Microscopic mechanism for shear thickening of non-Brownian suspensions

Characterizing sliding and rolling contacts between single particles

Contacts between particles in dense, sheared suspensions are believed to underpin much of their rheology. Roughness and adhesion are known to constrain the relative motion of particles, and thus globally affect the shear response, but an experimental description of how they microscopically influence the transmission of forces and relative displacements within contacts is lacking. Here, we show that an innovative colloidal-probe atomic force microscopy technique allows the simultaneous measurement of normal and tangential forces exchanged between tailored surfaces and microparticles while tracking their relative sliding and rolling, unlocking the direct measurement of coefficients of rolling friction, as well as of sliding friction. We demonstrate that, in the presence of sufficient traction, particles spontaneously roll, reducing dissipation and promoting longer-lasting contacts. Conversely, when rolling is prevented, friction is greatly enhanced for rough and adhesive surfaces, while smooth particles coated by polymer brushes maintain well-lubricated contacts. We find that surface roughness induces rolling due to load-dependent asperity interlocking, leading to large off-axis particle rotations. In contrast, smooth, adhesive surfaces promote rolling along the principal axis of motion. Our results offer direct values of friction coefficients for numerical studies and an interpretation of the onset of discontinuous shear thickening based on them, opening up ways to tailor rheology via contact engineering.

Attraction-Enhanced Emergence of Friction in Colloidal Matter

How frictional effects emerge at the microscopic level in particulate materials remains a challenging question, particularly in systems subject to thermal fluctuations due to the transient nature of interparticle contacts. Here, we directly relate particle-level frictional arrest to local coordination in an attractive colloidal model system. We reveal that the orientational dynamics of particles slows down exponentially with increasing coordination number due to the emergence of frictional interactions, the strength of which can be tuned simply by varying the attraction strength. Using a simple computer simulation model, we uncover how the interparticle interactions govern the formation of frictional contacts between particles. Our results establish quantitative relations between friction, coordination, and interparticle interactions. This is a key step toward using interparticle friction to tune the mechanical properties of particulate 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.

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.

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.

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.

Preparation of STF-loaded micron scale polyurethane polyurea double layer microcapsules and study on the mechanical properties of composites

In this study, we report on a novel and effective approach for the encapsulation of the shear thickening fluid in polyurethane polyurea double layer microcapsules. Under the action of dibutyltin disilicate as a catalyst, CD-MDI reacted with polyethylene glycol to form polyurethane inner shell and reacted with diethylenetriamine to form a polyurea outer shell. The results show that the shear thickening liquid was emulsified using liquid paraffin as a solvent and Span80 as a surfactant to form a lotion similar to water-in-oil. The shear thickened droplets can be stably and uniformly dispersed to a diameter of 100 μm at a rotation speed of 800 rpm min^-1. The bilayer shell material achieves a good coating effect on STF, which provides support for strength and stress conduction and improves the compatibility between STF and polyurea matrix. The toughness and impact resistance of the composites were analyzed by a universal testing machine and drop hammer impact tester. Finally, compared with the pure polyurea material, the elongation at break of 2% added amount is increased by 22.70%, and the impact resistance of 1% added amount is the best, which is 76.81 N more than that of the pure specimen.

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.

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.

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.

Roughness-dependent clogging of particle suspensions flowing into a constriction

When concentrated particle suspensions flow into a constricting channel, the suspended particles may either smoothly flow through the constriction or jam and clog the channel. These clogging events are typically detrimental to technological processes, such as in the printing of dense pastes or in filtration, but can also be exploited in micro-separation applications. Many studies have to date focused on important parameters influencing the occurrence of clogs, such as flow velocity, particle concentration, and channel geometry. However, the investigation of the role played by the particle surface properties has surprisingly received little attention so far. Here, we study the effect of surface roughness on the clogging of suspensions of silica particles under pressure-driven flows along a microchannel presenting a constriction. We synthesize micron-sized particles with uniform surface chemistry and tunable roughness and determine the occurrence of clogging events as a function of velocity and volume fraction for a given surface topography. Our results show that there is a clear correlation between surface roughness and flow rate, indicating that rougher particles are more likely to jam at the constriction for slower flows. These findings identify surface roughness as an essential parameter to consider in the formulation of particulate suspensions for applications where clogging plays an important role.

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.

Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear

In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divided by the strain amplitude and diameter of grains, at least for small values of the areas.

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.

The role of solvent molecular weight in shear thickening and shear jamming

The application of stress can drive a dense suspension into a regime of highly non-Newtonian response, characterized by discontinuous shear thickening (DST) and potentially shear jamming (SJ), due to the formation of a frictionally stabilized contact network. Investigating how the molecular weight of the suspending solvent affects the frictional particle-particle interactions, we report on experiments with suspensions of fumed silica particles in polyethylene glycol (PEG). Focusing on the monomer-to-oligomer limit, with n = 1 to 8 ethylene oxide repeat units, we find that increasing n enhances shear thickening under steady-state shear and even elicits rapidly propagating shear jamming fronts, as assessed by high-speed ultrasound imaging of impact experiments. We associate this behavior with a weakening of the solvation layers surrounding the particles as n is increased, which thereby facilitates the formation of frictional contacts. We argue that for n larger than the monomer-to-oligomer limit the trend reverses and frictional interactions are diminished, as observed in prior experiments. This reversal occurs because the polymeric solvent transitions from being enthalpically bound to entropically bound to the particle surfaces, which strengthens solvation layers.

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.

Shear thinning and thickening in dispersions of spherical nanoparticles

We present a molecular dynamics study of the flow of rigid spherical nanoparticles in a simple fluid. We evaluate the viscosity of the dispersion as a function of shear rate and nanoparticle volume fraction. We observe shear-thinning behavior at low volume fractions; as the shear rate increases, the shear forces overcome the Brownian forces, resulting in more frequent and more violent collisions between the nanoparticles. This in turn results in more dissipation. We show that in order to be in the shear-thinning regime the nanoparticles have to order themselves into layers longitudinal to the flow to minimize the collisions. As the nanoparticle volume fraction increases there is less room to form the ordered layers; consequently as the shear rate increases the nanoparticles collide more, which results in turn in shear thickening. Most interestingly, we show that at intermediate volume fractions the system exhibits metastability, with successions of ordered and disordered states along the same trajectory. Our results suggest that for nanoparticles in a simple fluid the hydroclustering phenomenon is not present; instead the order-disorder transition is the leading mechanism for the transition from shear thinning to shear thickening.

Shear Thickening and Jamming of Dense Suspensions: The "Roll" of Friction

Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gearlike rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and "rough" particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shear-thickening materials.

How clay particulates affect flow cessation and the coiling stability of yield stress-matched cementing suspensions

The remarkable increase in the flow resistance of dense suspensions can hinder 3D-printing processes on account of flow cessation in the extruder, and filament fragility/rupture following deposition. Understanding the nature of rheological changes that occur is critical to manipulate flow conditions or to dose flow modifiers for 3D-printing. Therefore, this paper elucidates the influences of clay particulates on controlling flow cessation and the shape stability of dense cementing suspensions that typically feature poor printability. A rope coiling method was implemented with varying stand-off distances to probe the buckling stability and tendency to fracture of dense suspensions that undergo stretching and bending during deposition. The contributions of flocculation and short-term percolation due to the kinetics of structure formation to deformation rate were deconvoluted using a stepped isostress method. It is shown that the shear stress indicates a divergence with a power-law scaling when the particle volume fraction approaches the jamming limit; φ → φj ≈ φmax. Such a power-law divergence of the shear stress decreases by a factor of 10 with increasing clay dosage. Such behavior in clay-containing suspensions arises from a decrease in the relative packing fraction (φ/φmax) and the formation of fractally-architected aggregates with stronger interparticle interactions, whose uniform arrangement controls flow cessation in the extruder and suspension homogeneity, thereby imparting greater buckling stability. The outcomes offer new insights for assessing/improving the extrudability and printability behavior during slurry-based 3D-printing process.

Shear jamming, discontinuous shear thickening, and fragile states in dry granular materials under oscillatory shear

We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus G^{'} and the loss modulus G^{''} in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying G^{'}>0) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed G^{'} after the reduction of the strain amplitude depends on the phase of the external shear strain. The loss modulus G^{''} exhibits a discontinuous jump corresponding to discontinuous shear thickening in the fragile state.

Role of particle orientational order during shear thickening in suspensions of colloidal rods

Rheology of dense anisotropic colloidal suspensions often exhibits unsteady flow at constant imposed shear stress and/or shear rate. Using simultaneous high-resolution confocal microscopy and rheology, we find that the temporal behavior arises due to a strong coupling between shear flow and particle orientation. At smaller applied stresses, the orientation of rods fluctuates around the flow direction. A transition to an intermittent disordered state is observed at higher stresses when the angle between the flow and the rod orientation reaches a critical value. This disordered state is associated with transient drop in shear rate and an increase in viscosity. Simultaneous visualization of boundary stresses and orientation shows that the disordered regions lead to heterogeneous stresses and positive normal forces at the boundary, indicating the formation of systems spanning disordered particle contact networks.

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.

Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Particle rotations and orientational ordering

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate γ[over ̇]. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions ϕ and particle asphericities α at small γ[over ̇], we study the angular rotation θ[over ̇]_{i} and the nematic orientational ordering S_{2} of the particles induced by the shear flow, finding a nonmonotonic behavior as the packing ϕ is varied. We interpret this nonmonotonic behavior as a crossover from dilute systems at small ϕ, where single-particle-like behavior occurs, to dense systems at large ϕ, where the geometry of the dense packing dominates and a random Poisson-like process for particle rotations results. We also argue that the finite nematic ordering S_{2} is a consequence of the shearing serving as an ordering field, rather than a result of long-range cooperative behavior among the particles. We arrive at these conclusions by consideration of (i) the distribution of waiting times for a particle to rotate by π, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter S_{2} when perturbed away from the steady state, and (iv) by construction, a numerical mean-field model for the rotational motion of a particle. Our results also help to explain the singular behavior observed when taking the α→0 limit approaching circular disks.

Discrete fluidization of dense monodisperse emulsions in neutral wetting microchannels

The rheology of pressure-driven flows of two-dimensional dense monodisperse emulsions in neutral wetting microchannels is investigated by means of mesoscopic lattice Boltzmann simulations, capable of handling large collections of droplets, in the order of several hundreds. The simulations reveal that the fluidization of the emulsion proceeds through a sequence of discrete steps, characterized by yielding events whereby layers of droplets start rolling over each other, thus leading to sudden drops of the relative effective viscosity. It is shown that such discrete fluidization is robust against loss of confinement, namely it persists also in the regime of small ratios of the droplet diameter over the microchannel width. We also develop a simple phenomenological model which predicts a linear relation between the relative effective viscosity of the emulsion and the product of the confinement parameter (global size of the device over droplet radius) and the viscosity ratio between the disperse and continuous phases. The model shows excellent agreement with the numerical simulations. The present work offers new insights to enable the design of microfluidic scaffolds for tissue engineering applications and paves the way to detailed rheological studies of soft-glassy materials in complex geometries.

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.

Shear-thickening fluids in biologically relevant agents

BACKGROUND

The rheology of shear thickening fluids is well characterized for many physical applications, however the literature surrounding biologically or cryobiologically compatible shear thickening fluids is less well understood.

OBJECTIVE

This study examined fluids consisting of corn-derived hydroxyethyl starch with a variety of sugars and cryoprotectants to characterize their shear-rate viscosity relationship. The objective was to establish if cryobiologically relevant materials could be used to afford biologics protection through shear-thickening.

RESULTS

Fluids consisting of 50% hydroxyethyl starch by weight exhibited shear thickening with a variety of cryoprotectants. Lowering the temperature of the fluid both reduced critical shear rates and enhanced thickening magnitude. Starch derived from corn, wheat, and rice all exhibited non-Newtonian shear-dependent viscosity behaviour at 50% by weight in water. Between the starch sources however, the shear-rate viscosity relationship varied widely, with wheat-derived starch shear thinning, and the remaining starches forming shear thickening fluids. Different starch sources had different baseline viscosities, critical shear rates, and rates of viscosity increase.

CONCLUSIONS

This study established that shear thickening is compatible with cryobiologically relevant agents, particularly so at lower temperatures. This forms the basis for harnessing these phenomena in biological processes such as cryopreservation.

Stress Controlled Rheology of Dense Suspensions Using Transient Flows

Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we can track how a dense suspension approaches its shear-jammed state dynamically and quantitatively map out the onset stress for solidification in a state diagram.

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.

Rheological Behavior of High Cell Density Pseudomonas putida LS46 Cultures during Production of Medium Chain Length Polyhydroxyalkanoate (PHA) Polymers

The rheology of high-cell density (HCD) cultures is an important parameter for its impact on mixing and sparging, process scale-up, and downstream unit operations in bioprocess development. In this work, time-dependent rheological properties of HCD Pseudomonas putida LS46 cultures were monitored for microbial polyhydroxyalkanoate (PHA) production. As the cell density of the fed-batch cultivation increased (0 to 25 g·L-1 cell dry mass, CDM), the apparent viscosity increased nearly nine-fold throughout the fed-batch process. The medium behaved as a nearly Newtonian fluid at lower cell densities, and became increasingly shear-thinning as the cell density increased. However, shear-thickening behavior was observed at shearing rates of approximately 75 rad·s-1 or higher, and its onset increased with viscosity of the sample. The supernatant, which contained up to 9 g·L-1 soluble organic material, contributed more to the observed viscosity effect than did the presence of cells. Owing to this behavior, the oxygen transfer performance of the bioreactor, for otherwise constant operating conditions, was reduced by 50% over the cultivation time. This study has shown that the dynamic rheology of HCD cultures is an important engineering parameter that may impact the final outcome in PHA cultivations. Understanding and anticipating this behavior and its biochemical origins could be important for improving overall productivity, yield, process scalability, and the efficacy of downstream processing unit operations.

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

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

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.

Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Stress, jamming, and contacts

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction ϕ, strain rate γ[over ̇], and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction μ=σ/p, and the divergence of the transport coefficient η_{p}=p/γ[over ̇] as ϕ is increased to the jamming transition ϕ_{J}. From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate ϕ_{J} as a function of asphericity α and show that the variation of ϕ_{J} with α is the main cause for differences in rheology as α is varied; when plotted as ϕ/ϕ_{J}, rheological curves for different α qualitatively agree. However, a detailed scaling analysis of the divergence of η_{p} for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming Z_{J} is a nonmonotonic function of α that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine and find that as α→0 this distribution seems to diverge at ϑ=π/2, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally, we consider the variation of the average contact force as a function of location on the particle surface.

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.

Controlling shear jamming in dense suspensions via the particle aspect ratio

Dense suspensions of particles in a liquid exhibit rich, non-Newtonian behaviors such as shear thickening (ST) and shear jamming (SJ). ST has been widely studied and is known to be enhanced by increasing the particles' frictional interactions and also by making their shape more anisotropic. SJ however has only recently been understood to be a distinct phenomenon and, while the role of interparticle friction has been investigated, the role of particle anisotropy in controlling the SJ regime has remained unknown. To address this we here synthesize silica particles for use in water/glycerol suspensions. This pairing of hydrogen-bonding particle surfaces and suspension solvent has been shown to elicit SJ with spherical particles. We then vary particle aspect ratio from Γ = 1 (spheres) to Γ = 11 (slender rods), and perform rheological measurements to determine the effect of particle anisotropy on the onset of shear jamming. We also show that the effect on the precursor to SJ, discontinuous shear thickening (DST), is consistent with prior work. We find that increasing aspect ratio significantly reduces φm, the minimum particle packing fraction at which SJ can be observed, to values as low φm = 33% for Γ = 11. The ability to fix the properties of the solvated particle surfaces, and thus the particle interactions at contact, while varying shape anisotropy, yields fundamental insights about the SJ capabilities of suspensions and provides a framework to rationally design and tune these behaviors.

Tuning Interparticle Hydrogen Bonding in Shear-Jamming Suspensions: Kinetic Effects and Consequences for Tribology and Rheology

The reversible shear-induced solidification of dense suspensions, known as shear jamming, critically depends on frictional interparticle contacts. Recently, it was shown that shear jamming can be strongly affected by molecular-scale interactions between particles, e.g., by chemically controlling their propensity for hydrogen bonding. However, hydrogen bonding not only enhances interparticle friction but also introduces (reversible) adhesion, whose interplay with friction in shear-jamming systems has so far remained unclear. Here, we present atomic force microscopy studies to assess interparticle adhesion, its relationship to friction, and how these attributes are influenced by urea, a molecule that interferes with hydrogen bonding. We characterize the kinetics of this process with nuclear magnetic resonance, relating it to the time dependence of the macroscopic flow behavior with rheological measurements. We find that time-dependent urea sorption reduces friction and adhesion, causing a reduction in the high-shear viscosity. These results extend our mechanistic understanding of chemical effects on the nature of shear jamming, promising new avenues for fundamental studies and applications alike.

Discontinuous rate-stiffening in a granular composite modeled after cornstarch and water

Cornstarch in water exhibits impact-activated solidification (IAS) and strong discontinuous shear thickening, with "shear jamming". However, these phenomena are absent in cornstarch in ethanol. Here we show that cornstarch granules swell under ambient conditions. We postulate that this granule swelling is linked to an interparticle force scale that introduces a discontinuous rate-dependence to the generation of stable contacts between granules. We studied this force scale by coating sand with ~ 2 μm-thick polydimethysiloxane, creating a material that exhibits a similar IAS and discontinuous deformation rate-stiffening despite being a granular composite, not a suspension. This result suggests rate-dependence can be tuned by coating granular materials, introducing an interparticle force scale from rate-dependent properties present in the coating material. Our work provides insights into the unique behavior of cornstarch in water, bridges our understanding of suspensions and dry granular materials, and introduces a method to make discontinuous rate-dependent materials without suspending particles.

From Yielding to Shear Jamming in a Cohesive Frictional Suspension

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, with an intermediate region of stress in which the material is flowable.

DEM simulation of the local ordering of tetrahedral granular matter

The formation and growth of local order clusters in a tetrahedral granular assembly driven by 3D mechanical vibration were captured in DEM (discrete element method) dynamic simulation using a multi-sphere model. Two important kinds of clusters, dimer and wagon wheel structures, were observed based on which the growth behavior and mechanism of each local cluster with different orientations/structures were investigated. The results show that during vibration, dimer clusters are formed first and then most of them grow into linear trimers and tetramers. Wagon wheel clusters are also frequently observed that grow into hexamers and, further, octamer and nonamer local clusters. Coordination number (CN) evolution indicates that the decrease of local mean CN can be regarded as the signal for the formation of local clusters in the tetrahedral particle packing system. Nematic order metric analysis shows that although the two basic structures (dimer and wagon wheel structures) grow into complex local clusters during packing densification, these local clusters are randomly distributed in the tetrahedral particle packing system. Stress analysis indicates that the dimer-based local clusters are mostly formed in the compaction state of the tetrahedral particle packing system during the vibrated packing densification process. In comparison, the wagon wheel-based local clusters need much stronger interaction forces from tetrahedral particles during vibrated packing densification.

Controlling the shear thickening behavior of suspensions by changing the surface properties of dispersed microspheres

To investigate the effect of the surface properties of dispersed particles on the shear thickening behavior of their corresponding suspensions and further control this characteristic, three kinds of suspensions were prepared by mixing SiO₂, SiO₂-NH₂, and SiO₂-COOH microspheres with a poly(ethylene glycol) fluid medium, and their rheological behavior was analyzed carefully. Compared to the SiO₂ microsphere suspension, the SiO₂-NH₂ and SiO₂-COOH microsphere suspensions show a weaker thickening behavior and a greater critical shear rate due to the aggregation tendency caused primarily by the organic chains. Moreover, the rheological behavior of the three suspensions display different dependencies on the pH value, which is comprehensively determined by the interaction between the microspheres and the medium. Moreover, the critical shear stress of suspensions with different pH values could be predicted by the Wagner model, which basically proves that the interaction between the particles significantly influences the beginning of thickening. The thickening degree could be interpreted by friction theory. The critical volume fraction corresponding to the onset of discontinuous shear thickening is determined by the friction coefficient between the particles, which is greatly affected by the pH value.

The physics of jamming for granular materials: a review

Granular materials consist of macroscopic grains, interacting via contact forces, and unaffected by thermal fluctuations. They are one of a class systems that undergo jamming, i.e. a transition between fluid-like and disordered solid-like states. Roughly twenty years ago, proposals by Cates et al for the shear response of colloidal systems and by Liu and Nagel, for a universal jamming diagram in a parameter space of packing fraction, ϕ, shear stress, τ, and temperature, T raised key questions. Contemporaneously, experiments by Howell et al and numerical simulations by Radjai et al and by Luding et al helped provide a starting point to explore key insights into jamming for dry, cohesionless, granular materials. A recent experimental observation by Bi et al is that frictional granular materials have a a re-entrant region in their jamming diagram. In a range of ϕ, applying shear strain, γ, from an initially force/stress free state leads to fragile (in the sense of Cates et al), then anisotropic shear jammed states. Shear jamming at fixed ϕ is presumably conjugate to Reynolds dilatancy, involving dilation under shear against deformable boundaries. Numerical studies by Radjai and Roux showed that Reynolds dilatancy does not occur for frictionless systems. Recent numerical studies by several groups show that shear jamming occurs for finite, but not infinite, systems of frictionless grains. Shear jamming does not lead to known ordering in position space, but Sarkar et al showed that ordering occurs in a space of force tiles. Experimental studies seeking to understand random loose and random close packings (rlp and rcp) and dating back to Bernal have probed granular packings and their response to shear and intruder motion. These studies suggest that rlp's are anisotropic and shear-jammed-like, whereas rcp's are likely isotropically jammed states. Jammed states are inherently static, but the jamming diagram may provide a context for understanding rheology, i.e. dynamic shear in a variety of systems that include granular materials and suspensions.

Interparticle hydrogen bonding can elicit shear jamming in dense suspensions

Dense suspensions of hard particles in a liquid can exhibit strikingly counter-intuitive behaviour, such as discontinuous shear thickening (DST)^1-7 and reversible shear jamming (SJ) into a state where flow is arrested and the suspension is solid-like^8-12. A stress-activated crossover from hydrodynamic interactions to frictional particle contacts is key for these behaviours^2-4,6,7,9,13. However, in experiments, many suspensions show only DST, not SJ. Here we show that particle surface chemistry plays a central role in creating conditions that make SJ readily observable. We find the system's ability to form interparticle hydrogen bonds when sheared into contact elicits SJ. We demonstrate this with charge-stabilized polymer microspheres and non-spherical cornstarch particles, controlling hydrogen bond formation with solvents. The propensity for SJ is quantified by tensile tests¹² and linked to an enhanced friction by atomic force microscopy. Our results extend the fundamental understanding of the SJ mechanism and open avenues for designing strongly non-Newtonian fluids.

Dynamic Vorticity Banding in Discontinuously Shear Thickening Suspensions

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show, however, that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.

Discontinuous shear thickening in Brownian suspensions

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