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 fraction of 62.7 0.3%.
Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyze a model of mutually-propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations when the nematic order parameter is allowed to vary in space and time. We analyze the model in two contexts: a quasi-one-dimensional channel with no-slip walls and a two-dimensional box with periodic boundaries. Using stability analysis and numerical calculations we show that the interplay between non-uniform nem…
We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering perturbations in the shear-rate and bacterial concentration. Non-linear simulations show that the instability eventually leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the bands. Our results show that long-ranged hydrodynamic interactions are sufficient to explain recent observations of shear-bands in bact…
Bacterial suspensions--a premier example of active fluids--show an unusual response to shear stresses. Instead of increasing the viscosity of the suspending fluid, the emergent collective motions of swimming bacteria can turn a suspension into a "superfluid" with zero apparent viscosity. Although the existence of active "superfluids" has been demonstrated in bulk rheological measurements, the microscopic origin and dynamics of such an exotic phase have not been experimentally probed. Here, using high-speed confocal rheometry, we study the dynamics of concentrated bacterial suspensions under si…
Formation mechanism of speed-dependent ice bandings in freezing colloidal suspensions, of significance in frost heaving and materials science, remains a mystery. With quantitative experiments, we propose a possible mechanism of speed-dependent ice bandings by focusing on the particle packing density and dynamic interface undercooling. The particle packing density ahead of the freezing interface decreases with increasing pulling speeds, attributed to the speed-dependent packing of particles. Through affecting the curvature undercooling of pore ices, the speed-dependent packing of particles can …
It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions, because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show however that the resulting vorticity bands are unsteady, with spatiotemporal patte…
The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier-Stokes'-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up-to the maximum packing density $ν_{m}$) and the shear viscosity is allowed to diverge at a density $ν_μ$ ($< ν_{m}$), with all other transport coefficients diverging at $ν_{m}$. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear…
One prototypical instability in granular flows is the shear-banding instability, in which a uniform granular shear flow breaks into alternating bands of dense and dilute clusters of particles having low and high shear (shear stress or shear rate), respectively. In this work, the shear-banding instability in an arbitrarily inelastic granular shear flow is analyzed through the linear stability analysis of granular hydrodynamic equations closed with Navier--Stokes-level constitutive relations. It is shown that the choice of appropriate constitutive relations plays an important role in predicting …
It is widely recognized in particle technology that adhesive powders show a wide range of different bulk behavior due to the peculiarity of the particle interaction. We use Discrete Element simulations to investigate the effect of contact cohesion on the steady state of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the {\em granular Bond number} ($Bo$), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenome…
We observe a novel type of shear banding in the rheology of thixotropic yield-stress fluids that is due to the coupling of both non-locality and thixotropy. The latter is known to lead to shear banding even in homogeneous stress fields, but the bands observed in the presence of non-local effects appear different as the shear rate varies continuously over the shear band. Here, we introduce a simple non-local model for the shear banding (NL-SB), and we implement it for the analysis of micron-scale rheo-MRI velocimetry measurements of a milk microgel suspension in a cone-and-plate geometry. The p…
We assess the possibility of shear banding of semidilute rod-like colloidal suspensions under steady shear ow very close to the isotropic-nematic spinodal, using a combination of rheology, small angle neutron scattering, and laser Doppler velocimetry. Model systems are employed which allow for a length and stiffness variation of the particles. The rheological signature reveals that these systems are strongly shear thinning at moderate shear rates. It is shown that the longest and most flexible rods undergo the strongest shear thinning and have the greatest potential to form shear bands. Althou…
We review and compare the phenomenological aspects and physical origin of shear-localization and shear-banding in various material types, namely emulsions, suspensions, colloids, granular materials and micellar systems. It appears that shear-banding, which must be distinguished from the simple effect of coexisting static-flowing regions in yield stress fluids, occurs in the form of a progressive evolution of the local viscosity towards two significantly different values in two adjoining regions of the fluids in which the stress takes slightly different values. This suggests that from a global …
Recent advances in shear-thickening suspension rheology suggest a relation between (wet) suspension flow below jamming and (dry) granular physics. To probe this connection, we simulated the contact force networks in suspensions of non-Brownian spheres using the discrete element method (DEM), varying the particle friction coefficient and volume fraction. We find that force networks in these suspensions show quantitative similarities to those in jammed dry grains. As suspensions approach the jamming point, the extrapolated volume fraction and coordination number at jamming are similar to critica…
Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we review a theoretical framework that gives a scaling description of stationary flows of frictionless particles. Our analysis applies both to suspensions and inertial flows of hard particles. We report numerical results in support of the theory, and show the phase diagram that results wh…
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…
We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after a sudden change in flow rate giving rise to a change in sta…
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…
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…
We study granular suspensions under a variety of extensional deformations and simple shear using numerical simulations. The viscosity and Trouton's ratio (the ratio of extensional to shear viscosity) are computed as functions of solids volume fraction $ϕ$ close to the limit of zero inertia. Suspensions of frictionless particles follow a Newtonian Trouton's ratio for $ϕ$ all the way up to $ϕ_0$, a universal jamming point that is independent of deformation type. In contrast, frictional particles lead to a deformation-type-dependent jamming fraction $ϕ_m$, which is largest for shear flows. Trouto…
We study the avalanche dynamics of a pile of micron-sized silica grains in miniaturized rotating drums filled with water. Contrary to what is expected for classical granular materials, the avalanches do not stop at a finite angle of repose. Below an angle $θ$\_c, we observe a creep regime where the piles slowly flow until they become flat. In this regime, the relaxation is logarithmic in time and is slower when the ratio between the weight of the grains and the thermal agitation is increased. We propose a simple 1D model based on Kramer's escape rate to describe this flow.
We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent Letter [Phys. Rev. Lett. 110 (2013) 086001]. In each case this criterion depends only on the shape of the experimentally measured rheological response fun…
Many soft materials, including foams, dense emulsions, micro gel bead suspensions, star polymers, dense packing of surfactant onion micelles, and textured morphologies of liquid crystals, share the basic "glassy" features of structural disorder and metastability. These in turn give rise to several notable features in the low frequency shear rheology (deformation and flow properties) of these materials: in particular, the existence of a yield stress below which the material behaves like a solid, and above which it flows like a liquid. In the last decade, intense experimental activity has also r…
We experimentally study the detachment of drops of granular suspensions using a density matched model suspension with varying volume fraction (ϕ = 15% to 55%) and grain diameter (d = 20 μm to 140 μm). We show that at the beginning of the detachment process, the suspensions behave as an effective fluid. The detachment dynamics in this regime can be entirely described by the shear viscosity of the suspension. At later stages of the detachment the dynamics become independent of the volume fraction and are found to be identical to the dynamics of the interstitial fluid. Surprisingly, visual observ…
The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction $ϕ_{p}$ increases. The suspensions jam - and therefore drainage stops - for values $ϕ_{p}^{*}$ which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that $ϕ_{p}^{*}$ accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of t…
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…
Acoustic transparency and absorption in dense granular suspensions
Institut Langevin, ESPCI Paris, Université PSL, CNRS（朗之万研究所，巴黎高等物理化工学院，巴黎文理研究大学，法国国家科学研究中心）；Laboratorio de Acústica Ultrasonora, Instituto de Física, Facultad de Ciencias, Universidad de la República（超声波声学实验室，物理研究所，理学院，共和国大学）
We present an experimental investigation of shear elastic wave propagation along the surface of a dense granular suspension. Using an ultrafast ultrasound scanner, we monitor the softening of the shear wave velocity inside the optically opaque medium as the driving amplitude increases. For such nonlinear behavior two regimes are found: in the first regime, we observe a significant shear modulus weakening, but without visible grain rearrangements. In the second regime, there is a clear grain rearrangement accompanied by a modulus decrease up to 88%. A friction model is proposed to describe the …
We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles under pressure-imposed conditions, 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 strongly differ 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 (2009), which prescribes …
We study in this work a steady shearing laminar flow with null heat flux (usually called "uniform shear flow") in a gas-solid suspension at low density. The solid particles are modeled as a gas of smooth hard spheres with inelastic collisions while the influence of the surrounding interstitial fluid on the dynamics of grains is modeled by means of a volume drag force, in the context of a rheological model for suspensions. The model is solved by means of three different but complementary routes, two of them being theoretical (Grad's moment method applied to the corresponding Boltzmann equation …
The Enskog kinetic theory of multicomponent granular suspensions employed previously [Gómez González, Khalil, and Garzó, Phys. Rev. E \textbf{101}, 012904 (2020)] is considered further to determine the four transport coefficients associated with the heat flux. These transport coefficients are obtained by solving the Enskog equation by means of the application of the Chapman--Enskog method around the local version of the homogeneous state. Explicit forms of the heat flux transport coefficients are provided in steady-state conditions by considering the so-called second Sonine approximation to th…
Observing and understanding the movement of an intruder through opaque dense suspensions such as quicksand remains a practical and conceptual challenge. Here we use an ultrasonic probe to investigate the dynamics of a steel ball sinking in a 3D dense glass bead packing saturated by water. We show that the frictional model developed for dry granular media can be used to describe the ball motion induced by horizontal vibration. From this rheology we infer the static friction coefficient and effective viscosity that decrease when increasing the vibration intensity. Our main finding is that the vi…
Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal suspensions and granular materials. A theory on the reversible elastic deformation of jammed states is presented. First, an explicit granular stress-strain relation is derived that captures many relevant features of sand, including especially the Coulomb yield surface and a third-order jamming transition. Then this approach is generalized, and employed to consider jammed magneto- and electro-rheological fluids, again producing results that compare well to experiments and simulations.
Dense suspensions are widespread in nature, manufacturing and process engineering. Particle-based simulations have proven to be an invaluable complement to experimental rheological characterisation, serving as a virtual rheometer that enables rapid exploration of parameter space and detailed scrutiny of microscopic dynamics. To maximise the utility of such simulations, it can be advantageous to exploit pre-existing, well-optimised, well-documented codes. Here we provide a simple description of how to use LAMMPS to study the rheology of dense, granular suspensions.
We use large scale computer simulations and finite size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size, and study carefully the asymptotic limits of large system sizes and infinitely hard particle repulsion. Extending earlier analysis by about two orders of magnitude, we first study the asymptotic behavior of the shear viscosity in the hard particle limit. We co…
We experimentally investigate the statistical behaviour of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned to be fully dispersed to fully crystallised as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a ther…
We study the injection of air in a granular suspension. We use a linear Hele-Saw cell filled with a suspension which is displaced by air, leading to a Saffman-Taylor (fingering) instability. For the suspension, we use an iso-dense mixture where the fluid and the particles have the same density. The volume fraction of particles can thus be adjusted over a wide range. We discuss the question of an effective rheology inside the cell as well as the pattern formation as a function of the granular compacity. We finally report results on the finger width for stable fingers and the thresholds for thei…
A 2D contact dynamics model is proposed as a microscopic description of a collapsing suspension/soil to capture the essential physical processes underlying the dynamics of generation and collapse of the system. Our physical model is compared with real data obtained from in situ measurements performed with a natural collapsing/suspension soil. We show that the shear strength behavior of our collapsing suspension/soil model is very similar to the behavior of this collapsing suspension soil, for both the unperturbed and the perturbed phases of the material.
The time evolution of a homogeneous bidisperse granular suspension is studied in the context of the Enskog kinetic equation. The influence of the surrounding viscous gas on the solid particles is modeled via a deterministic viscous drag force plus a stochastic Langevin-like term. It is found first that, regardless of the initial conditions, the system reaches (after a transient period lasting a few collisions per particle) a universal unsteady hydrodynamic regime where the distribution function of each species not only depends on the dimensionless velocity (as in the homogeneous cooling state)…
We present a phenomenological model for granular suspension rheology in which particle interactions enter as constraints to relative particle motion. By considering constraints that are formed and released by stress respectively, we derive a range of experimental flow curves in a single treatment and predict singularities in viscosity and yield stress consistent with literature data. Fundamentally, we offer a generic description of suspension flow that is independent of bespoke microphysics.
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…
Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fraction, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of banding experimentally observed we have performed interface resolved simulations of the two-fluid system. The experiments were perfomed starting with a random d…
We present a comprehensive study of the slip and flow of concentrated colloidal suspensions using cone-plate rheometry and simultaneous confocal imaging. In the colloidal glass regime, for smooth, non-stick walls, the solid nature of the suspension causes a transition in the rheology from Herschel-Bulkley (HB) bulk flow behavior at large stress to a Bingham-like slip behavior at low stress, which is suppressed for sufficient colloid-wall attraction or colloid-scale wall roughness. Visualization shows how the slip-shear transition depends on gap size and the boundary conditions at both walls an…
A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact-hardening in shear-thickening suspensions like cornstarch.
This paper establishes a link between the non-local behaviour of granular materials and the presence of transient clusters of jammed particles within the flow. These clusters are first evidenced in simulated dense granular flows subjected to plane shear, and are found to originate from a mechanism of multiple orthogonal shear banding. A continuum non-local model, similar in form to the non-local Cooperative model, is then derived by considering the spatial redistribution of vorticity induced by these clusters. The non-locality length scale is thus expressed in terms of the cluster size. The pu…
We present the results of an experimental study of pattern formation in horizontally oscillating granular suspensions. Starting from a homogeneous state, the suspension turns into a striped pattern within a specific range of frequencies and amplitudes of oscillation. We observe an initial development of layered structures perpendicular to the vibration direction and a gradual coarsening of the stripes. However, both processes gradually slow down and eventually saturate. The probability distribution of the stripe width approaches a nonmonotonic steady-state form which can be approximated by a P…
Granular suspensions present a transition from a Newtonian rheology in the Stokes limit to a Bagnoldian rheology when inertia is increased. A custom rheometer which can be run in a pressure or a volume-imposed mode is used to examine this transition in the dense regime close to jamming. By varying systematically the interstitial fluid, shear rate, and packing fraction in volume-imposed measurements, we show that the transition takes place at a Stokes number of 10 independent of the packing fraction. Using pressure-imposed rheometry, we investigate whether the inertial and viscous regimes can b…
We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range lubrication model for spherical particles, and (ii) a soft-core, stick/slide frictional contact model activated when particles overlap. We implement a version of the model using a modified velocity-Verlet algorithm that explicitly solves the $N$-body dynamical system in $\mathcal{O}(cN)$ operations, where $c$ is a kernel constant depending on the cutoff of pa…
We consider the shear rheology of concentrated suspensions of non-Brownian frictional particles. The key result of our study is the emergence of a pronounced shear-thickening regime, where frictionless particles would normally undergo shear-thinning. We clarify that shear thickening in our simulations is due to enhanced energy dissipation via frictional inter-particle forces. Moreover, we evidence the formation of dynamically correlated particle-clusters of size $ξ$, which contribute to shear thickening via an increase in \emph{viscous} dissipation. A scaling argument gives $η\sim ξ^2$, which …
We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contr…
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(ϕ,F)$: at low $ϕ$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $ϕ$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy w…
