Discontinuous shear thickening of frictional hard-sphere suspensions

Refractive-index and density-matched emulsions with programmable DNA interactions

Emulsion droplets on the colloidal length scale are a model system of frictionless compliant spheres. Direct imaging studies of the microscopic structure and dynamics of emulsions offer valuable insights into fundamental processes, such as gelation, jamming, and self-assembly. A microscope, however, can only resolve the individual droplets in a densely packed emulsion if the droplets are closely index-matched to their fluid medium. Mitigating perturbations due to gravity additionally requires the droplets to be density-matched to the medium. Creating droplets that are simultaneously index-matched and density-matched has been a long-standing challenge for the soft-matter community. The present study introduces a method for synthesizing monodisperse micrometer-sized siloxane droplets whose density and refractive index can be precisely and independently tuned by adjusting the volume fraction of three silane precursors. A systematic optimization protocol yields fluorescently labeled ternary droplets whose densities and refractive indexes match, to the fourth decimal place, those of aqueous solutions of glycerol or dimethylsiloxane. Because all of the materials in this system are biocompatible, we functionalize the droplets with DNA strands to endow them with programmed inter-droplet interactions. Confocal microscopy then reveals both the three-dimensional structure and the network of droplet-droplet contacts in a class of self-assembled droplet gels, free from gravitational effects. This experimental toolbox creates opportunities for studying the microscopic mechanisms that govern viscoelastic properties and self-assembly in soft materials.

Order-disorder transition during shear thickening in bidisperse dense suspensions

Shear thickening of multimodal suspensions has proven difficult to understand because the rheology depends largely on the microscopic details of stress-induced frictional contacts at different particle size distributions (PSDs). Our discrete particle simulations below a critical volume fraction ϕc over a broad range of shear rates and PSDs elucidate the basic mechanism of order-disorder transition. Around the theoretical optimal PSD (relative content of small particles ζ1= 0.26), particles order into a layered structure in the Newtonian regime. At the onset of shear thickening, this layered structure transforms to a disordered one, accompanied by an abrupt viscosity jump. Minor increase in large-large particle contacts after the order-disorder transition causes apparent increase in radial force along the compressional axis. Bidisperse suspensions with less regular but stable layered structure at ζ1= 0.50 show good fluidity in the shear thickening regime. This work shows that in inertial flows where particle collisions dominate, order-disorder transition could play an essential role in shear thickening for bidisperse suspensions.

Shear thickening fluid (STF) in engineering applications and the potential of cork in STF-based composites

Shear thickening fluids (STFs) are a unique type of fluids that can quickly transform into a solid-like state when subjected to forces (rate dependent). These fluids are created by dispersing micro and nanoparticles within a medium. When the force is removed, they return to their original liquid state. Shear thickening fluids can absorb a significant amount of impact energy, making them useful for reducing vibrations and serving as a damper. This study provides a comprehensive and brief overview of existing literature on shear thickening fluids, including their properties, classification, and the rheological mechanisms behind the shear thickening behaviour. It also examines the use of these fluids in various applications, such as improving resistance to stabs and spikes, protecting against low- and high-velocity impacts, and as a new medium for energy dissipation in industries such as battery safety, vibration control and adaptive structures. Lastly, this work reviews the promising combination of STFs with cork. Given the sustainability of cork and its energy absorption capacity, cork-STF composites are a promising solution for various impact-absorbing applications. Overall, the paper underscores the versatility and potential of STFs, and advocates for further research and exploration.

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.

Stress-activated friction in sheared suspensions probed with piezoelectric nanoparticles

A hallmark of concentrated suspensions is non-Newtonian behavior, whereby the viscosity increases dramatically once a characteristic shear rate or stress is exceeded. Such strong shear thickening is thought to originate from a network of frictional particle-particle contact forces, which forms under sufficiently large stress, evolves dynamically, and adapts to changing loads. While there is much evidence from simulations for the emergence of this network during shear thickening, experimental confirmation has been difficult. Here, we use suspensions of piezoelectric nanoparticles and exploit the strong local stress focusing within the network to activate charge generation. This charging can then be detected in the measured ac conductance and serve as a signature of frictional contact formation. The direct link between stress-activated frictional particle interactions and piezoelectric suspension response is further demonstrated by tracking the emergence of structural memory in the contact network under oscillatory shear and by showing how stress-activated friction can drive mechano-transduction of chemical reactions with nonlinear reaction kinetics. Taken together, this makes the ac conductance of piezoelectric suspensions a sensitive in-situ reporter of the micromechanics associated with frictional interactions.

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.

Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here, we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates.

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.

Toughening colloidal gels using rough building blocks

Colloidal gels, commonly used as mesoporous intermediates or functional materials, suffer from brittleness, often showing small yield strains on the order of 1% or less for gelled colloidal suspensions. The short-range adhesive forces in most such gels are central forces-combined with the smooth morphology of particles, the resistance to yielding and shear-induced restructuring is limited. In this study, we propose an innovative approach to improve colloidal gels by introducing surface roughness to the particles to change the yield strain, giving rise to non-central interactions. To elucidate the effects of particle roughness on gel properties, we prepared thermoreversible gels made from rough or smooth silica particles using a reliable click-like-chemistry-based surface grafting technique. Rheological and optical characterization revealed that rough particle gels exhibit enhanced toughness and self-healing properties. These remarkable properties can be utilized in various applications, such as xerogel fabrication and high-fidelity extrusion 3D-printing, as we demonstrate in this study.

Dense bidisperse suspensions under non-homogeneous shear

We study the rheological behaviour of bidisperse suspensions in three dimensions under a non-uniform shear flow, made by the superimposition of a linear shear and a sinusoidal disturbance. Our results show that (i) only a streamwise disturbance in the shear-plane alters the suspension dynamics by substantially reducing the relative viscosity, (ii) with the amplitude of the disturbance determining a threshold value for the effect to kick-in and its wavenumber controlling the amount of reduction and which of the two phases is affected. We show that, (iii) the rheological changes are caused by the effective separation of the two phases, with the large or small particles layering in separate regions. We provide a physical explanation of the phase separation process and of the conditions necessary to trigger it. We test the results in the whole flow curve, and we show that the mechanism remains substantially unaltered, with the only difference being the nature of the interactions between particles modified by the phase separation.

Effective viscosity and elasticity in dense suspensions under impact: Toward a modeling of walking on suspensions

The elastic response of dense suspensions under an impact is studied using coupled lattice Boltzmann method and discrete element method (LBM-DEM) and its reduced model. We succeed to extract the elastic force acting on the impactor in dense suspensions, which can exist even in the absence of percolating clusters of suspended particles. We then propose a reduced model to describe the motion of the impactor and demonstrate its relevancy through the comparison of the solution of the reduced model and that of LBM-DEM. Furthermore, we illustrate that the perturbation analysis of the reduced model captures the short-time behavior of the impactor motion quantitatively. We apply this reduced model to the impact of a foot-spring-body system on a dense suspension, which is the minimal model to realize walking on the suspension. Due to the spring force of the system and the stiffness of the suspension, the foot undergoes multiple bounces. We also study the parameter dependencies of the hopping motion and find that multiple bounces are suppressed as the spring stiffness increases.

Shear Thickening Fluid and Its Application in Impact Protection: A Review

Shear thickening fluid (STF) is a dense colloidal suspension of nanoparticles in a carrier fluid in which the viscosity increases dramatically with a rise in shear rate. Due to the excellent energy absorption and energy dissipation of STF, there is a desire to employ STFs in a variety of impact applications. In this study, a comprehensive review on STFs' applications is presented. First, several common shear thickening mechanisms are discussed in this paper. The applications of different STF impregnated fabric composites and the STF's contributions on improving the impact, ballistic and stab resistance performance have also been presented. Moreover, recent developments of STF's applications, including dampers and shock absorbers, are included in this review. In addition, some novel applications (acoustic structure, STF-TENG and electrospun nonwoven mats) based on STF are summarized, to suggest the challenges of future research and propose some more deterministic research directions, e.g., potential trends for applications of STF.

Model of Friction with Plastic Contact Nudging: Amontons-Coulomb Laws, Aging of Static Friction, and Nonmonotonic Stribeck Curves with Finite Quasistatic Limit

We introduce a model of friction between two contacting (stationary or cosliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact with each other only pairwise elastic repulsion and dissipative drag. These minimal ingredients are sufficient to capture a static state of jammed, interlocking contacting bumps, below a critical frictional force that is proportional to the normal load and independent of the apparent contact area, consistent with the Amontons-Coulomb laws of friction. However, they fail to capture two widespread observations: (i) that the dynamic friction coefficient (ratio of frictional to normal force in steady sliding) is a roughly constant or slightly weakening function of the sliding velocity U, at low U, with a nonzero quasistatic limit as U→0 and (ii) that the static friction coefficient (ratio of frictional to normal force needed to initiate sliding) increases ("ages") as a function of the time that surfaces are pressed together in stationary contact, before sliding commences. To remedy these shortcomings, we incorporate a single additional model ingredient: that contacting bumps plastically nudge one another slightly sideways, above a critical contact-contact load. With this additional insight, the model also captures observations (i) and (ii).

Leveraging the Polymer Glass Transition to Access Thermally Switchable Shear Jamming Suspensions

Suspensions of polymeric nano- and microparticles are fascinating stress-responsive material systems that, depending on their composition, can display a diverse range of flow properties under shear, such as drastic thinning, thickening, and even jamming (reversible solidification driven by shear). However, investigations to date have almost exclusively focused on nonresponsive particles, which do not allow in situ tuning of the flow properties. Polymeric materials possess rich phase transitions that can be directly tuned by their chemical structures, which has enabled researchers to engineer versatile adaptive materials that can respond to targeted external stimuli. Reported herein are suspensions of (readily prepared) micrometer-sized polymeric particles with accessible glass transition temperatures (T _g) designed to thermally control their non-Newtonian rheology. The underlying mechanical stiffness and interparticle friction between particles change dramatically near T _g. Capitalizing on these properties, it is shown that, in contrast to conventional systems, a dramatic and nonmonotonic change in shear thickening occurs as the suspensions transition through the particles' T _g. This straightforward strategy enables the in situ turning on (or off) of the system's ability to shear jam by varying the temperature relative to T _g and lays the groundwork for other types of stimuli-responsive jamming systems through polymer chemistry.

Rheology of Dense Suspensions under Shear Rotation

Dense non-Brownian suspensions exhibit a spectacular and abrupt drop in viscosity under change of shear direction, as revealed by shear inversions (reversals) or orthogonal superposition. Here, we introduce an experimental setup to systematically explore their response to shear rotations, where one suddenly rotates the principal axes of shear by an angle θ, and measure the shear stresses with a biaxial force sensor. Our measurements confirm the genericness of the transient decrease of the resistance to shear under unsteady conditions. Moreover, the orthogonal shear stress, which vanishes in steady state, takes non-negligible values with a rich θ dependence, changing qualitatively with solid volume fraction ϕ and resulting in a force that tends to reduce or enhance the direction of flow for small or large ϕ. These experimental findings are confirmed and rationalized by particle-based numerical simulations and a recently proposed constitutive model. We show that the rotation angle dependence of the orthogonal stress results from a ϕ-dependent interplay between hydrodynamic and contact stresses.

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.

Rheology of 3D printable ceramic suspensions: effects of non-adsorbing polymer on discontinuous shear thickening

Concentrated suspensions of particles at volume fractions (ϕ) ≥ 0.5 often exhibit complex rheological behavior, transitioning from shear thinning to shear thickening as the shear stress or shear rate is increased. These suspensions can be extruded to form 3D structures, with non-adsorbing polymers often added as rheology modifiers to improve printability. Understanding how non-adsorbing polymers affect the suspension rheology, particularly the onset of shear thickening, is critical to the design of particle inks that will extrude uniformly. In this work, we examine the rheology of concentrated aqueous suspensions of colloidal alumina particles and the effects of adding non-adsorbing polyvinylpyrrolidone (PVP). First, we show that suspensions with ϕ_alumina = 0.560-0.575 exhibited discontinuous shear thickening (DST), where the viscosity increased by up to two orders of magnitude above an onset stress (τ_min). Increasing ϕ_alumina from 0.550 to 0.575 increased the viscosity and yield stress in the shear thinning regime and decreased τ_min. Next, PVP was added at concentrations within the dilute and semi-dilute non-entangled regimes of polymer conformation (ϕ_PVP = 0.005-0.050) to suspensions with constant ϕ_alumina = 0.550. DST was observed in all cases and increasing ϕ_PVP increased the viscosity and yield stress. Interestingly, increasing ϕ_PVP also increased τ_min. We posit that the free PVP chains act as lubricants between alumina particles, increasing the stress needed to induce thickening. Finally, we demonstrate through direct comparisons of suspensions with and without PVP how non-adsorbing polymer addition can extend the extrusion processing window due to the increase in τ_min.

Solvents govern rheology and jamming of polymeric bead suspensions

Despite their apparent simplicity, suspensions of hard spheres in a Newtonian fluid show complex non-Newtonian behaviors and remain poorly understood. Recent works have pointed out the crucial role of interparticle contact forces in these behaviors. Here, we show that the same (polystyrene) particles, when immersed in different Newtonian solvents, show different behaviors at both the microscopic and macroscopic scales. Thanks to interparticle force measurements in each solvent together with rheological measurements, we show how the fine details of the pairwise particle interactions impact the macroscopic behavior. The rheological properties (shear thinning, shear thickening, jamming solid fraction value) of the suspensions, made up of same particles, are shown to depend on the nature of the solvent. Here, we highlight several mechanisms at the particle scale: the swelling of polymeric particles in an organic solvent, the role of colloidal repulsive forces and inertia for particles in a water solution, and the variation of the friction coefficient as a function of the load for particles immersed in silicone oils. Our study provides new quantitative data to test micromechanical models and simulations. It questions the interpretation of previous experimental works. Finally, it shows the need to systematically characterize the interparticle normal and tangential forces when studying a given suspension of hard spheres in a Newtonian fluid.

Shear jamming and fragility in fractal suspensions under confinement

Under applied stress, the viscosity of many dense particulate suspensions increases drastically, a response known as discontinuous shear-thickening (DST). In some cases, the applied stress can even transform the suspension into a solid-like shear jammed state. Although shear jamming (SJ) has been probed for dense suspensions with particles having well-defined shapes, such a phenomenon for fractal objects has not been explored. Here, using rheology and in situ optical imaging, we study the flow behaviour of ultra-dilute fractal suspensions of multi-walled carbon nanotubes (MWCNT) under confinement. We show a direct transition from flowing to SJ state without a precursory DST in fractal suspensions at an onset volume fraction, ϕ ∼ 0.5%, significantly lower than that of conventional dense suspensions (ϕ ∼ 55%). The ultra-low concentration enables us to demonstrate the fragility and associated contact dynamics of the SJ state, which remain experimentally unexplored in suspensions. Furthermore, using a generalized Wyart-Cates model, we propose a generic phase diagram for fractal suspensions that captures the possibility of SJ without prior DST over a wide range of shear stress and volume fractions.

Orientational-induced strain hardening of axisymmetric grains

The rheological response of oriented axisymmetric grains has additional degrees of complexity associated with their microstructure orientation. These additional kinematic degrees of freedom that give rise to complex transient macroscale rheological responses are not well understood. In this Letter, we study the rheology of axisymmetric grains subjected to transient flow. We identify strong coupling between the microstructure rearrangement and strain hardening which, under certain conditions, can yield jamming. We identify the critical conditions corresponding to jamming and the dependency on the shape of the grains. It is shown that this is a particular form of jamming that is directional in nature, since unjamming occurs if the shear direction is reversed.

Structure and Dynamics of Force Clusters and Networks in Shear Thickening Suspensions

Dense suspensions can exhibit shear thickening in response to large deformation. A consensus has emerged over the past few years on the formation of force networks, that span the entire system size, that lead to increased resistance to motion. Nonetheless, the characteristics of these networks are to a large extent poorly understood. Here, force networks formed in continuous and discontinuous shear thickening dense suspensions (CST and DST, respectively) are studied. We first show the evolution of the network formation and its topological heterogeneities as the applied stress increases. Subsequently, we identify force communities and coarse grain the suspension into a cluster network, and show that cluster-level dynamics are responsible for stark differences between the CST and DST behavior. Our results suggest that the force clusters formed in the DST regime are considerably more constrained in their motion, while CST clusters are loosely connected to their surrounding clusters.

Designing Stress-Adaptive Dense Suspensions Using Dynamic Covalent Chemistry

The non-Newtonian behaviors of dense suspensions are central to their use in technological and industrial applications and arise from a network of particle–particle contacts that dynamically adapt to imposed shear. Reported herein are studies aimed at exploring how dynamic covalent chemistry between particles and the polymeric solvent can be used to tailor such stress-adaptive contact networks, leading to their unusual rheological behaviors. Specifically, a room temperature dynamic thia-Michael bond is employed to rationally tune the equilibrium constant (K_eq) of the polymeric solvent to the particle interface. It is demonstrated that low K_eq leads to shear thinning, while high K_eq produces antithixotropy, a rare phenomenon where the viscosity increases with shearing time. It is proposed that an increase in K_eq increases the polymer graft density at the particle surface and that antithixotropy primarily arises from partial debonding of the polymeric graft/solvent from the particle surface and the formation of polymer bridges between particles. Thus, the implementation of dynamic covalent chemistry provides a new molecular handle with which to tailor the macroscopic rheology of suspensions by introducing programmable time dependence. These studies open the door to energy-absorbing materials that not only sense mechanical inputs and adjust their dissipation as a function of time or shear rate but also can switch between these two modalities on demand.

In Situ Observation of Shear-Induced Jamming Front Propagation during Low-Velocity Impact in Polypropylene Glycol/Fumed Silica Shear Thickening Fluids

Shear jamming, a relatively new type of phase transition from discontinuous shear thickening into a solid-like state driven by shear in dense suspensions, has been shown to originate from frictional interactions between particles. However, not all dense suspensions shear jam. Dense fumed silica colloidal systems have wide applications in the industry of smart materials from body armor to dynamic dampers due to extremely low bulk density and high colloid stability. In this paper, we provide new evidence of shear jamming in polypropylene glycol/fumed silica suspensions using optical in situ speed recording during low-velocity impact and explain how it contributes to impact absorption. Flow rheology confirmed the presence of discontinuous shear thickening at all studied concentrations. Calculations of the flow during impact reveal that front propagation speed is 3–5 times higher than the speed of the impactor rod, which rules out jamming by densification, showing that the cause of the drastic impact absorption is the shear jamming. The main impact absorption begins when the jamming front reaches the boundary, creating a solid-like plug under the rod that confronts its movement. These results provide important insights into the impact absorption mechanism in fumed silica suspensions with a focus on shear jamming.

Origin of Two Distinct Stress Relaxation Regimes in Shear Jammed Dense Suspensions

Many dense particulate suspensions show a stress induced transformation from a liquidlike state to a solidlike shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the bulk remains unknown. Here, we study transient stress relaxation behaviour of SJ states formed by a well-characterized dense suspension under a step strain perturbation. We observe a strongly nonexponential relaxation that develops a sharp discontinuous stress drop at short time for high enough peak-stress values. High resolution boundary imaging and normal stress measurements confirm that such stress discontinuity originates from the localized plastic events, whereas system spanning dilation controls the slower relaxation process. We also find an intriguing correlation between the nature of transient relaxation and the steady-state shear jamming phase diagram obtained from the Wyart-Cates model.

Microstructure of continuous shear thickening colloidal suspensions determined by rheo-VSANS and rheo-USANS

Research on shear thickening colloidal suspensions demonstrates that measurements of the microstructure can elucidate the source of the rheological material properties in the shear thickened state as well as critically test simulations and theory based on a variety of mechanisms such as enhanced lubrication hydrodynamics, elastohydrodynamics, and contact friction. Prior work on continuous shear thickening dispersions with a well-defined shear thickened state identified the formation of hydroclusters as characteristic of this state, determined the anisotropy in the nearest neighbor distribution, and used this information to test prevailing theories and simulations. However, important questions remain about the mesoscale (i.e., particle cluster scale) microstructure of the shear thickened state. Here we employ neutron scattering methods applied to shearing colloidal dispersions of spherical particles with two extremes of friction and lubrication surface properties to resolve the longer-length scale microstructure in the shear thickened state. Hydroclusters are shown to be highly localized, in agreement with prior neutron scattering and direct optical measurements, but in disagreement with the most recent simulations that predict a longer-range structure formation. These results combined with prior measurements provide experimental evidence about the length scale of microstructure formation in continuous shear thickening suspensions necessary to improve our understanding of the phenomenon as well as guide theoretical investigations that quantitatively link nanoscale forces to macroscopic properties in the shear thickened state.

Modeling colloidal interactions that predict equilibrium and non-equilibrium states

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as formation of non-equilibrium 'arrested states' such as gels and glasses. Faithful representation of such interactions are essential for using simulation to interrogate the microscopic details of non-equilibrium behavior, and for extrapolating observations to new regions of phase space that are difficult to explore in experiment. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions, and for predicting non-equilibrium phenomena in systems with either short-ranged or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.

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.

Fumed Silica-Based Suspensions for Shear Thickening Applications: A Full-Scale Rheological Study

Understanding shear thickening fluids (STFs) is critically important in a broad spectrum of fields ranging from biology to military. STFs are referred to the suspension of solid particles in an inert carrier liquid. Customizing the thickening behavior is vital for obtaining desired properties. Hence, comprehending shear thickening mechanisms is necessary to fully understand the factors affecting the shear thickening response of the STFs. Herein, we systematically investigate the effects of a wide range of parameters, from inherent properties of the constituents, including size and surface chemistry of the suspended particles, to practical conditions such as temperature and shear history, on the shear thickening behavior of fumed silica nanoparticles (NPs)-based suspensions in a polyethylene glycol (PEG) medium. Accordingly, increasing the hydrophobicity of the silica NPs or decreasing the NP size transforms the suspensions from sol to gel. The sol systems exhibit a strong shear thickening response, while shear thinning behavior is prominent in the strong gel systems. Hybridization of different silica NPs is also leveraged to tune the shear thickening behavior. In addition, we showcase the decisive role of operating temperature or shear history on the shear thickening behavior of suspensions. For instance, in terms of the shear history, above a critical value of preshear, the shear thickening behavior occurs at lower shear rates for STFs containing hydrophilic NPs. It is believed that the provided insights in this study can pave the way for developing advanced STFs with prescribed features.

X-ray computerized tomography observation of Lycopodium paste incorporating memory of shaking

In a uniform layer consisting of a mixture of granular material and liquid, it is known that desiccation cracks exhibit various anisotropic patterns that depend on the nature of the shaking that the layer experienced before drying. The existence of this effect implies that information regarding the direction of shaking is retained as a kind of memory in the arrangements of granular particles. In this work we make measurements in paste composed of Lycopodium powder using microfocus x-ray computerized tomography (μCT) in order to investigate the three-dimensional arrangements of particles. We find shaking-induced anisotropic arrangements of neighboring particles and density fluctuations forming interstices mainly in the lower part of the layer. We compare the observed properties of these arrangements with numerical results obtained in the study of a model of non-Brownian particles under shear deformation. In the experimental system, we also observe crack tips in the μCT images and confirm that these cracks grow along interstices in the direction perpendicular to the initial shaking.

Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial versus isotropic compression

We numerically study a three-dimensional system of athermal, overdamped, frictionless spheres, using a simplified model for a non-Brownian suspension. We compute the bulk viscosity under both uniaxial and isotropic compression as a means to address the question of whether stress-anisotropic and stress-isotropic jamming are in the same critical universality class. Carrying out a critical scaling analysis of the system pressure p, shear stress σ, and macroscopic friction μ=σ/p, as functions of particle packing fraction ϕ and compression rate ε[over ̇], we find good agreement for all critical parameters comparing the isotropic and anisotropic cases. In particular, we determine that the bulk viscosity diverges as p/ε[over ̇]∼(ϕ_{J}-ϕ)^{-β}, with β=3.36±0.09, as jamming is approached from below. We further demonstrate that the average contact number per particle Z can also be written in a scaling form as a function of ϕ and ε[over ̇]. Once again, we find good agreement between the uniaxial and isotropic cases. We compare our results to prior simulations and theoretical predictions.

Microstructure of the fluid particles around the rigid body at the shear-thickening state toward understanding of the fluid mechanics

We studied the shear-thickening behavior of systems containing rigid spherical bodies immersed in smaller particles using non-equilibrium molecular dynamics simulations. We generated shear-thickening states through particle mass modulation of the systems. From the microstructures, i.e., two-dimensional pair distribution functions, we found anisotropic structures resulting from shear thickening, that are explained by the difference between the velocities of rigid bodies and fluid particles. The increasing viscosity in our system originated from collisions between fluid particles and rigid bodies. The lubrication forces defined in macroscale physics are then briefly discussed.

Directional shear jamming of frictionless ellipses

In this work we study shear reversals of dense non-Brownian suspensions composed of cohesionless elliptical particles. By numerical simulations, we show that a new fragility appears for frictionless ellipses in the flowing states, where particles can flow indefinitely in one direction at applied shear stresses but shear jam in the other direction upon shear stress reversal. This new fragility, absent in the isotropic particle case, is linked to the directional order of the elongated particles at steady shear and its reorientation at shear stress reversal, which forces the suspensions to pass through a more disordered state with an increased number of contacts in which it might get arrested.

Jamming Distance Dictates Colloidal Shear Thickening

We report experimental and computational observations of dynamic contact networks for colloidal suspensions undergoing shear thickening. The dense suspensions are comprised of sterically stabilized poly(methyl methacrylate) colloids that are spherically symmetric and have varied surface roughness. Confocal rheometry and dissipative particle dynamics simulations show that the shear thickening strength β scales exponentially with the scaled deficit contact number and the scaled jamming distance. Rough colloids, which experience additional rotational constraints, require an average of 1.5-2 fewer particle contacts as compared to smooth colloids, in order to generate the same β. This is because the surface roughness enhances geometric friction in such a way that the rough colloids do not experience a large change in the free volume near the jamming point. The available free volume for colloids of different roughness is related to the deficiency from the maximum number of nearest neighbors at jamming under shear. Our results further suggest that the force per contact is different for particles with different morphologies.

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.

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear

We show here that rotations of round particles in amorphous disk packing reveal various nontrivial microscopic features when the packing is close to rigidification. We analyze experimental measurements on disk packing subjected to simple shear deformation with various inter-particle friction coefficients and across a range of volume fractions where the system is known to stiffen. The analysis of measurements indicates that shear induces diffusive microrotation, that can be both enhanced and suppressed depending upon the volume fraction as well as the inter-particle friction. Rotations also display persistent anticorrelated motion. Spatial correlations in microrotation are observed to be directly correlated with system pressure. These observations point towards the broader mechanical relevance of collective dynamics in the rotational degree of freedom of particles.

Shear stress dependence of force networks in 3D dense suspensions

The geometric organization and force networks of 3D dense suspensions that exhibit both shear thinning and thickening have been examined as a function of varying strength of interparticle attractive interactions using lubrication flow discrete element simulations. Significant rearrangement of the geometric topology does not occur at either the local or global scale as these systems transition across the shear thinning and shear thickening regimes. In contrast, massive rearrangements in the balance of attractive, lubrication, and contact forces are observed with interesting behavior of network growth and competition. In agreement with prior work, in shear thinning regions the attractive force is dominant, however as the shear thickening region is approached there is growth of lubrication forces. Lubrication forces oppose the attraction forces, but as viscosity continues to increase under increasing shear stress, the lubrication forces are dominated by contact forces that also resist attraction. Contact forces are the dominant interactions during shear thickening and are an order of magnitude higher than their values in the shear-thinning regime. At high attractive interaction strength, contact networks can form even under shear thinning conditions, however high shear stress is still required before contact networks become the driving mechanism of shear thickening. Analysis of the contact force network during shear thickening generally indicates a uniformly spreading network that rapidly forms across empty domains; however the growth patterns exhibit structure that is significantly dependent upon the strength of interparticle interactions, indicating subtle variations in the mechanism of shear thickening.

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.

The role of friction in statistics and scaling laws of avalanches

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.