Revealing the frictional transition in shear-thickening suspensions

Stress and flow inhomogeneity in shear-thickening suspensions

HYPOTHESIS

The viscosity of dense suspensions surges when the applied stress surpasses a material-specific critical threshold. There is growing evidence that the thickening transition involves non-uniform flow and stress with considerable spatiotemporal complexity. Nevertheless, it is anticipated that dense suspensions of calcium carbonate particles with purely repulsive interactions may not conform to this scenario, as indicated by local pressure measurements with millimeter spatial resolution.

EXPERIMENT

Here we utilize Boundary Stress Microscopy (BSM), a technique capable of resolving stresses down to the micron scale, to search for evidence of stress heterogeneity. In addition, we measure the flow field at the lower boundary of the suspension where the boundary stress is measured.

FINDINGS

We find localized regions of high-stresses that are extended in the vorticity direction and propagate in the flow direction at a speed approximately half that of the rheometer's top plate. These high-stress regions proliferate with the applied stress accounting for the increased viscosity. Furthermore, the velocity of particles at the lower boundary of the suspension shows a significant and complex nonaffine flow that accompanies regions of high-stresses. Hence, our findings demonstrate that stress and flow inhomogeneity are intrinsic characteristics of shear-thickening suspensions, regardless of the nature of interparticle interactions.

Non-Newtonian behaviour of suspensions and emulsions: Review of different mechanisms

The mechanisms of non-Newtonian behaviour of suspensions and emulsions in steady shear flow are reviewed. The review is divided into two parts. In the first part, the mechanisms of non-Newtonian behaviour in suspensions and emulsions composed of Newtonian matrix are reviewed. Both dilute and concentrated systems are discussed. In the second part, the mechanisms of non-Newtonian behaviour in suspensions and emulsions composed of non-Newtonian matrix are reviewed. Where appropriate, mathematical models describing the rheology are included.

On pressure-driven Poiseuille flow with non-monotonic rheology

Shear thickening fluids are liquids that stiffen as the applied stress increases. If many of these types of fluids follow a monotonic rheological curve, some experimental and numerical studies suggest that certain fluids, like cornstarch, may exhibit a non-monotonic, S-shaped rheology. Such non-monotonic behavior has however proved very difficult to observe experimentally in classical rheometer. To explain such difficulties, the possible presence of vorticity banding in the rheometer has been considered. To prevent such instabilities, we use a capillary rheometer, which is a cylindrical tube, measuring the flow rate versus the applied pressure drop. With this setup, we indeed observe a non-monotonic behavior: the flow rate increases monotonically at low pressure drops up to a maximum, after which it abruptly decreases to an almost constant flow rate regardless of further increases in pressure drop. This maximum-jump-plateau behavior occurs over a wide range of concentrations and is reproducible without hysteresis, which is in agreement with an S-shaped rheology. However, the obtained flow versus pressure difference function Q ( Δ P ) does not agree with the classical Wyart-Cates rheological model, which predicts an S-shaped non-monotonic function, but with neither a jump nor a plateau. To understand this jump-plateau behavior, we remark that any rheological model would establish a relationship between the flow rate and the local pressure gradient, but not the total pressure drop. We thus discuss and analyze the implications of having an S-shaped non-monotonic flow rate-pressure gradient in Poiseuille flow. In particular, we discuss the possibility of a non-uniform pressure gradient in the direction of the flow, i.e., a kind of streamwise banding. The key issue is then the selection of the gradient pressure distribution along the tube. One solution could arise from an analogy of this problem with the spinodal decomposition. It, however, leads to an increase in flow rate with∂ x P up to a plateau between two values of∂ x P as determined by the Maxwell construction. To account for the bump-jump behavior, we have implemented a simple dynamical stochastic version of the Wyart-Cates model, where the thickening occurs with a characteristic time. As a result, with increasing the total pressure drop, the flow rate increases monotonically up to a maximum value. Beyond this point, the flow rate drops abruptly to a lower value, forming a slowly decreasing plateau. This behavior is likely to account for the maximum-jump-plateau observed in the experiments. We also show that in such a system, the final state is quite sensitive to the initial state of the fluid, especially its homogeneity. Our results then demonstrate that the mere presence of a non-monotonic rheological curve is sufficient to predict the occurrence of stress banding in the streamwise direction and a plateau flow rate, even if the suspension remains homogeneous.

Granular aqueous suspensions with controlled interparticular friction and adhesion

We present a simple route to obtain large quantities of suspensions of non-Brownian particles with stimuli-responsive surface properties to study the relation between their flow and interparticle interactions. We perform an alkaline hydrolysis reaction on poly(methyl methacrylate) (PMMA) particles to obtain poly(sodium methacrylate) (PMAA-Na) particles. We characterize the quasi-static macroscopic frictional response of their aqueous suspensions using a rotating drum. The suspensions are frictionless when the particles are dispersed in pure water. We relate this state to the presence of electrosteric repulsion between the charged surfaces of the ionized PMAA-Na particles in water. Then we add monovalent and multivalent ions (Na+, Ca2+, La3+) and we observe that the suspensions become frictional whatever the valency. For divalent and trivalent ions, the quasi-static avalanche angle θc at large ionic strength is greater than that of frictional PMMA particles in water, suggesting the presence of adhesion. Finally, a decrease in the pH of the suspending solution leads to a transition between a frictionless plateau and a frictional one. We perform atomic force microscopy (AFM) to relate our macroscopic observations to the surface features of the particles. In particular, we show that the increase in friction in the presence of multivalent ions or under acidic conditions is driven by a nanoscopic phase separation and the bundling of polyelectrolyte chains at the surface of the particle. Our results highlight the importance of surface interactions in the rheology of granular suspensions. Our particles provide a simple, yet flexible platform to study frictional suspension flows.

Enzymatic degradation of pea fibers changes pea protein concentrate functionality

Pea proteins are gaining increased interest from both the food industry as well as from consumers. Pea protein isolates (PPI) excel at forming meat-like textures upon heating while pea protein concentrates (PPC) are more challenging to transform into highly sought-after foods. PPCs are richer in dietary fibers (DF) and are more sustainable to produce than PPI. In this work, degradative enzymes were used to modify the functionality of PPC-water blends with a focus on texturization upon heating. Three enzyme solutions containing β-glucanases, hemicellulases, pectinases, xylanase, and cellulases were added to 65 wt% PPC blends. The effect of these enzymatic pretreatments was measured by monitoring the torque in a mixing reactor during blending, differential scanning calorimetry (DSC), high-pressure shear rheology (HPSR), and DF content and size analysis. Four endothermic peaks were detected in the DSC thermograms of PPC, namely at 63 °C, 77 °C, 105 °C and 123 °C. The first three peaks were attributed to phase transition and gelation temperatures of the starches and proteins constituting PPC. No endothermic peaks were measured for PPI blends. Enzyme solutions containing β-glucanases, hemicellulases, pectinases, and xylanases increased the endothermic energy of all peaks, hinting at an effect on the gelation properties of PPC. The same enzymes decreased the resistance to flow of PPC blends and induced a shift of the weight average molecular weight (Mw) distribution of soluble dietary fibers (SDF) towards smaller values while increasing the fraction of SDF by decreasing the insoluble dietary fiber (IDF) content. The solution containing cellulases did not change the DSC results or the viscosity of the PPC mixture, nor did it affect the IDF and SDF contents. On the other hand HPSR measurements of heated PPC samples up to 125 °C showed that all tested enzyme solutions decreased the complex viscosity of PPC-water blends to values similar to PPI-water blends. We demonstrated that degradative enzymes can enhance the functionality of less refined protein-rich ingredients based on pea and other vegetal sources. Using optimized enzyme blends for targeted applications can prove to be a key changer in the development and improvement of sustainable protein-rich foods.

A frictional soliton controls the resistance law of shear-thickening suspensions in pipes

Pipe flows are commonly found in nature and industry as an effective mean of transporting fluids. They are primarily characterized by their resistance law, which relates the mean flow rate to the driving pressure gradient. Since Poiseuille and Hagen, various flow regimes and fluid rheologies have been investigated, but the behavior of shear-thickening suspensions, which jam above a critical shear stress, remains poorly understood despite important applications (e.g., concrete or food processing). In this study, we build on recent advances in the physics of shear-thickening suspensions to address their flow through pipes and establish their resistance law. We find that for discontinuously shear-thickening suspensions (large particule volume fractions), the flow rate saturates at high driving stress. Local pressure and velocity measurements reveal that this saturation stems from the emergence of a frictional soliton: a unique, localized, superdissipative, and backpropagating flow structure coexisting with the laminar frictionless flow phase observed at low driving stress. We characterize the remarkably steep effective rheology of the frictional soliton and show that it sets the resistance law at the whole pipe scale. These findings offer an unusual perspective on low-Reynolds suspension flows through pipes, intriguingly reminiscent of the transition to turbulence for simple fluids. They also provide a predictive law for the transport of such suspensions in pipe systems, with implications for a wide range of applications.

Effects of salinity on the flow of dense colloidal suspensions

We experimentally study the effects of salt concentration on the flowing dynamics of dense suspensions of micrometer-sized silica particles in microfluidic drums. In pure water, the particles are fully sedimented under their own weight, but do not touch each other due to their negative surface charges, which results in a "frictionless" dense colloidal suspension. When the pile is inclined above a critical angle θc ∼ 5° a fast avalanche occurs, similar to what is expected for classical athermal granular media. When inclined below this angle, the pile slowly creeps until it reaches flatness. Adding ions in solution screens the repulsive forces between particles, and the flowing properties of the suspension are modified. We observe significant changes in the fast avalanche regime: a time delay appears before the onset of the avalanche and increases with the salt concentration, the whole dynamics becomes slower, and the critical angle θc increases from ∼5° to ∼20°. In contrast, the slow creep regime does not seem to be heavily modified. These behaviors can be explained by considering an increase in both the initial packing fraction of the suspension Φ0, and the effective friction between the particles μp. These observations are confirmed by confocal microscopy measurements to estimate the initial packing fraction of the suspensions, and AFM measurements to quantify the particles surface roughness and the repulsion forces, as a function of the ionic strength of the suspensions.

Fracture and relaxation in dense cornstarch suspensions

Dense suspensions exhibit the remarkable ability to switch dynamically and reversibly from a fluid-like to a solid-like, shear-jammed (SJ) state. Here, we show how this transition has important implications for the propensity for forming fractures. We inject air into bulk dense cornstarch suspensions and visualize the air invasion into the opaque material using time-resolved X-ray radiography. For suspensions with cornstarch mass fractions high enough to exhibit discontinuous shear thickening and shear jamming, we show that air injection leads to fractures in the material. For high mass fractions, these fractures grow quasistatically as rough cavities with fractured interfaces. For lower mass fractions, remarkably, the fractures can relax to smooth bubbles that then rise under buoyancy. We show that the onset of the relaxation occurs as the shear rate induced by the air cavity growth decreases below the critical shear rate denoting the onset of discontinuous shear thickening, which reveals a structural signature of the SJ state.

Clogging of noncohesive suspensions through constrictions using an efficient discrete particle solver with unresolved fluid flow

When objects are forced to flow through constrictions their transport can be frustrated temporarily or permanently due to the formation of arches in the region of the bottleneck. While such systems have been intensively studied in the case of solid particles in a gas phase being forced by gravitational forces, the case of solid particles suspended in a liquid phase, forced by the liquid itself, has received much less attention. In this case, the influence of the liquid flow on the transport efficiency is not well understood yet, leading to several apparently trivial but yet unanswered questions, e.g., would an increase of the liquid flow improve the transport of particles or worsen it? Although some experimental data are already available, they lack enough detail to give a complete answer to such a question. Numerical models would be needed to scrutinize the system deeper. In this paper, we study this system making use of an advanced discrete particle solver (mercurydpm) and an approximated numerical model for the liquid drag and compare the results with experimental data.

Role of confinement in the shear banding and shear jamming in noncolloidal fiber suspensions

The jamming effect is critical in processing short fiber-reinforced thermoplastics (FRTs). Fiber jamming can induce discontinuous shear thickening (DST) in simple shear and result in fiber-matrix separation in more complex flows such as injection molding and compression molding of FRTs. The confinement effect commonly induces local jams and strongly enhances fiber jamming. However, the transient evolution of local fiber jams under confinement and its correlation with the tumbling of fibers are still elusive. In this study, we adopted rheo-PIV (particle image velocity) techniques to study this effect for glass fiber-reinforced thermoplastics (FRTs). The translational and tumbling motion of fiber were determined during rheological measurements, and the distribution of fiber orientation was determined by X-ray CT. Three shear banding regions appeared after the viscosity overshoot under high shear stress in suspensions with high fiber content, which was associated with the three regions of fiber orientation across the gap due to confinement. Shear banding was ascribed to the different tumbling speeds across the gap because of the different initial orientations and different wall confinements near and far from the wall. The local shear thickening and jamming behavior became most significant under intermediate confinement, and were affected by shear strain, shear stress, and fiber contents. 3D state diagrams were constructed to show the confinement effect on the evolution of shear banding and jamming.

Shear thickening in presence of adhesive contact forces: The singularity of cornstarch

HYPOTHESIS

A number of dense particle suspensions experience a dramatic increase in viscosity with the shear stress, up to a solid-like response. This shear-thickening process is understood as a transition under flow of the nature of the contacts - from lubricated to frictional - between initially repellent particles. Most systems are now assumed to fit in with this scenario, which is questionable.

EXPERIMENT

Using an in-house pressure sensor array, we provide a spatio-temporal map of the normal stresses in the flows of two shear-thickening fluids: a stabilized calcium carbonate suspension, known to fit in with the standard scenario, and a cornstarch suspension, which spectacular thickening behavior remains poorly understood.

FINDINGS

We evidence in cornstarch a unique, stable heterogeneous structure, which moves in the velocity direction and does not appear in calcium carbonate. Its nature changes from a stress wave to a rolling solid jammed aggregate at high solid fraction and small gap width. The modeling of these heterogenities points to an adhesive force between cornstarch particles at high stress, also evidenced in microscopic measurements. Cornstarch being also attractive at low stress, it stands out of the classical shear-thickening frame, and might be part of a larger family of adhesive and attractive shear-thickening fluids.

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity η and diffusivity D/ of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale ξ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that η and D/ are controlled by ξ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from D/ ∼ η (frictionless) to η1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.

Non-Newtonian fluid gating membranes with acoustically responsive and self-protective gas transport control

Control of gas transport through porous media is desired in multifarious processes such as chemical reactions, interface absorption, and medical treatment. Liquid gating technology, based on dynamically adaptive interfaces, has been developed in recent years and has shown excellent control capability in gas manipulation-the reversible opening and closing of a liquid gate for gas transport as the applied pressure changes. Here, we report a new strategy to achieve self-protective gas transport control by regulating the dynamic porous interface in a non-Newtonian fluid gating membrane based on the shear thickening fluid. The gas transport process can be suspended and restored via modulation of the acoustic field, owing to the transition of particle-to-particle interactions in a confined geometry. Our experimental and theoretical results support the stability and tunability of the gas transport control. In addition, relying on the shear thickening behaviour of the gating fluid, the transient response can be achieved to resist high-impact pressure. This strategy could be utilized to design integrated smart materials used in complex and extreme environments such as hazardous and explosive gas transportation.

Utilization of potato starch suspension for MR-microimaging in ex vivo mouse embryos

Magnetic resonance (MR) microimaging of the mouse embryo is a promising tool to noninvasively investigate the microstructure of the brain of a developing mouse. The proton-free fluid is used for the liquid surrounding the specimen in MR microimaging, but the potential issue of image quality remains due to the air bubbles on the specimen and the retained water proton in the curvature of the embryo. Furthermore, the specimen may move during the scanning, resulting in motion artifact. Here, we developed the new concept of the ex vivo microimaging protocol with the robust method using the potato starch-containing biological polymers. Potato starch suspension with PBS significantly reduced T1 and T2 signal intensity of the suspension and strongly suppressed the motion of the embryo. Furthermore, potato starch-PBS suspension is stable for long-time scanning at room temperature. These results indicate the utility of potato starch suspension for MR microimaging in mouse embryos.

Flow-Switched Bistability in a Colloidal Gel with Non-Brownian Grains

We show that mixing a colloidal gel with larger, non-Brownian grains generates novel flow-switched bistability. Using a combination of confocal microscopy and rheology, we find that prolonged moderate shear results in liquefaction by collapsing the gel into disjoint globules, whereas fast shear gives rise to a yield-stress gel with granular inclusions upon flow cessation. We map out the state diagram of this new "mechanorheological material" with varying granular content and demonstrate that its behavior is also found in separate mixture using different particles and solvents.

Flow and arrest in stressed granular materials

Flowing granular materials often abruptly arrest if not driven by sufficient applied stresses. Such abrupt cessation of motion can be economically expensive in industrial materials handling and processing, and is significantly consequential in intermittent geophysical phenomena such as landslides and earthquakes. Using discrete element simulations, we calculate states of steady flow and arrest for granular materials under the conditions of constant applied pressure and shear stress, which are also most relevant in practice. Here the material can dilate or compact, and flow or arrest, in response to the applied stress. Our simulations highlight that under external stress, the intrinsic response of granular materials is characterized by uniquely-defined steady states of flow or arrest, which are highly sensitive to interparticle friction. While the flowing states can be equivalently characterized by volume fraction, coordination number or internal stress ratio, to characterize the states of shear arrest, one needs to also consider the structural anisotropy in the contact network. We highlight the role of dilation in the flow-arrest transition, and discuss our findings in the context of rheological transitions in granular materials.

Cross-linked polymer microparticles with tunable surface properties by the combination of suspension free radical copolymerization and Click chemistry

We propose a general, versatile and broad in scope two-steps approach for the elaboration of cross-linked polymer microparticles (µPs) with tunable functionalities and surface properties. Surface-functionalized cross-linked polymer µPs with diameter in the 80 μm range are prepared by the combination of: 1) suspension free radical copolymerization of styrene, propargyl methacrylate and 1,6-hexanediol dimethacrylate, 2) subsequent covalent tethering of a variety of azide-functionalized moieties (i.e. rhodamine B fluorescent dye or poly(ethylene glycol) (PEG) brush precursor) by copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC) and, 3) optional N-alkylation of the 1,2,3-triazole groups followed by anion exchange reaction to afford covalently-tethered 1,2,3-triazolium ionic liquids with iodide or cresol red counter-anions. The resulting µPs are characterized by laser diffraction, differential scanning calorimetry, as well as by optical, confocal fluorescence, scanning electron and atomic force microscopies. Finally, the rheological properties of concentrated suspensions (volume fractions of 0.40 and 0.44) of the different synthesized µPs dispersed in a 1:1 (vol/vol) mixture of polyalkylene glycol and water are studied. The modification of µPs surface properties contributes not only to change the stability of the suspensions against flocculation, but also to significantly modify their rheological behavior at high shear stresses. This represents a clear experimental evidence of the importance of non-hydrodynamic contact forces in the rheology of non-Brownian suspensions (NBSs).

Shear Jamming and Fragility of Suspensions in a Continuum Model with Elastic Constraints

Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension can turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases. We show that, to reproduce the phenomenology of shear jamming in generic geometries, it is necessary to link this effect to the elastic response supported by the suspension microstructure rather than to a divergence of the viscosity.

Shear thickening behavior in dense repulsive and attractive suspensions of hard spheres

Shear thickening in stable dense colloidal suspensions is a reversible phenomenon and no hysteresis is observed in the flow curve measurements. However, a reduction in the stability of colloids promotes particle aggregation and introduces a time dependent rheological response. In this work, by using a model colloidal system of hard spherical silica particles (average diameter of 415 nm) with varying particle volume fractions 0.2 ≤ ϕ ≤ 0.56, we study the effect of particle stability on the hysteresis of the shear thickening behavior of these suspensions. The particle stability is manipulated by adding a simple monovalent salt (sodium chloride) in the silica suspension with varying concentrations α ∈ [0,0.5] M. For repulsive and weakly attractive suspensions, the flow behavior is history independent and the shear thickening behavior does not exhibit hysteresis. However, significant hysteresis is observed in rheological measurements for strongly attractive suspensions, with shear history playing a critical role due to the dynamic nature of particle clusters, resulting in time dependent hysteresis behavior. By performing numerical simulations, we find that this hysteresis behavior arises due to the competition among shear, electrostatic repulsive, van der Waals attractive, and frictional contact forces. The critical shear stress (i.e., the onset of shear thickening) decreases with increasing salt concentrations, which can be captured by a scaling relationship based on the force balance between particle-particle contact force and electrostatic repulsive force. Our combined experimental and simulation results imply the formation of particle contacts in our sheared suspensions.

Rheology of granular liquids in extensional flows: Beyond the μ(I)-law

The Granular Integration Through Transients (GITT) formalism gives a theoretical description of the rheology of moderately dense granular flows and suspensions. In this work, we extend the GITT equations beyond the case of simple shear flows studied before. Applying this to the particular example of extensional flows, we show that the predicted behavior is somewhat different from that of the more frequently studied simple shear case, as illustrated by the possibility of nonmonotonous evolution of the effective friction coefficient μ with the inertial number I. By the reduction of the GITT equations to simple toy models, we provide a generalization of the μ(I)-law true for any type of flow deformation. Our analysis also includes a study of the Trouton ratio, which is shown to behave quite similarly to that of dense colloidal suspensions.

Unifying disparate rate-dependent rheological regimes in non-Brownian suspensions

A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at low shear rate or stress followed by a Newtonian plateau (constant viscosity) at intermediate shear rate or stress values which transitions to shear thickening (increasing viscosity) beyond a critical shear rate or stress value and finally undergoes a second shear thinning transition at extremely high shear rate or stress values. In this study, we unify and quantitatively reproduce all the disparate rate-dependent regimes and the corresponding transitions for a dense non-Brownian suspension with increasing shear rate or stress. We employ discrete particle dynamics simulations based on the proposed mechanism to elucidate its accuracy. We find that a competition between interparticle interactions of hydrodynamic and nonhydrodynamic origins and the switching in the dominant stress scale with increasing the shear rate or stress lead to each of the above transitions. Inclusion of traditional hydrodynamic interactions, attractive or repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions the interparticle contact interactions, and a constant friction (or other constraint mechanism) reproduces the initial thinning as well as the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional nonhydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential, thus providing an explanation for the presence of the intermediate Newtonian plateau along with reproducing the second shear thinning in a single framework. Expressions utilized for various interactions and friction are determined from experimental measurements and hence result in excellent quantitative agreement between the simulations and previous experiments.

An experimental study on the role of inter-particle friction in the shear-thinning behavior of non-Brownian suspensions

This paper focuses on shear-thinning in non-Brownian suspensions. In particular, it proposes a quantitative experimental validation of the model proposed by Lobry et al. [J. Fluid Mech., 2019, 860, 682-710] that links viscosity to microscopic friction between particles and, in particular, shear-thinning to load-dependent friction coefficient. To this aim, Atomic Force Microscopy (AFM) is used to measure the pairwise friction coefficient of polystyrene particles (40 μm in diameter), immersed in a Newtonian liquid, for different normal loads ranging from 10 to 1000 nN. It is shown that the inter-particle friction coefficient decreases with the load, contrarily to what is expected for macroscopic contacting bodies. The experimental friction law is then introduced into the viscosity model proposed by Lobry et al. and the results are compared to the viscosity of suspensions made of the same particles dispersed in the same liquid as those used for AFM measurements. The very good agreement between the measured viscosity values and those predicted by the model of Lobry et al. with the friction coefficient measured by AFM as input data shows the relevance of the scenario proposed by Lobry et al. and highlights the close links between the microscopic friction properties of the particles and the macroscopic rheological behavior of suspensions.

Contact Force Mediated Rapid Deposition of Colloidal Microspheres Flowing over Microstructured Barriers

Deposition of particles while flowing past constrictions is a ubiquitous phenomenon observed in diverse systems. Some common examples are jamming of salt crystals near the orifice of salt shakers, clogging of filter systems, gridlock in vehicular traffic, etc. Our work investigates the deposition events of colloidal microspheres flowing over microstructured barriers in microfluidic devices. The interplay of DLVO, contact, and hydrodynamic forces in facilitating rapid deposition of microspheres is discussed. Noticeably, a decrease in the electrostatic repulsion among microspheres leads to linear chain formations, whereas an increase in roughness results in rapid deposition.

Nonlocal Effects Reflect the Jamming Criticality in Frictionless Granular Flows Down Inclines

The jamming transition is accompanied by a rich phenomenology such as hysteresis or nonlocal effects that is still not well understood. Here, we experimentally investigate a model frictionless granular layer flowing down an inclined plane as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis of the avalanche angle, yet the layer stability increases as it gets thinner. Steady rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting the idea that nonlocal effects are the consequence of the usual finite-size effects associated with the presence of a critical point. This collapse indicates that the so-called isostatic length l^{*}, the scale on which pinning a boundary freezes all remaining floppy modes, governs the effect of boundaries on flow and rules out other propositions made in the past.

Viscoelasticity of non-colloidal hydrogel particle suspensions at the liquid-solid transition

Suspensions of soft particles transition from a viscous fluid to a soft material upon increases in phase volume. The criteria defining the transition to this jammed state are difficult to define due to the porous and deformable nature of soft particles. Here, we characterise the rheology of aqueous suspensions of industrially relevant non-colloidal, polydisperse, frictional agarose microgels and evaluate shear and viscoelastic behaviour across a range of phase volumes from the dilute regime to the highly concentrated regime. In order to model the viscoelastic response of suspensions without free fitting parameters, the random close packing volume fraction (φrcp) and the particle modulus are determined, respectively, from particle size distribution measurements and direct measurements of reduced elastic modulus of individual particles (Erp) using Atomic Force Microscopy. It is found that at φrcp, previously shown to correspond to divergence of the viscosity, also corresponds to the suspension transition from a viscous to viscoelastic fluid. However, the transition to a jammed solid-like state (φj) occurs at phase volumes exceeding this value (i.e. φj > φrcp). The suspension modulus and its sudden growth at φj are well-predicted by the Evans and Lips model that incorporates the Erp of the hydrogel particles. This rheological behaviour showing a dual transition is reminiscent of two families of systems: (i) colloidal suspensions and (ii) frictional-adhesive non-colloidal suspensions. However, it does not strictly follow either case. We propose that the width of the transition region is dictated by frictional contact, particle size distribution and particle modulus, and plan to further probe this in future work.

Signature of Transition between Granular Solid and Fluid: Rate-Dependent Stick Slips in Steady Shearing

Despite extensive studies on either smooth granular-fluid flow or the solidlike deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of interparticle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers J decades below reported values, we answer how a granular system can transition to the regime sustained by solid-to-solid friction that goes beyond existing paradigms based on suspension rheology.

Dilatancy, shear jamming, and a generalized jamming phase diagram of frictionless sphere packings

Granular packings display the remarkable phenomenon of dilatancy, wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, also being the related phenomenon of shear-induced jamming, requires frictional interactions. Here, we show that the occurrence of isotropic jamming densities φ_j above the minimal density (or the J-point density) φ_J leads both to the emergence of shear-induced jamming and dilatancy in frictionless packings. Under constant pressure shear, the system evolves into a steady-state at sufficiently large strains, whose density only depends on the pressure and is insensitive to the initial jamming density φ_j. In the limit of vanishing pressure, the steady-state exhibits critical behavior at φ_J. While packings with different φ_j values display equivalent scaling properties under compression, they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when φ_j > φ_J, contrary to the continuous behaviour in generic packings that jam at φ_J. Our results thus lead to a more coherent, generalised picture of jamming in frictionless packings, which also have important implications on how dilatancy is understood in the context of frictional granular matter.

Exploring the roles of roughness, friction and adhesion in discontinuous shear thickening by means of thermo-responsive particles

Dense suspensions of colloidal or granular particles can display pronounced non-Newtonian behaviour, such as discontinuous shear thickening and shear jamming. The essential contribution of particle surface roughness and adhesive forces confirms that stress-activated frictional contacts can play a key role in these phenomena. Here, by employing a system of microparticles coated by responsive polymers, we report experimental evidence that the relative contributions of friction, adhesion, and surface roughness can be tuned in situ as a function of temperature. Modifying temperature during shear therefore allows contact conditions to be regulated, and discontinuous shear thickening to be switched on and off on demand. The macroscopic rheological response follows the dictates of independent single-particle characterization of adhesive and tribological properties, obtained by colloidal-probe atomic force microscopy. Our findings identify additional routes for the design of smart non-Newtonian fluids and open a way to more directly connect experiments to computational models of sheared suspensions.

Combined effects of contact friction and particle shape on strength properties and microstructure of sheared granular media

We present a systematic numerical investigation concerning the combined effects of sliding friction and particle shape (i.e., angularity) parameters on the shear strength and microstructure of granular packings. Sliding friction at contacts varied from 0 (frictionless particles) to 0.7, and the particles were irregular polygons with an increasing number of sides, ranging from triangles to disks. We find that the effect of local friction on shear strength follows the same trend for all shapes. Strength first increases with local friction and then saturates at a shape-dependent value. In contrast, the effect of angularity varies, depending on the level of sliding friction. For low friction values (i.e., under 0.3), the strength first increases with angularity and then declines for the most angular shapes. For high friction values, strength systematically increases with angularity. At the microscale, we focus on the connectivity and texture of the contact and force networks. In general terms, increasing local friction causes these networks to be less connected and more anisotropic. In contrast, increasing particle angularity may change the network topology in different directions, directly affecting the macroscopic shear strength. These analyses and data constitute a first step toward understanding the joint effect of local variables such as friction and grain shape on the macroscopic rheology of granular systems.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Integration through transients approach to the μ(I) rheology

This work generalizes the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)10.1103/PhysRevLett.121.148002] to the determination of the pressure. We focus on the Bagnold regime and provide theoretical support to the empirical μ(I) rheology laws that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the μ(I) laws apply.

Apparent Non-Newtonian Behavior of Ionic Liquids

A significant viscosity variation with the shear rate has been observed for several ionic liquids in rheometry experiments above a critical shear rate. Depending on the liquid and the rheological conditions, both viscosity increase and decrease have been reported. So far, these variations have been interpreted as a signature of a non-Newtonian behavior. However, the measured critical shear rates are orders of magnitude below the ones predicted by numerical simulations. In this work, we perform new rheometry experiments with both ionic liquids and Newtonian liquids to elucidate this discrepancy. For these two types of liquids, both a viscosity decrease and increase have been measured depending on the geometry of the rheometer and the zero-shear viscosity of the liquid. We interpret the viscosity decrease as resulting from viscous heating, since the viscosity of the investigated liquids is also highly temperature-dependent, and the viscosity increase as resulting from the development of instabilities at high shear rates.

Density waves in shear-thickening suspensions

Shear thickening corresponds to an increase of the viscosity as a function of the shear rate. It is observed in many concentrated suspensions in nature and industry: water or oil saturated sediments, crystal-bearing magma, fresh concrete, silica suspensions, and cornstarch mixtures. Here, we reveal how shear-thickening suspensions flow, shedding light onto as yet non-understood complex dynamics reported in the literature. When shear thickening is important, we show the existence of density fluctuations that appear as periodic waves moving in the direction of flow and breaking azimuthal symmetry. They come with strong normal stress fluctuations of the same periodicity. The flow includes small areas of normal stresses of the order of tens of kilopascals and areas of normal stresses of the order of hundreds of pascals. These stress inhomogeneities could play an important role in the damage caused by thickening fluids in the industry.

Signature of jamming under steady shear in dense particulate suspensions

Under an increasing applied shear stress ([Formula: see text]), the viscosity of many dense particulate suspensions increases drastically beyond a stress onset ([Formula: see text]), a phenomenon known as discontinuous shear-thickening. Recent studies point out that some suspensions can transform into a stress induced solid-like shear jammed (SJ) state at high particle volume fraction ([Formula: see text]). SJ state develops a finite yield stress and hence is distinct from a shear-thickened state. Here, we study the steady state shear-thickening behaviour of dense suspensions formed by dispersing colloidal polystyrene particles (PS) in polyethylene glycol (PEG). We find that for small [Formula: see text] values the viscosity of the suspensions as a function of [Formula: see text] can be well described by Krieger-Dougherty (KD) relation. However, for higher values of [Formula: see text] ([Formula: see text] [Formula: see text]), KD relation systematically overestimates the measured viscosity, particularly for higher [Formula: see text] values. This systematic deviation can be rationalized by the weakening of the sample due to flow induced failures of the solid-like SJ state. Using Wyart-Cates model, we propose a method to predict the SJ onset from the steady state rheology measurements. Our results are further supported by in situ optical imaging of the sample boundary under shear.

Testing the Wyart-Cates model for non-Brownian shear thickening using bidisperse suspensions

There is a growing consensus that shear thickening of concentrated dispersions is driven by the formation of stress-induced frictional contacts. The Wyart-Cates (WC) model of this phenomenon, in which the microphysics of the contacts enters solely via the fraction f of contacts that are frictional, can successfully fit flow curves for suspensions of weakly polydisperse spheres. However, its validity for "real-life", polydisperse suspensions has yet to be seriously tested. By performing systematic simulations on bidisperse mixtures of spheres, we show that the WC model applies only in the monodisperse limit and fails when substantial bidispersity is introduced. We trace the failure of the model to its inability to distinguish large-large, large-small and small-small frictional contacts. By fitting our data using a polydisperse analogue of f that depends separately on the fraction of each of these contact types, we show that the WC picture of shear thickening is incomplete. Systematic experiments on model shear-thickening suspensions corroborate our findings, but highlight important challenges in rigorously testing the WC model with real systems. Our results prompt new questions about the microphysics of thickening for both monodisperse and polydisperse systems.

Unsteady flow, clusters, and bands in a model shear-thickening fluid

We analyze the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strain rates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strain rate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in the compressional direction and propagate in the dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.

Rheology in dense assemblies of spherocylinders: Frictional vs. frictionless

Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses the alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations in aspect ratio, quite contrary to what is known from frictionless systems.

Brownian Granular Flows Down Heaps

We study the avalanche dynamics of a pile of micrometer-sized silica grains in water-filled microfluidic drums. Contrary to what is expected for classical granular materials, avalanches do not stop at a finite angle of repose. After a first rapid phase during which the angle of the pile relaxes to an angle θ_{c}, a creep regime is observed where the pile slowly flows until the free surface reaches the horizontal. This relaxation is logarithmic in time and strongly depends on the ratio between the weight of the grains and the thermal agitation (gravitational Péclet number). We propose a simple one-dimensional model based on Kramers' escape rate to describe these Brownian granular avalanches, which reproduces the main observations.

Effect of Roughness and Elasticity on Interactions between Charged Colloidal Spheres

The effects of realistic roughness and elasticity on the interactions between charged silica spheres are studied as a function of surface potential, screening length, interfacial energy, and roughness. The repulsive force F_rep that must be overcome to bring charged spheres into contact is relatively insensitive to elasticity unless spheres are hundreds of times softer than silica. F_rep is also insensitive to roughness and interfacial energy. In contrast, roughness has a large effect on the binding energy of spheres and the force F_sep to separate them. Both are lowered by 1 to 2 orders of magnitude by the measured surface roughness of less than 1 nm on 1 μm silica spheres. The reason is that interactions between rigid spheres are dominated by the highest surface peaks rather than the entire spherical surface. Elasticity can increase the pull-off force of rough spheres by a factor of 2 or more because additional surface area can be brought into contact. The implications of these results for shear-thickening transitions are discussed.

Constitutive Model for Time-Dependent Flows of Shear-Thickening Suspensions

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discrete-element simulations whose results we also present.

A general constitutive model for dense, fine-particle suspensions validated in many geometries

Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect-for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of "shear jamming fronts," 3) the time-dependent propagation of "impact-activated jamming fronts," and 4) the non-Newtonian, "running on oobleck" effect, wherein fast locomotors stay afloat while slow ones sink.

Using Acoustic Perturbations to Dynamically Tune Shear Thickening in Colloidal Suspensions

Colloidal suspensions in industrial processes often exhibit shear thickening that is difficult to control actively. Here, we use piezoelectric transducers to apply acoustic perturbations to dynamically tune the suspension viscosity in the shear-thickening regime. We attribute the mechanism of dethickening to the disruption of shear-induced force chains via perturbations that are large relative to the particle roughness scale. The ease with which this technique can be adapted to various flow geometries makes it a powerful tool for actively controlling suspension flow properties and investigating system dynamics.

Force transmission and the order parameter of shear thickening

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 the 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 σ, which is directly linked to the distribution of the normal components of non-hydrodynamic interparticle forces. Here, we develop a model for this force distribution, based on the so-called q-model, which we borrow from granular physics. This model explains the known f(σ) 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 the 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(σ) in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.

Competing Timescales Lead to Oscillations in Shear-Thickening Suspensions

Competing timescales generate novelty. Here, we show that a coupling between the timescales imposed by instrument inertia and the formation of interparticle frictional contacts in shear-thickening suspensions leads to highly asymmetric shear-rate oscillations. Experiments tuning the presence of oscillations by varying the two timescales support our model. The observed oscillations give access to a shear-jamming portion of the flow curve that is forbidden in conventional rheometry. Moreover, the oscillation frequency allows us to quantify an intrinsic relaxation time for particle contacts. The coupling of fast contact network dynamics to a slower system variable should be generic to many other areas of dense suspension flow, with instrument inertia providing a paradigmatic example.

Conching chocolate is a prototypical transition from frictionally jammed solid to flowable suspension with maximal solid content

The mixing of a powder of 10- to 50-μm primary particles into a liquid to form a dispersion with the highest possible solid content is a common industrial operation. Building on recent advances in the rheology of such "granular dispersions," we study a paradigmatic example of such powder incorporation: the conching of chocolate, in which a homogeneous, flowing suspension is prepared from an inhomogeneous mixture of particulates, triglyceride oil, and dispersants. Studying the rheology of a simplified formulation, we find that the input of mechanical energy and staged addition of surfactants combine to effect a considerable shift in the jamming volume fraction of the system, thus increasing the maximum flowable solid content. We discuss the possible microscopic origins of this shift, and suggest that chocolate conching exemplifies a ubiquitous class of powder-liquid mixing.

Transition from Continuous to Discontinuous Shear Thickening: An Excluded-Volume Effect

In this Letter, we present a new mechanism under the action of which a shear thickening suspension transitions from a continuous to a discontinuous regime. This transition occurs by adding high concentrations of large spheres to a continuous shear thickening suspension. We show that the solid volume fraction of the interstitial shear thickening matrix is locally enhanced due to the presence of large particles and the excluded-volume shells surrounding the large particles, thus leading to a continuous to discontinuous shear thickening transition at the local scale.