Shear-Induced Collective Shape Oscillations in Dense Soft Suspensions
Rudolf Peierls Centre for Theoretical Physics, University of Oxford（鲁道夫·皮尔斯理论物理中心，牛津大学）；Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（理论与计算物理中心，理学院，里斯本大学）；Departamento de Física, Faculdade de Ciências, Universidade de Lisboa（物理系，理学院，里斯本大学）
Ioannis Hadjifrangiskou, Rahil N. Valani, Diogo E. P. Pinto
Dense suspensions of deformable particles can exhibit rich nonequilibrium dynamics arising from complex flow-structure coupling. Using a multi-phase field model, we show that steady shear drives an initially disordered, dense, soft suspension into a positionally and orientationally ordered state, within which particles undergo robust self-sustained shape oscillations. These oscillations originate from repeated T1 neighbor exchanges that force the ordered particle lattice to cyclically traverse different ordered configurations, coupling particle deformation to evolving lattice topology. By identifying the lattice angle as a key variable, we construct a minimal one-degree-of-freedom model that quantitatively captures the limit cycle oscillation. Because these mechanisms rely only on deformability, packing, and shear, they provide a generic route to collective time-dependent behavior in dense soft suspensions.
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 so…
We experimentally investigate shear thickening in dense granular suspensions under oscillatory shear. Directly imaging the suspension-air interface, we observe dilation beyond a critical strain $γ_c$ and the end of shear thickening as the maximum confining stress is reached and the contact line moves. Analyzing the shear profile, we extract the viscosity contributions due to hydrodynamics $η_μ$, dilation $η_c$ and sedimentation $η_g$. While $η_g$ governs the shear thinning regime, $η_μ$ and $η_c$ together determine the shear thickening behavior. As the suspending liquid's viscosity varies from…
In a recent Nature Materials article, Brown et al. reported a generality of shear thickening in dense suspensions and demonstrated that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased to below a threshold. However, the generality of the shear thickening reported in the article may not be necessary true when a high electric/magnetic field is applied on an ER/MR fluid. Shear thickening of ER fluid and MR fluid under high electric/magnetic fields at low shear rates, indicating an obvious phase change inside the dense suspensions has been ob…
Using a novel bi-axial confocal rheoscope, we investigate the structure and rheology of sheared colloidal suspensions under confinement. Consistent with previous work [X. Cheng \textit{et al., Proc. Natl. Acad. Sci. U. S. A.}, 2011, 109, 63], we observe a vorticity-aligned string phase in moderate concentrated colloidal suspensions under uniaxial shear. Using bi-axial shear protocols, we directly manipulate the orientation and morphology of the string structures. Simultaneously, we measure the suspension rheology along both the flow and vorticity directions with a bi-axial force measurement de…
We introduce a novel approach to reveal ordering fluctuations in sheared dense suspensions, using line scanning in a combined rheometer and laser scanning confocal microscope. We validate the technique with a moderately dense suspension, observing modest shear-induced ordering and a nearly linear flow profile. At high concentration ($ϕ= 0.55$) and applied stress just below shear thickening, we report ordering fluctuations with high temporal resolution, and directly measure a decrease in order with distance from the suspension's bottom boundary as well as a direct correlation between order and …
Shear thickening of particle suspensions is characterized by a transition between lubricated and frictional contacts between the particles. Using 3D numerical simulations, we study how the inter-particle friction coefficient influences the effective macroscopic friction coefficient and hence the microstructure and rheology of dense shear thickening suspensions. We propose expressions for effective friction coefficient in terms of distance to jamming for varying shear stresses and particle friction coefficient values. We find effective friction coefficient to be rather insensitive to interparti…
A theory is presented for the onset of shear thickening in colloidal suspensions of particles, stabilized by an electrostatic repulsion. Based on an activation model a critical shear stress can be derived for the onset of shear thickening in dense suspensions for a constant potential and a constant charge approach of the spheres. Unlike previous models the total interaction potential is taken into account (sum of attraction and repulsion). The critical shear stress is related to the maximum of the total interaction potential scaled by the free volume per particle. A comparison with experimenta…
Shear viscosity and wall slip of dense suspensions of a silicone polymer incorporated with polydisperse particles were investigated. Three types of particles with low aspect ratios were used to achieve a relatively high maximum packing fraction of 0.86. Such a high maximum packing fraction allowed the preparation of suspensions with a wide range of solid volume fractions in the range of 0.62 to 0.82. The wall slip velocities of the suspensions in steady torsional and capillary flows were characterized and determined to be fully consistent with the mechanism of apparent slip layer formation at …
The dynamics and rheology of suspensions of fluid vesicles or red blood cells is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip walls, which are driven externally to generate a shear flow with shear rate $\dotγ$. The flow behavior is studied as a function of $\dotγ$, the volume fraction of vesicles, and the viscosity contrast between inside and outside fluids. Results are obtained for the encounter and interactions of two vesicles, the intrinsic viscosity of the suspension, an…
Recent studies have highlighted that oscillatory and time-dependent shear flows might help increase flowability of dense suspensions. While most focus has been on cross-flows we here study a simple two-dimensional suspensions where we apply simultaneously oscillatory and stationary shear along the same direction. We first show that the viscosities in this set-up significantly decrease with an increasing magnitude of the oscillations, contrary to previous claims. The decrease can be attributed to the large decrease in the number of contacts and an altered microstructure as the magnitude of the …
We study the emergence of shear thickening in dense suspensions of non-Brownian particles. We combine local velocity and concentration measurements using Magnetic Resonance Imaging with macroscopic rheometry experiments. In steady state, we observe that the material is heterogeneous, and we find that that the local rheology presents a continuous transition at low shear rate from a viscous to a shear thickening, Bagnoldian, behavior with shear stresses proportional to the shear rate squared, as predicted by a scaling analysis. We show that the heterogeneity results from an unexpectedly fast mig…
Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology exp…
This paper exposes an extension of an activation model previously published by the authors. When particles arranged along the compression axis of a sheared suspension, they may overcome the electrostatic repulsion and form force chains associated with shear thickening. A percolation based consideration, allows an estimation of the impact of the force chains on a flowing suspension. It suggests that, similar to mode-coupling models, the suspension becomes unstable before the critical stress evaluated from the activation model is reached. The theory is applicable only to discontinuous shear thic…
We show that the shear-induced solidification of dilute charge-stabilized (DLVO) colloids is due to the interplay between the shear-induced formation and breakage of large non-Brownian clusters. While their size is limited by breakage, their number density increases with the shearing-time. Upon flow cessation, the dense packing of clusters interconnects into a rigid state by means of grainy bonds, each involving a large number of primary colloidal bonds. The emerging picture of shear-driven solidification in dilute colloidal suspensions combines the gelation of Brownian systems with the jammin…
Dense particulate suspensions often become more dilute as they move downstream through a constriction. We find that as a shear-thickening suspension is extruded through a narrow die and undergoes such liquid migration, the extrudate maintains a steady concentration $ϕ_c$, independent of time or initial concentration. This concentration $ϕ_c$ varies with volumetric flow rate $Q$ and die radius $r_{\rm d}$, but at low $Q$ collapses onto a universal function of $Q/r_{\rm d}^3$, a characteristic shear rate in the die. We explain quantitatively the onset of liquid migration in extrusion by coupling…
Oscillatory shear has been widely used to study the rheological properties of suspensions under unsteady shear. Furthermore, recent works have shown that oscillatory flows can improve the flowability of dense suspensions. While most studies have been done under constant volume we here study oscillatory shear flows of a two-dimensional suspensions using a normal pressure-controlled set-up. To characterise the rheology, we introduce both a complex macroscopic friction coefficient $μ^{*}$, following the convention of the complex viscosity $η^{*}$, and a shear-rate averaged viscous number $J'$. Th…
Using Brownian dynamics simulations we perform a systematic investigation of the shear-induced migration of colloidal particles subject to Poiseuille flow in both cylindrical and planar geometry. We find that adding an attractive component to the interparticle interaction enhances the migration effect, consistent with recent simulation studies of platelet suspensions. Monodisperse, bidisperse and polydisperse systems are studied over a range of shear rates, considering both steady states and the transient dynamics arising from the onset of flow. For bidisperse and polydisperse systems size seg…
We report direct measurements of spatially resolved surface stresses of a dense suspension during large amplitude oscillatory shear (LAOS) in the discontinuous shear thickening regime using boundary stress microscopy. Consistent with previous studies, bulk rheology shows a dramatic increase in the complex viscosity above a frequency-dependent critical strain. We find that the viscosity increase is coincident with that appearance of large heterogeneous boundary stresses, indicative of the formation of transient solid-like phases (SLPs) on spatial scales large compared to the particle size. The …
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 leve…
We study the fronts that appear when a shear-thickening suspension is submitted to a sudden driving force at a boundary. Using a quasi-one-dimensional experimental geometry, we extract the front shape and the propagation speed from the suspension flow field and map out their dependence on applied shear. We find that the relation between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a pre-factor that can be much larger than the material density. We show that these experimental findings can be explained by an extension of the Wyart-Cates model, …
We propose a model for the evolution of the conductivity tensor for a flowing suspension of electrically conductive particles. We use discrete particle numerical simulations together with a continuum physical framework to construct an evolution law for the suspension microsutructure during flow. This model is then coupled with a relationship between the microstructure and the electrical conductivity tensor. The parameters of the joint model are fit experimentally using rheo- electrical conductivity measurements of carbon black suspensions under flow over a range of shear rates. The model is ap…
The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both rela…
We propose a simple model, supported by contact-dynamics simulations as well as rheology and friction measurements, that links the transition from continuous to discontinuous shear-thickening in dense granular pastes to distinct lubrication regimes in the particle contacts. We identify a local Sommerfeld number that determines the transition from Newtonian to shear-thickening flows, and then show that the suspension's volume fraction and the boundary lubrication friction coefficient control the nature of the shear-thickening transition, both in simulations and experiments.
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 characterise 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, lub…
We propose a unifying rheological framework for dense suspensions of non-Brownian spheres, predicting the onsets of particle friction and particle inertia as distinct shear thickening mechanisms, while capturing quasistatic and soft particle rheology at high volume fractions and shear rates respectively. Discrete element method simulations that take suitable account of hydrodynamic and particle-contact interactions corroborate the model predictions, demonstrating both mechanisms of shear thickening, and showing that they can occur concurrently with carefully selected particle surface propertie…
We study the rheology of cornstarch suspensions, a non-Brownian particle system that exhibits discontinuous shear thickening. Using magnetic resonance imaging (MRI), the local properties of the flow are obtained by the determination of local velocity profiles and concentrations in a Couette cell. For low rotational rates, we observe shear localization characteristic of yield stress fluids. When the overall shear rate is increased, the width of the sheared region increases. The discontinuous shear thickening is found to set in at the end of this shear localization regime when all of the fluid i…
Discontinuous shear thickening (DST) is associated with a sharp rise of a suspension's viscosity with increasing applied shear rate. A key signature of DST, highlighted in recent studies, is the very large fluctuations of the measured stress as the suspension thickens. A clear link between microstructural development and the dramatic increase of the stress fluctuations has not been established yet. To identify the microstructural underpinnings of this behavior, we perform simulations of sheared dense suspensions. By analyzing particle contact networks, we identify a subset of constrained parti…
Dense suspension of particles in a liquid exhibit rich, non-Newtonian behaviors such as shear thickening and shear jamming. Shear thickening is known to be enhanced by increasing the particles' frictional interactions and also by making their shape more anisotropic. For shear jamming, however, only the role of interparticle friction has been investigated, while the effect of changing particle shape has so far not been studied systematically. To address this we here synthesize smooth silica particles and design the particle surface chemistry to generate strong frictional interactions such that …
We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-indu…
Under an increasing applied shear stress ($σ$), viscosity of many dense particulate suspensions increases drastically beyond a stress onset ($σ_0$), a phenomenon known as discontinuous shear-thickening (DST). Recent studies point out that some suspensions can transform into a stress induced solid-like shear jammed (SJ) state at high particle volume fraction ($ϕ$). 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 …
Competing time scales generate novelty. Here, we show that a coupling between the time scales imposed by instrument inertia and the formation of inter-particle frictional contacts in shear-thickening suspensions leads to highly asymmetric shear-rate oscillations. Experiments tuning the presence of oscillations by varying the two time-scales validate our model. The observed oscillations give access to a shear-jamming portion of the flow curve that is forbidden in conventional rheometry. Moreover, the oscillation frequency allows us to quantify an intrinsic relaxation time for particle contacts.…
We study the rheological behavior of concentrated granular suspensions of simple spherical particles. Under controlled stress, the system exhibits an S-shaped flow curve (stress vs. shear rate) with a negative slope in between the low-viscosity Newtonian regime and the shear thickened regime. Under controlled shear rate, a discontinuous transition between the two states is observed. Stress visualization experiments with a novel fluorescent probe suggest that friction is at the origin of shear thickening. Stress visualization shows that the stress in the system remains homogeneous (no shear ban…
A remarkable property of dense suspensions is that they can transform from liquid-like at rest to solid-like under sudden impact. Previous work showed that this impact-induced solidification involves rapidly moving jamming fronts; however, details of this process have remained unresolved. Here we use high-speed ultrasound imaging to probe non-invasively how the interior of a dense suspension responds to impact. Measuring the speed of sound we demonstrate that the solidification proceeds without a detectable increase in packing fraction, and imaging the evolving flow field we find that the shea…
We study the emergence of a yield stress in dense suspensions of non-Brownian particles, by combining local velocity and concentration measurements using Magnetic Resonance Imaging with macroscopic rheometric experiments. We show that the competition between gravity and viscous stresses is at the origin of the development of a yield stress in these systems at relatively low volume fractions. Moreover, it is accompanied by a shear banding phenomenon that is the signature of this competition. However, if the system is carefully density matched, no yield stress is encountered until a volume fract…
In periodically sheared suspensions there is a dynamical phase transition characterized by a critical strain amplitude $γ_c$ between an absorbing state where particle trajectories are reversible and an active state where trajectories are chaotic and diffusive. Repulsive non-hydrodynamic interactions between "colliding" particles' surfaces have been proposed as a source of this broken time reversal symmetry. A simple toy model called Random Organization qualitatively reproduces the dynamical features of this transition. Random Organization and other absorbing state models exhibit hyperuniformit…
Shear thickening is a type of non-Newtonian behavior in which the stress required to shear a fluid increases faster than linearly with shear rate. Many concentrated suspensions of particles exhibit an especially dramatic version, known as Discontinuous Shear Thickening (DST), in which the stress suddenly jumps with increasing shear rate and produces solid-like behavior. The best known example of such counter-intuitive response to applied stresses occurs in mixtures of cornstarch in water. Over the last several years, this shear-induced solid-like behavior together with a variety of other unusu…
The dynamics of elastic dumbbells in linear shear flow is investigated by fluid particle dynamics simulations at small Reynolds numbers. The positive contribution of a single dumbbell to the effective shear viscosity is determined via the extra stress exerted at the boundaries of the shear cell and the difference to the contributions obtained via the Kramers-Kirkwood formula are described. For a small Weissenberg number and when the mean dumbbell length becomes larger than the mean next-neighbor distance, the contribution of interacting dumbbells to the mean shear viscosity exceeds significant…
We show that a suspension of non-Brownian calcite particles in glycerol-water mixtures can be tuned continuously from being a yield-stress suspension to a shear-thickening suspension--without a measurable yield stress--by the addition of various surfactants. We interpret our results within a recent theoretical framework that models the rheological effects of stress-dependent constraints on inter-particle motion. Bare calcite particle suspensions are found to have finite yield stresses. In these suspensions, frictional contacts that constrain inter-particle sliding form at an infinitesimal appl…
Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over $10^5$ particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for $Pe>1$, the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering …
We investigate dilation-induced surface deformations in a Discontinuous Shear Thickening (DST) suspension to determine the relationship between dilation and stresses in DST. Video is taken at two observation points on the surface of the suspension in a rheometer while shear and normal stresses are measured. A roughened surface of the suspension is observed as particles poke through the liquid-air interface, corresponding to dilation. Dilation events are found to be intermittent and localized spatially. Shear and normal stresses also fluctuate between high- and low-stress states, and dilation i…
Unlike dry granular materials, a dense granular suspension like cornstarch in water can strongly resist extensional flows. At low extension rates, such a suspension behaves like a viscous liquid, but rapid extension results in a response where stresses far exceed the predictions of lubrication hydrodynamics and capillarity. To understand this remarkable mechanical response, we experimentally measure the normal force imparted by a large bulk of the suspension on a plate moving vertically upward at a controlled velocity. We observe that above a velocity threshold, the peak force increases by ord…
