Continuous Shear Thickening Research Articles

Discontinuous Shear Thickening in Biological Tissue Rheology.

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

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

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

K -core analysis of shear-thickening suspensions

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

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

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

Dilatancy in dense suspensions of model hard-sphere-like colloids under shear and extensional flow

Dense suspensions of model hard-sphere (HS)-like colloids, with different particle sizes, are examined experimentally near and in the glass state, under shear and extensional rheology. Under steady shear flow, we detect both continuous and discontinuous shear thickening (DST) above a critical shear rate (or shear stress), depending on the particle size and volume fraction. Start-up shear experiments show stress overshoots in the vicinity of the onset of DST indicative of microscopic structural changes, while the sample macroscopically shows dilatancy effects. Measurement of shear and normal stresses together with direct video imaging of the sample probes the appearance of the positive first normal stress difference, N1, at the onset of shear thickening at high shear rates and glassy states. This is followed by dilatancy effects accompanied by large fluctuations of shear and normal stress and stick-slip phenomena. Similarly, under extensional flow probed by capillary breakup and filament stretching setups, we find liquidlike response for low strain rates, while above a critical strain rate, the samples exhibit a solidlike behavior where thickening is accompanied by a macroscopic dilatancy and granulation. Monitoring the filament thinning processes under different conditions (volume fractions and strain rates), we have created a state diagram where all responses of a HS suspension (liquidlike, shear thinning, shear thickening, and dilatant) are shown. We, finally, compare the shear thickening response of these HS-like suspensions and glasses in shear with that in the extensional flow.

Interaction network analysis in shear thickening suspensions

Dense, stabilized, frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, $\phi$, increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. The rheology and networks of frictional forces from two and three-dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress the frictional interaction networks are predominantly quasi-linear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chain-like structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks and provide a key link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity and displays a scaling law near the jamming fraction for both dimensionalities simulated.

Experimental test of a frictional contact model for shear thickening in concentrated colloidal suspensions

Rheological experiments on model and industrial colloidal dispersions that exhibit reversible shear thickening are compared to a recent model that correlates simulation results for the shear rheology of bidisperse suspensions of particles with varying levels of contact friction. Comparisons are presented with rheological results for a variety of colloidal dispersions varying from model systems to industrially relevant, commercial dispersions where both shear and first normal stress differences are available. Particle-scale measurements of particle friction coefficients are provided through a survey of the literature. The comparisons show under which conditions the model can quantitatively describe the measured rheology and how the model can be used to correlate data for systems with more complex interactions when allowances are made for effective volume fractions and adjustments in friction coefficients. Discrepancies evident in comparisons for the first normal stress differences highlight the importance of enhanced hydrodynamic friction in many systems, especially for continuous shear thickening, in qualitative agreement with recent simulations that incorporate enhanced lubrication hydrodynamics due to elastohydrodynamics or particle roughness. Finally, a literature survey of measurements of jamming volume fractions and particle friction coefficients indicates that the model overestimates the experimentally observed jamming volume fraction. The comparisons presented in this work provide quantitative information valuable for those modeling suspension processing as well as suggestions for further model improvement.

Continuous shear thickening and discontinuous shear thickening of concentrated monodispersed silica slurry

Concentrated slurry is known to exhibit shear thickening behavior, in which viscosity increases as the shear rate ascends. However, to identify the differences between this shear thickening behavior and rapid increases in viscosity (such as the dilatancy behavior of starch, sand, and other concentrated slurries) and the smooth increases in viscosity exhibited by concentrated slurries, this research investigated the rheological behavior of a polyethylene glycol suspension containing monodispersed silica particles with a size of 2.5 μm. The results found that the increases in viscosity as the shear rate ascends or the increases in elasticity as the strain ascends change consecutively from smooth and reversible behavior (i.e., continuous shear thickening (CST)) to rapid and irreversible behavior (i.e., discontinuous shear thickening (DST)) simply by increasing the concentration of the slurry, even in the case of concentrated slurries comprising of the same particles. DST is a manifestation of dilatancy in which a jamming transition occurs due to collisions between particles. Because CST transitions successively to DST, and the on-set shear stress of shear thickening of CST is almost the same with that of DST, shear thickening in the CST region may, therefore, also be regarded as the result of friction due to collisions between particles. This supports the research by Seto, Mari, Poon et al., which stated that shear thickening occurs due to friction from particle collisions.

Soft armor materials constructed with Kevlar fabric and a novel shear thickening fluid

This study presents the dynamic stab resistance and quasi-static mechanical properties of soft armor materials constructed with Kevlar fabric impregnated with a novel shear thickening fluid (STF) composed of silica microsphere and ionic liquids (ILs). Rheological results indicate that this STF presents a unique double continuous shear thickening behavior and good conductivity. Both the stab resistance and mechanical properties of the Kevlar fabric are enhanced significantly due to the presence of the STF. With increasing the addition of STF, the stab resistance of the STF-processed Kevlar fabrics (STKF) is enhanced, and the optimal stab resistance is obtained when the STKF contains 34.89 wt % STF. By comparison with the neat Kevlar fabric, the maximum friction between the yarns in the STKF increases by dozens of times, and the tensile strength of the STKF and yarn increases by approximately 2 times and 1.5 times, respectively. Tensile and pull-out tests demonstrate that both filaments and yarns are restrained for the unique double continuous shear thickening of the STF. Furthermore, the STKF has conductivity and the electrical resistance of it has high sensitivity to the applied deformation. The electromagnetic interference shielding of the STKF was as high as 27 dB. These provide a potential to exploit the novel next generation of soft armor with both excellent protective performance and intelligent wearable property.

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

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

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.

Deconstructing the role of shear thickening fluid in enhancing the impact resistance of high-performance fabrics

The role of shear thickening fluid (STF) in enhancing the impact resistance of STF treated fabrics has long been debated. There is a need to clarify whether the dominant mechanism of energy absorption is shear thickening (dilatancy) or friction enhancement. This study establishes that the inherent shear thickening behaviour of STF has a decisive role to play other than just improving the yarn to yarn friction. Kevlar® 363 and Kevlar® 802 F fabrics were treated with STF comprising of 65% (w/w) silica and 35% polyethylene glycol (PEG) 200. Three monodispersed STFs and nine bi-dispersed STFs were prepared from three different particle sizes of silica (100 nm, 300 nm and 500 nm) and their binary mixtures keeping the mass fraction of silica constant (65%). Rheological results showed that STFs prepared form monodispersed silica resulted in higher peak viscosity as well as discontinuous shear thickening. However, bi-dispersed STFs prepared by mixing two different sizes of silica particles, in general, showed lower peak viscosity and continuous shear thickening. In both the fabrics (Kevlar® 363 and Kevlar® 802 F), yarn pull-out force, a measure of yarn to yarn friction, did not show much difference among the fabrics treated with different STFs. However, low velocity impact tests clearly showed enhanced performance in terms of energy absorption and peak force in case of fabrics treated with monodispersed STFs. This correlation between shear thickening and impact resistance conclusively establishes that the former has a dominant role in enhancing the latter of high-performance fabrics.

A constitutive model for simple shear of dense frictional suspensions

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as the solid volume fraction [Formula: see text] increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed in a range of [Formula: see text]. When studied at controlled stress, the DST behavior is associated with nonmonotonic flow curves of the steady-state shear rate as a function of stress. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over wide ranges of concentration, dimensionless shear stress, and coefficient of interparticle friction. The simulation data have been used to populate the lubricated-to-frictional rheology model of Wyart and Cates [Phys. Rev. Lett. 112, 098302 (2014)], which is based on the concept of two viscosity divergences or “jamming” points at volume fraction [Formula: see text] (random close packing) for the low-stress lubricated state, and at [Formula: see text] for any nonzero μ in the frictional state; a generalization provides the normal stress response as well as the shear stress, allowing a description of the full stress tensor. A flow state map of this material is developed based on the simulation results. At low stress and/or intermediate [Formula: see text], the system exhibits CST, and DST appear at volume fractions below but approaching the frictional jamming point. For [Formula: see text], DST is associated with a material transition from one stress-independent rheology to another, while for [Formula: see text], the system exhibits DST to shear jamming as the stress increases.

Unsteady flow and particle migration in dense, non-Brownian suspensions

We present experimental results on dense corn-starch suspensions as examples of non-Brownian, nearly-hard particles that undergo continuous and discontinuous shear thickening (CST and DST) at intermediate and high densities respectively. Our results offer strong support for recent theories involving a stress-dependent effective contact friction among particles. We show however that in the DST regime, where theory might lead one to expect steady-state shear bands oriented layerwise along the vorticity axis, the real flow is unsteady. To explain this, we argue that steady-state banding is generically ruled out by the requirement that, for hard non-Brownian particles, the solvent pressure and the normal-normal component of the particle stress must balance separately across the interface between bands. (Otherwise there is an unbalanced migration flux.) However, long-lived transient shear-bands remain possible.

Study of a shear thickening fluid: the suspensions of monodisperse polystyrene microspheres in polyethylene glycol

ABSTRACTThe monodisperse polystyrene (PS) microspheres were prepared by dispersion polymerization. The rheological properties of shear thickening fluid (STF) based on PS microspheres dispersing in polyethylene glycol with different concentrations were studied through the steady and oscillatory shear at different temperatures, respectively. All suspensions successively present the first shear thinning, the shear thickening, and the second shear thinning. The experimental results indicate that the shear thickening behavior of STF is controlled by the concentration of PS microspheres and temperature, as changed from continuous shear thickening (CST) to discontinuous shear thickening (DST) with increasing solid content or decreasing temperature. The STF is affected by shear rate, temperature, and the viscosity of the dispersed medium, and it is reversible absolutely and presents transient response ability. Both CST and DST behave as dilatancy. The PS microsphere aggregations formed under shear stress may result in the shear thickening in STFs.

Hydrodynamic and Contact Contributions to Continuous Shear Thickening in Colloidal Suspensions.

Shear thickening is a widespread phenomenon in suspension flow that, despite sustained study, is still the subject of much debate. The longstanding view that shear thickening is due to hydrodynamic clusters has been challenged by recent theory and simulations suggesting that contact forces dominate, not only in discontinuous, but also in continuous shear thickening. Here, we settle this dispute using shear reversal experiments on micron-sized silica and latex particles to measure directly the hydrodynamic and contact force contributions to shear thickening. We find that contact forces dominate even continuous shear thickening. Computer simulations show that these forces most likely arise from frictional interactions.

The role of shear in the transition from continuous shear thickening to discontinuous shear thickening

Dense non-Brownian suspension has rich rheology and is hard to understand, especially for distinguishing continuous shear thickening (CST) from discontinuous shear thickening (DST). By studying the shear stress dependent rheology of a well-known DST suspension of cornstarch in water, we find that the transition from CST to DST could occur not only by increasing the volume fraction ϕ but also by increasing the shear stress σ. For the recovery process of jammed suspension, we observe that the shear activates the time-dependent nature of particle rearrangement. DST can then be interpreted as the consequence of shear-induced jamming. Based on the test data, we plot the schematic phase diagram in the ϕ-σ plane and find out that ϕ and σ perform almost the same effect on flow-state transition.

Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.

“Contact networks” in continuously shear thickening colloids

Many body effects that occur in continuous shear thickening of concentrated colloid suspensions are examined by using a Stokesian dynamics simulation of model systems of polymer coated particles. The shear thickening state is probed in a number of ways: computed scattering intensities, imaging of density variation using Voronoi constructions, examination of the distribution of interparticle forces, and computation of the fabric of contacts. The shear thickening transition in these systems is found to be associated with the growth of a network of close particle contacts and shear induced density variations. This paper focuses on the network of contacts. The distributions of force magnitude are found to be exponential. The network directly relates to the normal stress differences. Both the data and simple physical argument suggest that thickening can be viewed as an approach to “jamming.”

Continuous Shear Thickening and Colloid Surfaces.

We elucidate the basic physics of shear thickening in colloids from the viewpoint of the dissipative interactions between close approaching particles. With just hard-sphere lubrication, Brownian spheres show a logarithmic thickening at high stresses. We use a model of interactions due to porous surfaces to show that thickening is enhanced by stronger dissipative surface forces, and compare successfully simulation with experiment. The onset of thickening is sensitive to the degree of order and history of shear.