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The origin of the abrupt shear thickening observed in some dense suspensions has been recently argued to be a transition from frictionless (lubricated) to frictional interactions between immersed particles. The Wyart-Cates rheological model, built on this scenario, introduced the concept of fraction of frictional contacts $f$ as the relevant order parameter for the shear thickening transition. Central to the model is the equation-of-state relating $f$ to the applied stress $sigma$, which is directly linked to the distribution of the normal components of non-hydrodynamics interparticle forces. Here, we develop a model for this force distribution, based on the so-called $q$-model that we borrow from granular physics. This model explains the known $f(sigma)$ in the simple case of sphere contacts displaying only sliding friction, but also predicts strong deviation from this usual form when stronger kinds of constraints are applied on relative motion. We verify these predictions in the case of contacts with rolling friction, in particular a broadening of the stress range over which shear thickening occurs. We finally discuss how a similar approach can be followed to predict $f(sigma)$ in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.
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We study the rheology of cornstarch suspensions, a non-Brownian particle system that exhibits discontinuous shear thickening. Using magnetic resonance imaging (MRI), the local properties of the flow are obtained by the determination of local velocity profiles and concentrations in a Couette cell. For low rotational rates, we observe shear localization characteristic of yield stress fluids. When the overall shear rate is increased, the width of the sheared region increases. The discontinuous shear thickening is found to set in at the end of this shear localization regime when all of the fluid is sheared: the existence of a nonflowing region, thus, seems to prevent or delay shear thickening. Macroscopic observations using different measurement geometries show that the smaller the gap of the shear cell, the lower the shear rate at which shear thickening sets in. We, thus, propose that the discontinuous shear thickening of cornstarch suspensions is a consequence of dilatancy: the system under flow attempts to dilate but instead undergoes a jamming transition, because it is confined. This proposition is confirmed by an independent measurement of the dilation of the suspension as a function of the shear rate. It is also explains the MRI observations: when flow is localized, the nonflowing region plays the role of a dilatancy reservoir which allows the material to be sheared without jamming.
Nearly all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition, and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems -- cornstarch in glycerol and silica spheres in glycerol -- the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes, due to a crossover between frictionless isotropic jamming and a frictional shear jamming point with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into an additive analytic background (given by the viscosity at low shear rates) and a scaling variable governing the proximity to shear jamming that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.
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.
Shear thickening of suspensions is studied by discrete-particle simulation, accounting for hydrodynamic, repulsive, and contact forces. The contact forces, including friction, are activated when the imposed shear stress $sigma$ is able to overcome the repulsive force. The simulation method captures strong continuous and discontinuous shear thickening (CST and DST) in the range of solid volume fraction $0.54 le phile 0.56$ studied here. This work presents characteristics of the contact force network developed in the suspension under shear. The number of frictional contacts per particle $Z$ is shown to have a one-to-one relationship with the suspension stress, and the conditions for simple percolation of frictional contacts are found to deviate strongly from those of a random network model. The stress is shown to have important correlations with topological invariant metrics of the contact network known as $k$-cores; the $k$-cores are maximal subgraphs (`clusters) in which all member particles have $k$ or more frictional contacts to other members of the same subgraph. Only $kle 3$ is found in this work at solid volume fractions $phi le 0.56$. Distinct relationships between the suspension rheology and the $k$-cores are found. One is that the stress susceptibility, defined as $partial sigma/partial dot{gamma}$ where $dot{gamma}$ is the shear rate, is found to peak at the condition of onset of the $3$-core, regardless of whether the system exhibits CST or DST. A second is that the stress per particle within cores of different $k$ increases sharply with increase of $k$ at the onset of DST; in CST, the difference is mild.
Shear thickening of particle suspensions is characterized by a transition between lubricated and frictional contacts between the particles. Using 3D numerical simulations, we study how the inter-particle friction coefficient influences the effective macroscopic friction coefficient and hence the microstructure and rheology of dense shear thickening suspensions. We propose expressions for effective friction coefficient in terms of distance to jamming for varying shear stresses and particle friction coefficient values. We find effective friction coefficient to be rather insensitive to interparticle friction, which is perhaps surprising but agrees with recent theory and experiments.
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