Imaging the Microscopic Structure of Shear Thinning and Thickening Colloidal Suspensions

Particle surface roughness plays a pivotal role in dictating the rheological behavior of dense suspensions of rigid particles as it promotes interparticle contacts, leading to friction and contact stresses. This suggests that roughness must have a significant impact on the shear thickening behavior of suspensions, as friction is considered to be the underlying mechanism for shear thickening in dense suspensions. To this end, we numerically investigate the effects of systematically increasing the particle surface roughness on shear thickening suspensions. We show that increasing roughness leads to early onset of shear thickening, especially discontinuous shear thickening, in terms of both the critical shear rate and the critical volume fraction. In addition, roughness enhances the strength of the shear thickening effect as it leads to increase in the viscosity of dense suspensions. We explain these results by investigating the role of roughness in the evolution of contact networks and the jamming fraction. Increasing roughness leads to denser contact networks with high contact stresses and reduction in the jamming fraction. Finally, we visualize the effect of roughness on the phase diagram for viscosity in the shear rate–volume fraction plane. The results presented in the paper are consistent with recent experimental studies, which indicates that the computational framework developed can be utilized to predict and tune suspension behavior for specific applications.Particle surface roughness plays a pivotal role in dictating the rheological behavior of dense suspensions of rigid particles as it promotes interparticle contacts, leading to friction and contact stresses. This suggests that roughness must have a significant impact on the shear thickening behavior of suspensions, as friction is considered to be the underlying mechanism for shear thickening in dense suspensions. To this end, we numerically investigate the effects of systematically increasing the particle surface roughness on shear thickening suspensions. We show that increasing roughness leads to early onset of shear thickening, especially discontinuous shear thickening, in terms of both the critical shear rate and the critical volume fraction. In addition, roughness enhances the strength of the shear thickening effect as it leads to increase in the viscosity of dense suspensions. We explain these results by investigating the role of roughness in the evolution of contact networks and the jamming fraction....

Many densely packed suspensions and colloids exhibit a behavior known as Discontinuous Shear Thickening in which the shear stress jumps dramatically and reversibly as the shear rate is increased. We performed rheometry and video microscopy measurements on a variety of suspensions to determine the mechanism for this behavior. We distinguish Discontinuous Shear Thickening from inertial effects by showing that the latter are characterized by a Reynolds number but are only found for lower packing fractions and higher shear rates than the former. Shear profiles and normal stress measurements indicate that, in the shear thickening regime, stresses are transmitted through frictional rather than viscous interactions. We come to the surprising conclusion that for concentrated suspensions such as cornstarch in water which exhibit the phenomenon of Discontinuous Shear Thickening, the local constitutive relation between stress and shear rate is not necessarily shear thickening. If the suspended particles are heavy enough to settle, we find the onset stress of shear thickening τmin corresponds to a hydrostatic pressure from the weight of the particle packing where neighboring particles begin to shear relative to each other. Above τmin⁠, dilation is seen to cause particles to penetrate the liquid–air interface of the sheared sample. The upper stress boundary τmax of the shear thickening regime is shown to roughly match the ratio of surface tension divided by a radius of curvature on the order of the particle size. These results suggest a new model in which the increased dissipation in the shear thickening regime comes from frictional stresses that emerge as dilation is frustrated by a confining stress from surface tension at the liquid–air interface. We generalize this shear thickening mechanism to other sources of a confining stress by showing that, when instead the suspensions are confined by solid walls and have no liquid–air interface, τmax is set by the stiffness of the most compliant boundary which frustrates dilation. All of this rheology can be described by a nonlocal constitutive relation in which the local relation between stress and shear rate is shear thinning, but where the stress increase comes from a normal stress term which depends on the global dilation.

Vortex-induced vibrations (VIV) of a cylinder in a Newtonian fluid is a model problem in fluid–structure interactions and has been studied extensively. In this work, we study the influence of shear-thinning and shear-thickening fluids on the VIV response of a one-degree-of-freedom flexibly-mounted cylinder. We consider a system with a mass ratio of $m^*=2$ and zero structural damping in shear-thinning and shear-thickening power-law fluids at $Re_0 = 15$ and $Re_0 = 200$ , respectively, defined based on the zero-shear-rate viscosity of the fluids. We investigate how the VIV amplitude and frequency, flow forces, and the vorticity contours change as the reduced velocity, $U^*$ , and fluid's time constant, $\lambda$ , change. When the results are compared based on $Re_0$ , shear-thinning fluids enhance the oscillations while shear-thickening fluids suppress them. If, however, we define a characteristic Reynolds number, $Re_{char}$ , based on a viscosity evaluated at the characteristic shear rate, $\dot {\gamma } = U/D$ , then at a constant $Re_{char}$ , the amplitude of response stays very similar for the shear-thinning, shear-thickening and Newtonian fluids. Despite this similarity, the observed far wake is different: shear thinning amplifies the generation of vorticity and reduces the extent of the wake, whereas shear thickening limits the generation of vorticity and extends the wake. Our findings show that the local apparent viscosity observed close to the cylinder placed in shear-thinning or shear-thickening fluids governs the VIV response of the cylinder.

The response of shear thickening fluids (STFs) under ballistic impact has received considerable attention due to its field-responsive nature. While efforts have primarily focused on traditional ballistic fabrics impregnated with these fluids, the response of pure STFs to penetration has received limited attention. In the present study, the ballistic response of particle-based STFs is investigated and the effects of fluid density and particle strength on ballistic performance are isolated. It is shown that the loss of ballistic resistance in the STFs at higher impact velocities is governed by the material strength of the particles in suspension. The results illustrate the range of velocities over which these STFs may provide effective armor solutions.

ABSTRACTThe effects of particle–particle interaction and viscosity of carrier fluid on steady and dynamic rheological responses and quasi-static penetration resistance of Twaron® fabrics treated with shear thickening and shear thinning suspensions have been investigated. The suspensions have been made by mechanically dispersing 60 nm silica (SiO2) and calcium carbonate (CaCO3) nanoparticles in poly ethylene glycol (PEG) with molecular weights of 200 and 400 g/mol. The CaCO3 suspensions display shear thinning behaviour along with the total dominance of the elastic state over the viscous state while the SiO2 suspensions exhibit shear thickening behaviour with the emergence of both the elastic and viscous states. With the increase of molecular weight of PEG, viscosity, viscoelastic modules and instability of the suspensions increase and critical shear rate and frequency of transition to elastic state diminish. The PEG200 and PEG400-contained SiO2 suspensions-treated Twaron® composites at 35 wt.% have quasi-static penetration resistances which are nearly 2.63 and 2.48 times and maximum absorbed energies which are about 1.54 and 1.55 times higher, respectively, than those of the corresponding CaCO3 ones. However, the influence of increasing the PEG's molecular weight is not as considerable as the effect of particle–particle interaction on the enhancement of penetration resistance performance.

The rheology and particle alignment of suspensions of anisotropic-precipitated calcium carbonate particles of various aspect ratios is investigated using small-angle neutron scattering simultaneous with rheological measurement (Rheo-SANS). Rheo-SANS experiments were performed at concentrations from dilute to those exhibiting continuous and discontinuous shear thickening behavior. Long axis flow alignment is evident in all systems over the range of shear rates investigated. The flow alignment is shown to increase with particle aspect ratio, the applied shear stress (up to the point of shear thickening), and particle loading. For samples exhibiting shear thickening behavior, the highest degree of flow alignment occurs at the critical stress associated with the onset of shear thickening. Irrespective of particle aspect ratio, a gradual reduction in flow alignment with increasing applied stress is observed beyond the critical stress in continuously shear thickening samples, whereas discontinuously shear thickening samples maintain nearly the same degree of flow alignment within the shear thickening regime. The results are shown to be consistent with hydrocluster formation as the mechanism of shear thickening. The critical volume fraction for discontinuous shear thickening is shown to coincide with the equilibrium isotropic-nematic phase transition at higher aspect ratios.

Shear thickening and flow induced structures in foods and biopolymer systems

A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.

Stochastic particle based models for suspended particle movement in surface flows

Colloidal dispersions play an important role in nearly every aspect of life, from paint to biofuels to nano-therapeutics. In the study of these so-called complex fluids, a connection is sought between macroscopic material properties and the micromechanics of the suspended particles. Such properties include viscosity, diffusivity, and the osmotic pressure, for example. But many such systems are themselves only microns in size overall; recent years have thus seen a dramatic growth in demand for exploring microscale systems at a much smaller length scale than can be probed with conventional macroscopic techniques. Microrheology is one approach to such microscale interrogation, in which a Brownian “probe” particle is driven through a complex fluid, and its motion tracked in order to infer the mechanical properties of the embedding material. With no external forcing the probe and background particles form an equilibrium microstructure that fluctuates thermally with the solvent. Probe motion through the dispersion distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, F ext , compared to thermal forces, kT/b, defining a P´eclet number, P e = F ext /(kT /b), where kT is the thermal energy and b the bath-particle size. Both the mean and the fluctuating motion of the probe are of interest. Recent studies showed that the reduction in mean probe speed gives the effective material viscosity. But the velocity of the probe also fluctuates due to collisions with the suspended particles, causing the probe to undergo a random walk process. It is shown that the long-time mean-square fluctuational motion of the probe is diffusive and the effective diffusivity of the forced probe is determined for the full range of P´eclet number. At small Pe Brownian motion dominates and the diffusive behavior of the probe characteristic of passive microrheology is recovered, but with an incremental flow-induced “micro-diffusivity” that scales as Dmicro ∼ Da P e 2 φb , where viii φb is the volume fraction of bath particles and Da is the self-diffusivity of an isolated probe. At the other extreme of high P´eclet number the fuctuational motion is still diffusive, and the diffusivity becomes primarily force-induced , scaling as (F ext /η)φb , where η is the viscosity of the solvent. The force-induced “microdiffusivity” is anisotropic, with diffusion longitudinal to the direction of forcing larger in both limits compared to transverse diffusion, but more strongly so in the high-P e limit. Previous work in microrheology defined a scalar viscosity; however, a tensorial expression for the suspension stress in microrheology was still lacking. The notion that diffusive flux is driven by gradients in particle-phase stress leads to the idea that the microdiffusivity can be related directly to the suspension stress. In consequence, the anisotropy of the diffusion tensor may reflect the presence of normal stress differences in non-linear microrheology. While the particle-phase stress tensor can be determined as the second moment of the deformed microstructure, in this study a connection is made between diffusion and stress gradients, and an analytical expression for particle-phase stress as a function of the microdiffusivity and microviscosity is obtained. The two approaches agree, suggesting that normal stresses and normal stress differences can be measured in active microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in P e for P e ≫ 1 and vanishes as P e 3 for P e ≪ 1. An additional important outcome is that the analytical expression obtained for stress-induced migration can be viewed as a generalized non-equilibrium Stokes-Einstein relation. Studies of steady-state dispersion behavior reveal the hydrodynamic and microstructural mechanisms that underlie non-Newtonian behaviors (e.g. shear-thinning, shear-thickening, and normal stress differences). But an understanding of how the microstructures evolve from the equilibrium state, and how non-equilibrium properties develop in time is much less well understood. Transient suspension behavior in the near-equilibrium, linear response regime has been studied via its connection to low-amplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium fluctuations. But important information about the basic physical aspects of structural development and relaxation ix in a medium are captured by start-up and cessation of the imposed deformation in the non-linear regime, where the structure is driven far from equilibrium. Here we study the evolution of stress and microstructure in a colloidal dispersion by tracking transient probe motion during start-up and cessation of a strong flow. For large P e, steady state is reached when a boundary layer (in which advection balances diffusion) forms at particle contact on the timescale of the flow, a/U , where a is the probe size and U its speed. On the other hand, relaxation following cessation occurs over several timescales corresponding to distinct physical processes. For very short times, the timescale for relaxation is set by the diffusion over the boundary-layer thickness. Nearly all stress relaxation occurs during this process, owing to the dependence of the bath-particle drag on the contact value of the microstructure. At longer times the collective diffusion of the bath particles acts to close the wake. In this long-time limit as structural isotropy is restored, the majority of the microstructural relaxation occurs with very little change in suspension stress. Theoretical results are presented and compared with Brownian dynamics simulation. Two regimes of probe motion are studied: an externally applied constant force and an imposed constant velocity. The microstructural evolution is qualitatively different for the two regimes, with a longer transient phase and a thinner boundary layer and longer wake at steady state in the latter case. The work is also compared to analogous results for sheared suspensions undergoing start-up and cessation. The study moves next to investigations of dual-probe microrheology. Motivated by the phenomenon of equilibrium depletion interactions, we study the interaction between a pair of probe particles translating with equal velocity through a dispersion with their line of centers transverse to the external forcing. The character of the microstructure surrounding the probes is determined both by the distance R by which the two probes are separated and by the strength of the external forcing, P e = U a/Db , where U is the constant probe velocity and Db the diffusivity of the bath particles. Osmotic pressure gradients develop as the microstructure is deformed, giving rise to an interactive force between the probes. This force is studied for a range of P e and R. For all separations R > 2a, the probes attract when P e is small. As the strength of the forcing increases, a qualitative change in the interactive force occurs: the probes repel each other. The probe separation R at which the x attraction-to-repulsion transition occurs decreases as P e increases, because the entropic depletion attraction becomes weak compared to the force-induced osmotic repulsion. The non-equilibrium interactive force is strictly repulsive for two separated probes. But non-linear microrheology provides far more than a microscale technique for interrogating complex fluids. In 1906, Einstein published the famous thought experiment in which he proposed that if a liquid were indeed composed of atoms, then the motion of a small particle suspended in the fluid would move with the same random trajectories as the solvent atoms. Combining the theories of kinetics, diffusion, and thermodynamics, he showed that the diffusive motion of a small particle is indeed evidence of the existence of the atom. Perrin confirmed the theory with measurement in 1909. This is a profound conclusion, drawn by simply watching a particle move in a liquid. Here, we follow this example and watch a particle move in a complex fluid—but now for a system that is not at equilibrium. In equilibrium systems, the relationship between fluctuation and dissipation is fundamental to our understanding of colloid physics. By studying fluctuations away from equilibrium, we have discovered an analogous non-equilibrium relation between fluctuation and dissipation—and that the balance between the two is stored in the material stress. A final connection can be made between this stress and energy storage.

Highly concentrated particle suspensions (also called slurries) can undergo a sharp increase in viscosity, or shear thickening, under applied stress. Understanding the fundamental features leading to such rheological change is crucial to optimize flow conditions or to design flow modifiers for slurry processing. While local changes to the particle environment under applied shear can be related to changes in viscosity, there is a broader need to connect the shear thickening transition to the fundamental organization of particle-interaction forces which lead to long-range organization. In particular, at a high volume fraction of particles, recent evidence indicates frictional forces between contacting particles is of importance. Herein, the network of frictional contact forces is analyzed within simulated two-dimensional shear thickening suspensions. Two topological metrics are studied to characterize the response of the contact force network (CFN) under varying applied shear stress. The metrics, geodesic index and the void parameter, reflect complementary aspects of the CFN: One is the connectedness of the contact network and the second is the distribution of spatial areas devoid of particle-particle contacts. Considered in relation to the variation of the viscosity, the topological metrics show that the network grows homogeneously at large scales but with many local regions devoid of contacts, indicating clearly the role of CFN growth in causing the large change in the rheological response at the shear thickening transition.

Simple shear deformation experiments on three‐phase, hydrous, haplogranitic magmas, composed of quartz crystals (24–65 vol.%), CO2‐rich gas bubbles (9–12 vol.%) and melt in different proportions, were performed with a Paterson‐type rock deformation apparatus. Strain rates from 5 · 10−6 s−1 to 4 · 10−3 s−1 were applied at temperatures between 723 and 1023 K and at pressure of 200 MPa. The results show that the three‐phase suspension rheology is strongly strain rate dependent (non‐Newtonian behavior). Two non‐Newtonian regimes were observed: shear thinning (viscosity decreases with increasing strain rate) and shear thickening (viscosity increases with increasing strain rate). Shear thinning occurs in crystal‐rich magmas (55–65 vol.% crystals; 9–10 vol.% bubbles) as a result of crystal size reduction and shear zoning. Shear thickening prevails in dilute suspensions (24 vol.% crystals; 12 vol.% bubbles), where bubble coalescence and outgassing dominate. At intermediate crystallinity (44 vol.% crystals; 12 vol.% bubbles) both shear thickening and thinning occur. Based on the microstructural observations using synchrotron radiation X‐ray tomographic microscopy, bubbles can develop two different shapes: oblate at low temperature (<873 K) and prolate at high temperature (>873 K). These differences in shape are caused by different conditions of flow: unsteady flow, where the relaxation time of the bubbles is much longer than the timescale of deformation (oblate shapes); steady flow, where bubbles are in their equilibrium deformation state (prolate shapes). Three‐phase magmas are characterized by a rheological behavior that is substantially different with respect to suspensions containing only crystals or only gas bubbles.

Summary Polymer transport and fluid rheology were implemented in a fully implicit hydraulic-fracturing and reservoir simulator. For flow in the matrix, a fluid-rheology function was used with shear thickening at high shear rates and shear thinning at medium and low shear rates. For flow in fractures, a shear-thinning constitutive law with a zero shear-rate plateau was used. The average viscosity in each fracture element was calculated by assuming smooth and parallel fracture walls and numerically solving for the velocity, shear rate, and viscosity distribution across the aperture. The simulator was used to investigate the effect on injectivity of shear thickening at high shear rates near the wellbore. For comparison, simulations were performed by use of the full shear-thickening and shear-thinning rheology function and by use of a shear-thinning-only rheology function. In the former case, the shear thickening caused rapid buildup of fluid pressure and the creation of a hydraulic fracture at the wellbore. Once the fracture formed, shear thickening no longer occurred because there was lower Darcy velocity in the matrix caused by lower concentration of flow at the wellbore. As a result, after the formation of the hydraulic fracture, injectivity in the simulation with shear thickening and thinning was nearly identical to that in the simulation with only shear thinning. The simulations were repeated with the constraint that a hydraulic fracture was not permitted to form. In this case, the simulation with shear thickening had a significantly lower injectivity than the simulation with shear thinning only. This result shows that formation of an induced fracture is a plausible explanation for unexpectedly high injectivity during polymer injection because it prevents shear thickening caused by high flow rate because of concentration of flow at the wellbore. Simulations were performed to investigate the effect of polymer rheology on the pressure transients occurring after shut-in of an injection well. Shear thickening affected the shut-in transient only at very-early time. Shear thinning affected the entire duration of the transient, causing an increase in effective fluid viscosity as the Darcy velocity gradually decreased over time. Despite fluid-rheology effects, linear flow was clearly identifiable after shut-in in the simulations with hydraulic fractures. This result shows that hydraulic fractures around polymer-injection wells can be diagnosed in field data from the linear-flow regime in the shut-in transient, regardless of fluid-rheology effects.

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.

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.