Shear Thickening In Dense Suspensions Research Articles

Shear thickening in dense suspensions driven by particle interlocking

The processing of dense suspensions is a crucial step in many industries including mining; the production of ceramics; and the manufacture of pharmaceuticals. It is widely reported that these suspensions exhibit nonlinear behaviours such as shear thinning and thickening, with particle surface contacts recently being accepted as a primary culprit in the latter. In light of this, the modelling community have started to explore the role of particle surface tribology, predominantly by incorporating Coulombic friction models borrowed from the field of dry granular matter. Full details of the interactions between particle surfaces remain unclear, however, and it is suggested that physical interlocking of particle asperities may be key. Here, we use particle-based simulations to explore explicitly the effect of interlocking on the rheology of dense suspensions of micron-sized solids in a Newtonian fluid. Our simplified model recovers shear thinning, thickening and jamming phenomena commonly seen in experiments.

Shear thickening in dense suspension: A master-curve and “roll” of friction

The mechanism of shear thickening in dense suspensions has been linked to a stress-controlled transition from unconstrained lubricated (“frictionless”) to constrained unlubricated (“frictional”) rheology. However, it is unclear how these constraints are affected by particle surface chemistry. We show that simulations incorporating reasonable values of sliding friction with a small amount of rolling friction can collapse experimental data covering orders of magnitude in particle size and different particle-fluid chemistries simply by scaling the onset stress for shear thickening. Still, there are notable exceptions where enhanced hydrogen bonding between particles decreases the jamming volume fraction in a manner analogous to sticky or rough particles, which can only be modeled using higher rolling and/or sliding friction coefficients. These observations thus connect the stress-activated formation of hydrogen bonds at the particle surface to rolling and sliding constraints and macroscopic shear thickening behavior.

Shear thickening in dense suspensions: an experimental study

<h2>Abstract</h2> Shear thickening is an intriguing rheological behaviour which consists in a brutal increase in the viscosity above a critical shear rate. It is famously encountered in suspensions of corn starch in water. Despite having been discovered in the early 1930's, its underlying mechanisms remained a mystery for a long time. In 2013–14, numerical and theoretical works [1–3] put forward a frictional transition scenario to explain this phenomenon. In this talk, I will present experimental work investigating this frictional transition scenario. In order to test the ideas of this model, one has to go further than standard rheological techniques, since they do not provide access to the frictional state of the measured suspension. I will thus focus on the techniques that we developed in order to evidence the frictional transition and link it to the presence of a shear-thickening behaviour.

Roughness induced shear thickening in frictional non-Brownian suspensions: A numerical study

Particle surface roughness plays a pivotal role in dictating the rheological behavior of dense suspensions of rigid particles as it promotes interparticle contacts, leading to friction and contact stresses. This suggests that roughness must have a significant impact on the shear thickening behavior of suspensions, as friction is considered to be the underlying mechanism for shear thickening in dense suspensions. To this end, we numerically investigate the effects of systematically increasing the particle surface roughness on shear thickening suspensions. We show that increasing roughness leads to early onset of shear thickening, especially discontinuous shear thickening, in terms of both the critical shear rate and the critical volume fraction. In addition, roughness enhances the strength of the shear thickening effect as it leads to increase in the viscosity of dense suspensions. We explain these results by investigating the role of roughness in the evolution of contact networks and the jamming fraction. Increasing roughness leads to denser contact networks with high contact stresses and reduction in the jamming fraction. Finally, we visualize the effect of roughness on the phase diagram for viscosity in the shear rate–volume fraction plane. The results presented in the paper are consistent with recent experimental studies, which indicates that the computational framework developed can be utilized to predict and tune suspension behavior for specific applications.Particle surface roughness plays a pivotal role in dictating the rheological behavior of dense suspensions of rigid particles as it promotes interparticle contacts, leading to friction and contact stresses. This suggests that roughness must have a significant impact on the shear thickening behavior of suspensions, as friction is considered to be the underlying mechanism for shear thickening in dense suspensions. To this end, we numerically investigate the effects of systematically increasing the particle surface roughness on shear thickening suspensions. We show that increasing roughness leads to early onset of shear thickening, especially discontinuous shear thickening, in terms of both the critical shear rate and the critical volume fraction. In addition, roughness enhances the strength of the shear thickening effect as it leads to increase in the viscosity of dense suspensions. We explain these results by investigating the role of roughness in the evolution of contact networks and the jamming fraction....

A hydrodynamic model for discontinuous shear-thickening in dense suspensions

Restricted sliding or rotational motion of colloidal particles plays a key role in the emergence of discontinuous shear thickening (DST). From viscometric functions to the number of contacting neighbors under an applied deformation, a hindrance to sliding motion significantly changes the behavior of dense suspensions on all scales. In this work, implicitly by using a modified hydrodynamic model based on Stokesian dynamics and explicitly by solving for the hydrodynamics of nonsmooth colloids, we show that lubrication forces that arise from surface asperities effectively provide such constraints to tangential particle motion. A transition from continuous shear thickening to DST is observed as the surface roughness of the particles is systematically increased. In this hydrodynamic model for DST, normal stress differences remain negative in the shear-thickened state (STS). Study of the spatial stress distribution indicates the onset of DST to be a highly localized event; however, particle self-diffusivity and the microstructural network suggest a rather uniform structure in the STS.

Shear thickening of dense suspensions: The role of friction

Shear thickening of particle suspensions is caused by a transition between lubricated and frictional contacts between the particles. Using three-dimensional (3D) numerical simulations, we study how the interparticle friction coefficient (μm) influences the effective macroscopic friction coefficient (μ) and hence the microstructure and rheology of dense shear thickening suspensions. We propose expressions for μ in terms of distance to jamming for varying shear stresses and μm values. We find μ to be rather insensitive to interparticle friction, which is perhaps surprising but agrees with recent theory and experiments. Unifying behaviors were observed between the average coordination numbers of particles across a wide range of viscous numbers and μm values.

Alternative Frictional Model for Discontinuous Shear Thickening of Dense Suspensions: Hydrodynamics.

A consensus has emerged that a constraint to rotational or sliding motion of particles in dense suspensions under flow is the genesis of the discontinuous shear thickening (DST) phenomenon. We show that tangential fluid lubrication interactions due to finite-sized asperities on particle surfaces effectively provide these constraints, changing the dynamics of particle motion. By explicitly resolving for the surface roughness of particles, we show that, while smooth particles exhibit continuous shear thickening, purely hydrodynamic interactions in rough particles result in DST. In contrast to the frictional contact model, the hydrodynamic model predicts negative first and second normal stress differences for dense suspensions in the shear thickened state.

Discontinuous shear thickening in Brownian suspensions.

Discontinuous shear thickening in dense suspensions naturally emerges from the activation of frictional forces by shear flow in non-Brownian systems close to jamming. Yet, this physical picture is incomplete as most experiments study soft colloidal particles subject to thermal fluctuations. To characterize discontinuous shear thickening in colloidal suspensions, we use computer simulations to provide a complete description of the competition between athermal jamming, frictional forces, thermal motion, particle softness, and shear flow. We intentionally neglect hydrodynamics, electrostatics, lubrication, and inertia, but can nevertheless achieve quantitative agreement with experimental findings. In particular, shear thickening corresponds to a crossover between frictionless and frictional jamming regimes which is controlled by thermal fluctuations and particle softness and occurs at a softness dependent Péclet number. We also explore the consequences of our findings for constant pressure experiments, and critically discuss the reported emergence of "S-shaped" flow curves. Our work provides the minimal ingredients to quantitatively interpret a large body of experimental work on discontinuous shear thickening in colloidal suspensions.

Localized stress fluctuations drive shear thickening in dense suspensions

Dense particulate suspensions exhibit a dramatic increase in average viscosity above a critical, material-dependent shear stress. This thickening changes from continuous to discontinuous as the concentration is increased. Using direct measurements of spatially resolved surface stresses in the continuous thickening regime, we report the existence of clearly defined dynamic localized regions of substantially increased stress that appear intermittently at stresses above the critical stress. With increasing applied stress, these regions occupy an increasing fraction of the system, and the increase accounts quantitatively for the observed shear thickening. The regions represent high-viscosity fluid phases, with a size determined by the distance between the shearing surfaces and a viscosity that is nearly independent of shear rate but that increases rapidly with concentration. Thus, we find that continuous shear thickening arises from increasingly frequent localized discontinuous transitions between distinct fluid phases with widely differing viscosities.

Friction-induced shear thickening: A microscopic perspective

We develop a microscopic picture of shear thickening in dense suspensions which emphasizes the role of frictional forces, coupling rotational and translational degrees of freedom. Simulations with contact forces and viscous drag only, reveal pronounced shear thickening with a simultaneous increase in contact number and energy dissipation by frictional forces. At high densities, when the translational motion is severely constrained, we observe liquid-like gear states with pronounced relative rotations of the particles coexisting with solid-like regions which rotate as a whole. The latter are stabilised by frustrated loops which become more numerous and persistent with increasing pressure, giving rise to an increasing lengthscale of this mosaique-like structure and a corresponding increase in viscosity.

Shear Thickening in Concentrated Soft Sphere Colloidal Suspensions: A Shear Induced Phase Transition

A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.

Shear thickening of dense suspensions due to energy dissipation in lubrication layers between particles

This paper deals with a theoretical study of the shear thickening effects in concentrated suspensions of non-Brownian particles. Our analysis shows that an increase of the shear rate of the suspension flow leads to a decrease of the mean thickness of the gaps between the nearest particles in dense suspensions. In turn, this leads to the growth of energy dissipation in these gaps, which means an increase of the suspension effective viscosity with the shear rate.

The role of dilation and confining stresses in shear thickening of dense suspensions

Many densely packed suspensions and colloids exhibit a behavior known as Discontinuous Shear Thickening in which the shear stress jumps dramatically and reversibly as the shear rate is increased. We performed rheometry and video microscopy measurements on a variety of suspensions to determine the mechanism for this behavior. We distinguish Discontinuous Shear Thickening from inertial effects by showing that the latter are characterized by a Reynolds number but are only found for lower packing fractions and higher shear rates than the former. Shear profiles and normal stress measurements indicate that, in the shear thickening regime, stresses are transmitted through frictional rather than viscous interactions. We come to the surprising conclusion that for concentrated suspensions such as cornstarch in water which exhibit the phenomenon of Discontinuous Shear Thickening, the local constitutive relation between stress and shear rate is not necessarily shear thickening. If the suspended particles are heavy enough to settle, we find the onset stress of shear thickening τmin corresponds to a hydrostatic pressure from the weight of the particle packing where neighboring particles begin to shear relative to each other. Above τmin⁠, dilation is seen to cause particles to penetrate the liquid–air interface of the sheared sample. The upper stress boundary τmax of the shear thickening regime is shown to roughly match the ratio of surface tension divided by a radius of curvature on the order of the particle size. These results suggest a new model in which the increased dissipation in the shear thickening regime comes from frictional stresses that emerge as dilation is frustrated by a confining stress from surface tension at the liquid–air interface. We generalize this shear thickening mechanism to other sources of a confining stress by showing that, when instead the suspensions are confined by solid walls and have no liquid–air interface, τmax is set by the stiffness of the most compliant boundary which frustrates dilation. All of this rheology can be described by a nonlocal constitutive relation in which the local relation between stress and shear rate is shear thinning, but where the stress increase comes from a normal stress term which depends on the global dilation.

Shear Thickening and Migration in Granular Suspensions

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 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.

Generality of shear thickening in dense suspensions

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response.

Shear thickening in electrically-stabilized colloidal suspensions

A theory is presented for the onset of shear thickening in colloidal suspensions of particles, stabilized by an electrostatic repulsion. Based on an activation model, a critical shear stress can be derived for the onset of shear thickening in dense suspensions for a constant potential and a constant charge approach of the spheres. Unlike previous models, the total interaction potential is taken into account (sum of attraction and repulsion). The critical shear stress is related to the maximum of the total interaction potential scaled by the free volume per particle. A comparison with experimental investigations shows the applicability of the theory.

Letter to the editor: Comment on “Effect of attractions on shear thickening in dense suspensions” [J. Rheology 48, 1321 (2004)

First Page

Effect of attractions on shear thickening in dense suspensions

Shear thickening in dense suspensions is investigated as the strength of interparticle attraction is increased. Starting with hard spheres, attractions are induced through depletion interactions up to and beyond the point where the suspensions gel and the zero shear rate viscosity diverges. For a range of volume fractions we find that the stress at the onset of shear thickening is a weakly increasing function of the strength of attraction but the extent of shear thickening is diminished. For attractions of sufficient strength to gel the suspension, shear thickening is completely absent. These observations are discussed in terms of a time scale argument for hydrocluster formation and how the shear rate where hydroclusters are formed is influenced by interparticle attractions. For this purpose we develop methods to deconvolute hydrodynamic and thermodynamic contributions to the viscosity and find that the shear rate characterizing the onset of hydrocluster formation is a decreasing function of strength of attraction. Shear thickening is lost because the thermodynamic contributions to the viscosity increase more rapidly than do the hydrodynamic contributions. This conclusion is supported by extension of force balance models for hydrocluster formation to the case where particles experience attractive interactions. These results suggest gelation and shear thickening may be linked as localization phenomena where, in the former case the localization is thermodynamically driven while in the later case, localization is hydrodynamically driven.