the concentration and velocity profiles, we have provided for the first time local measurements of the concentration dependence of viscosity; we find a Krieger-Dougherty law η(φ) = η 0 (1 − φ/0.605) −2 . Shear induced migration is almost instantaneous and seems inconsistent with most observations: it would imply that the diffusion coefficients strongly depend 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.

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We review and compare the phenomenological aspects and physical origin of shear-localization and shear-banding in various material types, namely emulsions, suspensions, colloids, granular materials and micellar systems. It appears that shear-banding, which must be distinguished from the simple effect of coexisting static-flowing regions in yield stress fluids, occurs in the form of a progressive evolution of the local viscosity towards two significantly different values in two adjoining regions of the fluids in which the stress takes slightly different values. This suggests that from a global point of view shear-banding in these systems has a common physical origin: two physical phenomena (for example, in colloids, destructuration due to flow and restructuration due to aging) are in competition and, depending on the flow conditions, one of them becomes dominant and makes the system evolve in a specific direction.

We carried out systematic creep tests after different times of rest and over sufficiently long times with pasty materials of various internal structures in a Couette geometry. From an analysis of the data taking into account the inertia of the system and the heterogeneous distribution of stress, we show that: ͑i͒ for a stress below the yield stress these materials remain solid but undergo residual, irreversible deformations over long time which exhibit some trends typical of aging in glassy systems; ͑ii͒ as a result of thixotropy ͑or aging͒ in the solid regime the elastic modulus increases logarithmically with the time of rest; ͑iii͒ in the liquid regime the effective behavior of the material can be well represented by a truncated power-law model; ͑iv͒ a fundamental parameter of the solid-liquid transition is a critical effective shear rate ͑associated with the yield stress͒ below which the material cannot flow steadily.

We study the emergence of shear thickening in dense suspensions of non-Brownian particles. We combine local velocity and concentration measurements using Magnetic Resonance Imaging with macroscopic rheometry experiments. In steady state, we observe that the material is heterogeneous, and we find that that the local rheology presents a continuous transition at low shear rate from a viscous to a shear thickening, Bagnoldian, behavior with shear stresses proportional to the shear rate squared, as predicted by a scaling analysis. We show that the heterogeneity results from an unexpectedly fast migration of grains, which we attribute to the emergence of the Bagnoldian rheology. The migration process is observed to be accompanied by macroscopic transient discontinuous shear thickening, which is consequently not an intrinsic property of granular suspensions.