Discontinuous Shear Thickening Research Articles

Discontinuous Shear Thickening of Suspensions of Magnetic Particles in Relation to the Polymer Coating on Their Surfaces

The phenomenon of discontinuous shear thickening (DST) is observed in suspensions of solid particles with a very high-volume fraction. It is characterized by an abrupt decrease in the shear rate for critical stress during a ramp of stress. This behavior can be reproduced in numerical simulations by introducing a local friction between two particles above a given local force. We present experimental results showing this DST behavior obtained with suspensions of magnetic (iron) and nonmagnetic (calcium carbonate) particles and different amounts of a superplasticizer molecule used in the cement industry. For both types of particles, the same behavior was observed with first an increase in critical stress with the amount of plasticizer followed by a decrease at higher concentrations but with a larger viscosity before critical stress was reached. At a low concentration of plasticizer, the low critical stress is interpreted by the local sliding of plasticizer molecules on the surface of particles. At higher concentrations, when total coverage is achieved, the critical stress is higher since it has to remove the molecules out of the surface. At still higher concentrations, the increase in viscosity is explained by the formation of multilayers of molecules on the surface of the particles. This interpretation is supported by the measurement of the adsorption isotherm of the plasticizer on the surface of the particles.

Rheology of a crowd: from faster-is-slower to shear thickening

The evacuation speed of pedestrians through bottlenecks usually leads to the faster-is-slower (FIS) phenomenon, which relies on frictional clogging and clusters’ size. However, less attention is given in literature to the rheology of pedestrian crowds and the forces ruling their dynamics. Here, we establish a link between the faster-is-slower phenomenon (FIS) in pedestrian crowds and the shear-thickening rheological behavior of (non)Brownian suspensions. We analyze pedestrian room egress through particle-based simulations using the Social Force Model, revealing an S-shaped shear rate dependency characteristic of discontinuous shear thickening (DST). At the same time, the crowd flow viscosity near the exit exhibits a steep increase coinciding with FIS occurrence, establishing a correlation between FIS and shear thickening. Our results prove that crowd evacuations are governed by two distinct critical jamming densities, one frictional and another frictionless, and that contact forces alone cannot lead to FIS, but social force interactions are necessary to avoid contacts at low desired speeds. Our results point at the suitability of (non)Brownian suspensions as models that provide an original rheological perspective to pedestrian dynamics.

Exact Results for Non-Newtonian Transport Properties in Sheared Granular Suspensions: Inelastic Maxwell Models and BGK-Type Kinetic Model.

The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a coarse-grained description, our suspension model accounts for the real collisions between grains and particles of the surrounding molecular gas. The latter is modeled as a bath (or thermostat) of elastic hard spheres at a given temperature. Two independent but complementary approaches are followed to reach exact expressions for the rheological properties. First, the Boltzmann equation for the so-called inelastic Maxwell models (IMM) is considered. The fact that the collision rate of IMM is independent of the relative velocity of the colliding spheres allows us to exactly compute the collisional moments of the Boltzmann operator without the knowledge of the distribution function. Thanks to this property, the transport properties of the sheared granular suspension can be exactly determined. As a second approach, a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to granular suspensions is solved to compute the velocity moments and the velocity distribution function of the system. The theoretical results (which are given in terms of the coefficient of restitution, the reduced shear rate, the reduced background temperature, and the diameter and mass ratios) show, in general, a good agreement with the approximate analytical results derived for inelastic hard spheres (IHS) by means of Grad's moment method and with computer simulations performed in the Brownian limiting case (m/mg→∞, where mg and m are the masses of the particles of the molecular and granular gases, respectively). In addition, as expected, the IMM and BGK results show that the temperature and non-Newtonian viscosity exhibit an S shape in a plane of stress-strain rate (discontinuous shear thickening, DST). The DST effect becomes more pronounced as the mass ratio m/mg increases.

Microstructural smoothed particle hydrodynamics model and simulations of discontinuous shear-thickening fluids

Despite the recent interest in the discontinuous shear-thickening (DST) behavior, few computational works tackle the rich hydrodynamics of these fluids. In this work, we present the first implementation of a microstructural DST model in smoothed particle hydrodynamic (SPH) simulation. The scalar model was implemented in an SPH scheme and tested in two flow geometries. Three distinct ratios of local to non-local microstructural effects were probed: zero, moderate, and strong non-locality. Strong and moderate cases yielded excellent agreement with flow curves constructed via the Wyart–Cates (WC) model, with the moderate case exhibiting banding patterns. We demonstrate that a local model is prone to a stress-splitting instability, resulting in discontinuous stress fields and poor agreement with the WC model. The mechanism of stress splitting has been explored and contextualized by the interaction of local microstructure evolution and the stress-control scheme. Analytic solutions for a body-force-driven DST channel flow have been derived and used to validate the SPH simulations with excellent agreement in velocity profiles. Simulations carried out at increasing driving forces exhibited a decrease in flow. We showed that even the simple scalar model can capture some of the key properties of DST materials, laying the foundation for further SPH study of instabilities and pattern formation.

Discontinuous Shear Thickening in Biological Tissue Rheology.

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

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.

Tribological variable-friction coefficient models for the simulation of dense suspensions of rough polydisperse particles

The rheology of concentrated suspensions of particles is complex and typically exhibits a shear-thickening behavior in the case of repulsive interactions. Despite the recent interest arisen, the causes of the shear-thickening remain unclear. Frictional contacts have been able to explain the discontinuous shear thickening in simulations. However, the interparticle friction coefficient is considered to be constant in most simulations and theoretical works reported to date despite the fact that tribological experiments demonstrate that the friction coefficient can not only be constant (boundary regime) but also decrease (mixed regime) or even increase (full-film lubrication regime), depending on the normal force and the relative velocity between the particles and the interstitial liquid between them. Interestingly, the transition between the boundary regime and the full-lubrication regime is governed by the particle average roughness. Particle-level simulations of suspensions of hard spheres were carried out using short-range lubrication and roughness-dependent frictional forces describing the full Stribeck curve. Suspensions with different particle’s roughness were simulated to show that the particle roughness is a key factor in the shear-thickening behavior; for sufficiently rough particles, the suspension exhibits a remarkable shear-thickening, while for sufficiently smooth particles, the discontinuous shear-thickening disappears.

Discontinuous shear thickening (DST) transition with spherical iron particles coated by adsorbed brush polymer

We explore the rheology of very concentrated (0.55 < Φ < 0.67) suspensions of carbonyl iron particles coated by a small polymer. A strong discontinuous shear thickening (DST) is observed in a large range of volume fraction presenting some specific behaviors in comparison with other systems. In particular, the DST transition can appear suddenly without being preceded by shear thickening. The presence of a frictional network of particles is confirmed by a simultaneous measurement of the electric resistance of the suspension and of the rheological curve. Using the Wyart–Cates (W–C) model, we show that with increasing the volume fraction, the fraction of frictional contacts increases more quickly with the stress, contrary to the prediction of numerical simulations. The same behavior is observed in the presence of a magnetic field with a strong increase in the viscosity before the DST transition. We interpret this behavior by the interpenetration of the polymer layer under the effect of the shear stress—and of the magnetic stress—followed by the expulsion of the polymer out of the surfaces between two particles in contact. We point out that above the DST transition, we do not observe a jamming in the range of volume fraction, whereas it is predicted by the W–C model. The frictional contacts are created by a shear stress and not by a static stress, so in the absence of shear flow, the polymer can adsorb again on the surface and lubricate the frictional contacts. We thus predict an asymptotic non-zero shear rate reproducing the experimental behavior.

The shattering of abrupt shear thickening suspension jet in an air-blast atomizer

The primary breakup process of shear thickening is observed via high-speed photography. It is indicated that discontinuous shear thickening (DST) suspension jets exhibit the unique shattering-type breakup mode when air velocity increases up to a high region. In the shattering-type breakup mode, solid-like cracks grow inside the suspension jets, which results in the shattering of the suspension jets. After the shattering, the suspension jets break into tiny fragments with granular and matte surfaces. Combined with the rheological measurement and force analysis, the shattering-type breakup of DST suspension is due to aerodynamic force overwhelming the maximum shear stress. The critical Weber number Wec and a dimensionless number N studied in our previous research (Wang et al., 2022) are used to divide different breakup modes.

Jet instability of suspensions of different shaped particles exhibiting discontinuous shear thickening

This work is devoted to the detailed study of jet instability occurring in concentrated aqueous mixtures of calcium carbonate (CC) isotropic-shaped particles and rigid polyamide (PA) fibers. These mixtures exhibit very sharp discontinuous shear thickening (DST). The jets were subjected to a free fall under gravitational stretching at a constant flow rate. In the absence of PA fibers, we observed relatively strong lateral oscillations occurring for jet lengths L≳6cm and accompanied by small periodic undulations of the jet diameter. Two-dimensional Direct Fourier Transform analysis reveals approximately linear dispersion relations for propagation of lateral oscillations and diameter undulations with similar wave speeds ∼1m/s. This instability is ascribed to complex rheological behavior in an extensional flow above the DST transition. Theoretical modeling reveals abrupt jumps of the tensile stress along the jet likely leading to fluctuation of longitudinal and transverse velocity fields within the jet perceived through jet diameter and centerline undulations. The addition of PA fibers to CC suspension damps lateral oscillations but favors ruptures along the jet. This is tentatively explained by the interplay between growing lower and decreasing upper DST threshold stresses with increasing fiber volume fraction φf along with the thinning of the jet diameter down to the size of fiber flocs. Quantitatively, the stabilizing effect of PA fibers is manifested through an abrupt decrease in the lateral drift amplitude at φf≳0.75vol%.

Tuning the shear thickening of suspensions through surface roughness and physico-chemical interactions

Shear thickening denotes the reversible increase in viscosity of a suspension of rigid particles under external shear. This ubiquitous phenomenon has been documented in a broad variety of multiphase particulate systems, while its microscopic origin has been successively attributed to hydrodynamic interactions and frictional contact between particles. The relative contribution of these two phenomena to the magnitude of shear thickening is still highly debated, and we report here a discriminating experimental study using a model shear-thickening suspension that allows us to independently tune both the surface chemistry and the surface roughness of the particles. We show here that both properties matter when it comes to continuous shear thickening (CST) and that the presence of hydrogen bonds between the particles is essential to achieve discontinuous shear thickening (DST) by enhancing solid friction between closely contacting particles. Moreover, a simple argument allows us to predict the onset of CST, which for these very rough particles occurs at a critical volume fraction much lower than that previously reported in the literature. Finally, we demonstrate how mixtures of particles with opposing surface chemistry make it possible to finely tune the shear-thickening response of the suspension at a fixed volume fraction, paving the way for a fine control of the shear-thickening transition in engineering applications.

Stick-Slip Dynamics in a Granular Material With Varying Grain Angularity

Experiments, simulations, and theoretical treatments of granular materials typically feature circular or elliptical grains. However, grains found in natural systems often have flat faces that introduce local rotational constraints; these rotational constraints have been shown to affect, for example, the jamming transition, discontinuous shear thickening, and ordered states in colloids and thermalized grains. In this work, we experimentally investigate the effects of grain angularity on stick-slip dynamics. A weighted slider is pulled by a spring over a gravity-packed granular bed composed of polygonal grains with varying angularity. We find that packings of triangular or square grains have higher shear strengths than packings of pentagons, hexagons, heptagons, or disks. Additionally, as the number of sides increases, sticking periods, during which the slider remains motionless while the spring force on it increases, become shorter on average, with the material yielding at smaller applied stresses. Lastly, we find that dilation of the medium during sticking periods tends to be larger for grains with higher angularity, in part because of the presence of stilt-like columnar structures that prop the slider up. We report on measurements of the pulling force on the slider, particle dynamics during slip events, and properties of force-bearing contact networks identified via photoelasticity. Our findings indicate that high angularity of grains (pentagons, squares, triangles) leads to differences in grain-scale flow and macroscopic stick-slip dynamics of bulk granular materials. Our experiments also indicate a continuous change in dynamics with decreasing angularity as the circular grain limit is approached.

Lasting effects of discontinuous shear thickening in cornstarch suspensions upon flow cessation

Discontinuous shear-thickening (DST) fluids exhibit complex stress relaxation upon flow cessation. We investigate the relaxation behavior of dense cornstarch suspensions via rotational rheometry and find that the relaxation timescales and the residual stress increase with the apparent viscosity measured in the DST state prior to the flow cessation. Within the framework that attributes DST to the lubricated-to-frictional transition of interparticle contact, our results indicate that the lasting effects of the DST state arise from partial retention of frictional force chains after flow cessation.

Rheology and microstructure of discontinuous shear thickening suspensions

We report experimental studies on rheology and microstructure in discontinuous shear thickening of fumed silica suspensions. Formation of particle clusters was observed after the critical shear rate, and their size increases during shear thickening. At higher shear rates, these clusters were found to break down due to strong shear forces, and a continuous decrease in viscosity was observed. The suspension viscosity and the first normal stress difference variation with the shear rate showed similar dependence. The sign of first normal stress difference was negative during shear thickening, which is consistent with the hydrodynamic model of cluster formation. A linear variation of the first normal stress difference with shear rate during shear thickening further indicates its predominant hydrodynamic origin and supports the recent Stokesian dynamics simulation studies on discontinuous shear thickening based on the hydrodynamic model of nonsmooth colloids by Wang et al. [J. Rheol. 64, 379–394 (2020)]. On the other hand, a nonlinear decrease in the first normal stress difference with shear rate in the second shear-thinning region is primarily due to breaking of large clusters into smaller ones and with a possibility of frictional contacts within these hydroclusters. The oscillatory shear measurements were also performed and the samples displayed strain thickening similar to shear thickening. The similarity between the steady and dynamic shear rheology at high strain amplitudes was observed using the modified Cox–Merz rule.

Flow reversal triggers discontinuous shear thickening response across an erodible granular bed in a Couette-Poiseuille-like flow

Granular rheology is experimentally investigated in a vertical Couette-Poiseuille-like channel flow of photoelastic disks, where an erodible bed is sheared intermittently by an upward-moving shear band and a gravity-induced reverse flow. The shear band conforms to the existing nonlocal Eyring-like rheology but the bed exhibits discontinuous shear thickening from the Bagnold inertial regime near the band-bed interface to the Herschel-Bulkley plastic regime near the static wall. This newly discovered bed rheology is rate dependent and is associated with the fragility of the contact networks indicated by the statistics of local stress states inferred from the material photoelastic responses.

K -core analysis of shear-thickening suspensions

Strong continuous and discontinuous shear thickening (CST and DST) have been shown to be rationalized by the formation of a network of frictional contacts. This continuously evolving network is investigated here using k-core analysis of configurations obtained based on a discrete-particle simulation method. The approach identifies clusters in which each particle has at least k contacts with other particles in the same cluster. We find that the k-core structures display universal behavior as a function of contact number except at the shear thickening transition, where there is a sharp increase in the stress carried by the 3-cores in DST, with this increase largely absent for CST.

Primary breakup of shear‐thickening suspension jet by an annular air jet

AbstractAn experimental investigation is conducted to study the influence of shear‐thickening behavior on the primary breakup process of suspension jets. The primary breakup morphologies of cornstarch–water suspension are observed via a high‐speed camera. The unique hardened breakup mode only occurs when the suspension exhibits discontinuous shear thickening (DST). During hardened breakup mode, the oscillating portion of the suspension jet becomes perpendicular to the air direction and keeps cylindrical instead of deforming into a thin sheet or membrane structure. The suspension jets break off into large pieces rather than tiny droplets. The dimensionless number N is established to describe the relative magnitude of the increment of the viscous force and aerodynamic force during the primary breakup process. The primary breakup regime map of Newtonian fluids and shear‐thickening suspensions is also promoted based on the dimensionless number N and the Weber number We.

Effect of graphene oxide doping on the room temperature shear and dynamic rheological behaviour of PVDF

Poly (vinylidene fluoride) (GO/PVDF) nanocomposites (NCs) are prepared via dispersing 1 mg and 5 mg of graphene oxide (GO) sheets in PVDF/Tetrahydrofuran (THF) and 2-dimethylformamide (DMF) solution. X-Ray Diffraction (XRD) and FTIR analysis confirm that NCs exhibits β-phase and their crystallinity increased with GO doping. This paper presents a solution method for GO/PVDF NCs preparation and explored their shear and dynamic rheology at room temperature than that of melt state/rheology. GO/PVDF NCs show shear-thinning to discontinuous shear thickening (DST) behavior, increase of the flow viscosity (20045.16 mPa.s and 50311.81 mPa.s for 1 mg and 5 mg) and altered critical shear rate as a function of increasing GO doping concentration. The observed rheological behaviors could be a result of hydrodynamic forces. Dynamic rheology and relaxation frequency and time measurements confirm that the doping GO leads to the viscoelastic behavior in NCs than that of glassy behavior of neat PVDF. Viscoelastic and gelation properties of GO/PVDF NCs make them potential candidates for lubrication applications.

Capillary flow of a suspension in the presence of discontinuous shear thickening

The rheology of suspensions showing discontinuous shear thickening (DST) is well documented in conventional rheometer with rotating tools, but their study in capillary flow is still lacking. We present results obtained in a homemade capillary rheometer working in an imposed pressure regime. We show that the shape of the experimental curve giving the volume flow rate versus the wall stress in a capillary can be qualitatively reproduced from the curve obtained in rotational geometry at imposed stress but instead of a sharp decrease of the volume flow rate observed at a critical stress, this transposition predicts a progressive decrease in flow rate. The Wyart-Cates theory is used to reproduce the stress-shear rate curve obtained in rotational geometry and then applied to predict the volume flow rate at imposed pressure. The theoretical curve predicts a total stop of the flow at high stress, whereas experimentally it remains constant. We propose a modification of the theory which, by taking into account the relaxation of the frictional contacts in the absence of shear rate, well predicts the high stress behavior. We also hypothesized that the DST transition propagates immediately inside the capillary, once the wall shear stress has reached its critical value: $\tau_R=\tau_c$, even if the internal shear stress $\tau(r<R)$ is below the critical one. In this way the whole experimental curve can be well reproduced by the modified W-C model.

Concerted effect of boron and porosity on shear thickening behavior of hybrid mesoporous silica dispersions

In the present work, the influence of porosity and boron on shear thickening behavior of hybrid mesoporous silica has been studied. Three different levels of boron modification were performed by varying the molar composition of boric acid viz., 1.5 mmol, 2.5 mmol, and 3.5 mmol in a co-condensation approach. The incorporation of boron in mesoporous silica network was confirmed by various techniques such as Fourier transform infra-red (FTIR), and 11B solid- state nuclear magnetic resonance (NMR) spectroscopy. The morphology and particle size were confirmed by using scanning and transmission electron microscopy. To evaluate the effect of boron and porosity on the shear thickening behavior, dispersions were prepared from mesoporous boron- modified silica (MSiB), control mesoporous silica (MSi), non-porous boron-modified silica (SiB), and control non-porous silica (Si) in polyethylene glycol. The shear thickening behavior was studied using steady shear rheology. The dispersion prepared from different loadings of synthesized MSiB containing 1.5 mmol boron showed more than 16 times increase in viscosity (657.7 Pa.s) compared to that of MSi (39.2 Pa.s) at a fairly low volume fraction (φ = 0.15) of silica. It is expected that the highly ordered mesoporous architecture of hybrid silica has improved the interaction between the particle and the dispersing medium through hydrogen bonding. The porous morphology of the hybrid mesoporous silica as well as the incorporation of boron in the silica network favors the formation of a frictional contact network, and a transition from continuous shear thickening (CST) to discontinuous shear thickening (DST) behavior was observed. Therefore, silica prepared via incorporation of boron as well as porosity can be material of interest in variety of applications, for example, soft body armors, sporting goods, and shear thickening electrolytes for high impact resistant batteries.