Shear Thickening In Suspensions Research Articles

A frictional soliton controls the resistance law of shear-thickening suspensions in pipes

Pipe flows are commonly found in nature and industry as an effective mean of transporting fluids. They are primarily characterized by their resistance law, which relates the mean flow rate to the driving pressure gradient. Since Poiseuille and Hagen, various flow regimes and fluid rheologies have been investigated, but the behavior of shear-thickening suspensions, which jam above a critical shear stress, remains poorly understood despite important applications (e.g., concrete or food processing). In this study, we build on recent advances in the physics of shear-thickening suspensions to address their flow through pipes and establish their resistance law. We find that for discontinuously shear-thickening suspensions (large particule volume fractions), the flow rate saturates at high driving stress. Local pressure and velocity measurements reveal that this saturation stems from the emergence of a frictional soliton: a unique, localized, superdissipative, and backpropagating flow structure coexisting with the laminar frictionless flow phase observed at low driving stress. We characterize the remarkably steep effective rheology of the frictional soliton and show that it sets the resistance law at the whole pipe scale. These findings offer an unusual perspective on low-Reynolds suspension flows through pipes, intriguingly reminiscent of the transition to turbulence for simple fluids. They also provide a predictive law for the transport of such suspensions in pipe systems, with implications for a wide range of applications.

Inhibitory Effects of Convergent Annular Nozzles on the Primary Breakup of Discontinuous Shear-Thickening Suspensions

Inhibitory Effects of Convergent Annular Nozzles on the Primary Breakup of Discontinuous Shear-Thickening Suspensions

Emergence of a hexagonal pattern in shear-thickening suspensions under orbital oscillations

A dense particle suspension under shear may lose its uniform state to large local density and stress fluctuations, which challenge the mean-field description of the system. Here, we explore the novel dynamics of a non-Brownian suspension under orbital oscillations, where localized density waves along the flow direction appear beyond an excitation frequency threshold and self-organize into a hexagonal pattern across the system. The spontaneous occurrence of the inhomogeneity pattern arises from a coupling between particle advection and the shear-thickening nature of the suspension. Through linear stability analysis, we show that they overcome the stabilizing effects of particle pressure at sufficient particle volume fraction and oscillation frequency. In addition, the long-standing density waves degenerate into random fluctuations when replacing the free surface with rigid confinement. It indicates that the shear-thickened state is intrinsically heterogeneous, and the boundary conditions are crucial for developing local disturbance.

Drag of a shear-thickening suspension on a rotating cylinder

We investigate experimentally the two-dimensional flow of a shear-thickening suspension around a rotating cylinder to which a constant torque is applied. While for low torques both the drag and the flow are steady and close to those for a Newtonian fluid, above the onset torque for discontinuous shear thickening the average velocity of the cylinder saturates and large periodic oscillations of the cylinder velocity are observed. The oscillations result from a hydrodynamic instability of the flow: slow-acceleration phases are followed by high-deceleration phases, triggered by the propagation of a thickening front, and so on. The slow-acceleration phases set the oscillation period, which is limited by the cylinder inertia and inversely proportional to the applied torque. Combined analyses of the cylinder motion and the flow reveal that the front typically nucleates when the shear rate at the cylinder surface reaches the discontinuous shear-thickening threshold. In addition, the characteristics (duration, stress) of the deceleration are set by the interplay between the thickening front propagation and the suspension and cylinder inertiae or the container size. Since for a slow acceleration the shear rate at the cylinder surface is essentially the cylinder angular velocity, this description of the unsteadiness elucidates the saturation of the average velocity. More generally, it illustrates how the hydrodynamics of a shear-thickening suspension with a strongly re-entrant rheology can lead to a marginally re-entrant, although steep, drag curve.

Shear-thickening suspensions down inclines: from Kapitza to Oobleck waves

We investigate experimentally and theoretically the stability of a shear-thickening suspension flowing down an inclined plane. In a previous paper (Darbois Texier et al., Commun. Phys., vol. 3, 2020), we have shown that for particle volume fractions $\phi$ above the discontinuous shear-thickening fraction $\phi _{DST}$ , long surface waves grow spontaneously at a flow Reynolds number much below 1. This motivated a simplified analysis based on a purely inertialess mechanism, called the ‘Oobleck waves’ mechanism, which couples the negatively sloped rheology of the suspension with the free-surface deflection and captures well the experimental instability threshold and the wave speed, for $\phi >\phi _{DST}$ . However, neglecting inertia does not allow us to describe the inertial Kapitza regime observed for $\phi <\phi _{DST}$ , nor does it allow us to discriminate between Oobleck waves and other inertial instabilities expected above $\phi _{DST}$ . This paper fills this gap by extending our previous analysis, based on a depth-averaged approach and the Wyart–Cates constitutive shear-thickening rheology, to account for inertia. The extended analysis recovers quantitatively the experimental instability threshold in the Kapitza regime, below $\phi _{DST}$ , and in the Oobleck waves regime, above $\phi _{DST}$ . By providing additional measurements of the wave growth rate and investigating theoretically the effect of a strain delay in the rheology, it also confirms that the instability observed above $\phi _{DST}$ stems from the non-inertial Oobleck wave mechanism, which is specific to free-surface flows and dominates modes of inertial origin. These results emphasize the variety of instability mechanisms for shear-thickening suspensions and might be relevant to free-surface flows of other complex fluids displaying velocity-weakening rheology.

Capillary-Stress Controlled Rheometer Reveals the Dual Rheology of Shear-Thickening Suspensions

The rheology of dense colloidal suspensions, which may undergo discontinuous shear thickening or shear jamming, is particularly difficult to analyze with conventional rheometers. Here, we develop a rheometer adapted to colloidal suspensions: the “capillarytron,” which uses the air-suspension capillary interface to impose particle (or osmotic) pressure during shear. The main virtues of this new device are that (i) it gives direct access to the suspension friction coefficient, (ii) it operates for very dense suspensions up to jamming, and, most importantly, (iii) it decouples the stresses developed within the suspension from the applied shear rate. We can, thus, smoothly move through the different frictional states of the system, precisely in the range of volume fractions where discontinuous shear thickening or shear jamming occur under volume-imposed conditions. Our results obtained with the capillarytron provide the first complete characterization of the dual frictional behavior of a model shear-thickening suspension, in agreement with the recently proposed frictional transition scenario. Based on a new concept in rheometry, the capillarytron unlocks the path to pressure-imposed rheology on colloidal and Brownian suspensions. Moreover, its fine control of the particle pressure via the soft capillary interface opens the possibility to explore the flow of “fragile” particles close to jamming, such as Brownian colloids, active particles, and living cells.Received 18 November 2022Revised 15 December 2022Accepted 9 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011024Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasJammingNon-Newtonian fluidsRheologyPhysical SystemsComplex fluidsGranular fluidsPolymers & Soft Matter

Macaroni-type breakup in the primary breakup of discontinuous shear-thickening suspension

The primary breakup of discontinuous shear-thickening suspension is studied experimentally. A divergent nozzle was used as the annular passage of a coaxial two-fluid nozzle. The breakup morphology was observed with a DSLR camera and a high-speed camera. According to the experimental results, the discontinuous shear-thickening behavior and the geometry of the annular air nozzle of divergent section significantly affect the breakup morphology of the suspension jet. Under the action of the annular air, the suspension jet near the exit of the nozzle tends to expand radially and becomes hardened and incompressible in the axial direction. For discontinuous shear-thickening suspensions, the axial hardening does not affect the good fluidity in the radial direction because of their anisotropic microstructure. Therefore, a hollow structure appears, and the suspension jet exhibits the macaroni-type breakup. This breakup mode strengthens when the radial expansion increases. Based on the equation of continuity, the force analysis and mechanism of the macaroni-type breakup are discussed.

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions.

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity η and diffusivity D/ of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale ξ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that η and D/ are controlled by ξ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from D/ ∼ η (frictionless) to η1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.

Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy

We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles in pressure-imposed rheology configuration, subject to a sudden change in shear rate or external pressure. Discrete element method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may differ strongly from the prediction of the suspension balance model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (J. Fluid Mech., vol. 633, 2009, pp. 115–135), which prescribes the dilation rate of the suspension over a strain scale $\gamma _0$ , captures quantitatively the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is non-local, with a non-local length scale $\ell$ that scales with the particle size and diverges algebraically at jamming. In regions affected by $\ell$ , the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below the critical volume fraction at which the suspension jams, thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions.

The shattering of abrupt shear thickening suspension jet in an air-blast atomizer

The primary breakup process of shear thickening is observed via high-speed photography. It is indicated that discontinuous shear thickening (DST) suspension jets exhibit the unique shattering-type breakup mode when air velocity increases up to a high region. In the shattering-type breakup mode, solid-like cracks grow inside the suspension jets, which results in the shattering of the suspension jets. After the shattering, the suspension jets break into tiny fragments with granular and matte surfaces. Combined with the rheological measurement and force analysis, the shattering-type breakup of DST suspension is due to aerodynamic force overwhelming the maximum shear stress. The critical Weber number Wec and a dimensionless number N studied in our previous research (Wang et al., 2022) are used to divide different breakup modes.

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

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

Structure of propagating high-stress fronts in a shear-thickening suspension

We report direct measurements of spatially resolved stress at the boundary of a shear-thickening cornstarch suspension revealing persistent regions of high local stress propagating in the flow direction at the speed of the top boundary. The persistence of these propagating fronts enables precise measurements of their structure, including the profile of boundary stress measured by boundary stress microscopy (BSM) and the nonaffine velocity of particles at the bottom boundary of the suspension measured by particle image velocimetry (PIV). In addition, we directly measure the relative flow between the particle phase and the suspending fluid (fluid migration) and find the migration is highly localized to the fronts and changes direction across the front, indicating that the fronts are composed of a localized region of high dilatant pressure and low particle concentration. The magnitude of the flow indicates that the pore pressure difference driving the fluid migration is comparable to the critical shear stress for the onset of shear thickening. The propagating fronts fully account for the increase in viscosity with applied stress reported by the rheometer and are consistent with the existence of a stable jammed region in contact with one boundary of the system that generates a propagating network of percolated frictional contacts spanning the gap between the rheometer plates and producing strong localized dilatant pressure.

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.

Scaling Analysis of Shear Thickening Suspensions

Dense suspensions of particles in viscous liquid often demonstrate the striking phenomenon of abrupt shear thickening, where their viscosity increases strongly with increase of the imposed stress or shear rate. In this work, discrete-particle simulations accounting for short-range hydrodynamic, repulsive, and contact forces are performed to simulate flow of shear thickening bidisperse suspensions, with the packing parameters of large-to-small particle radius ratio δ = 3 and large particle fraction ζ = 0.15, 0.50, and 0.85. The simulations are carried out for volume fractions 0.54 ≤ ϕ ≤ 0.60 and a wide range of shear stresses. The repulsive forces, of magnitude FR, model the effects of surface charge and electric double-layer overlap, and result in shear thinning at small stress, with shear thickening beginning at stresses σ ∼ FRa−2. A crossover scaling analysis used to describe systems with more than one thermodynamic critical point has recently been shown to successfully describe the experimentally-observed shear thickening behavior in suspensions. The scaling theory is tested here on simulated shear thickening data of the bidisperse mixtures, and also on nearly monodisperse suspensions with δ = 1.4 and ζ = 0.50. Presenting the viscosity in terms of a universal crossover scaling function between the frictionless and frictional maximum packing fractions collapses the viscosity for most of the suspensions studied. Two scaling regimes having different exponents are observed. The scaling analysis shows that the second normal stress difference N2 and the particle pressure Π also collapse on their respective curves, with the latter featuring a different exponent from the viscosity and normal stress difference. The influence of the fraction of frictional contacts, one of the parameters of the scaling analysis, and its dependence on the packing parameters are also presented.

Breakup of shear-thickening suspension

The processes of droplet formation and breakup of cornstarch-water suspensions is divided into three stages: thinning stage, thickening stage, and diluted stage. In the thickening stage, shear thickening behavior apparently slows the deformation of the droplet throat. Unique solid-like phenomenon occurs when the volume fraction of the suspension is \ensuremath{\varphi}>43% and a slip plane forms. The upper and lower parts of the droplet slip along this section, which resembles a cylindrical metal rod stretched by a uniaxial tensile load.

Cavitation bubble dynamics in a shear-thickening fluid

Cylindrical cavitation bubbles, capable of generating extreme strain rates, are experimentally and theoretically studied in shear-thickening suspensions. Starting from the limit between continuous and discontinuous shear thickening regimes, cavitation bubbles deform increasingly with increasing solid volume fraction until bubbles are replaced by cavitation-induced fractures.

A new pressure sensor array for normal stress measurement in complex fluids

A new pressure sensor array, positioned on the bottom plate of a standard torsional rheometer, is presented. It is built from a unique piezo-capacitive polymeric foam and consists of 25 capacitive pressure sensors (of surface 4.5×4.5mm2 each) built together in a 5×5 regular array. The sensor array is used to obtain a mapping of the normal stresses in complex fluids, which dramatically extends the capability of the rheometer. We demonstrate this with three examples. First, a pressure profile is reconstructed in a polymer solution, which enables the simultaneous measurement of the first and the second normal stress differences N1 and N2, with a precision of 2 Pa. In a second part, we show that negative pressures can also be measured. Finally, we focus on the normal stress fluctuations that extend both spatially and temporally in a shear-thickening suspension of cornstarch particles. We evidence the presence of a unique heterogeneity rotating very regularly. In addition to their low cost and high versatility, the sensors show here their potential to finely characterize the normal stresses in viscosimetric flows.

Prediction of shear thickening of particle suspensions in viscoelastic fluids by direct numerical simulation

Abstract

Relation between dilation and stress fluctuations in discontinuous shear thickening suspensions.

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, an indication of dilation in a suspension. These surface roughening events are found to be intermittent and localized spatially. Shear and normal stresses also fluctuate between high- and low-stress states, and surface roughening is observed frequently in the high-stress state. On the other hand, a complete lack of surface roughening is observed when the stresses remain at low values for several seconds. Surface roughening is most prominent while the stresses grow from the low-stress state to the high-stress state, and the roughened surface tends to span the entire surface by the end of the stress growth period. Surface roughening is found only at stresses and shear rates in and above the shear thickening range. These observed relations between surface roughening and stresses confirm that dilation and stresses are coupled in the high-stress state of DST.

Surface-wave instability without inertia in shear-thickening suspensions

Recent simulations and experiments have shown that shear-thickening of dense particle suspensions corresponds to a frictional transition. Based on this understanding, non-monotonic rheological laws have been proposed and successfully tested in rheometers. These recent advances offer a unique opportunity for moving beyond rheometry and tackling quantitatively hydrodynamic flows of shear-thickening suspensions. Here, we investigate the flow of a shear-thickening suspension down an inclined plane and show that, at large volume fractions, surface kinematic waves can spontaneously emerge. Curiously, the instability develops at low Reynolds numbers, and therefore does not fit into the classical framework of Kapitza or ‘roll-waves’ instabilities based on inertia. We show that this instability, that we call ‘Oobleck waves’, arises from the sole coupling between the non-monotonic (S-shape) rheological laws of shear-thickening suspensions and the flow free surface.