Rheological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that the shear stress, the pressure, and the kinetic temperature obey critical scaling near the jamming transition point, which is considered as a critical point. These scaling laws have some peculiar properties in view of conventional critical phenomena because the exponents depend on the interparticle force models so that they are not universal. It is also found that these scaling laws imply the relation between the exponents that describe the growing correlation length.
The rheology near jamming of a suspension of soft colloidal spheres is studied using a custom microfluidic rheometer that provides stress versus strain rate over many decades. We find non-Newtonian behavior below the jamming concentration and yield stress behavior above it. The data may be collapsed onto two branches with critical scaling exponents that agree with expectations based on Hertzian contacts and viscous drag. These results support the conclusion that jamming is similar to a critical phase transition, but with interaction-dependent exponents.
We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning and yield stress regimes near the `colloidal' glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the `jamming' transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar mac…
We study the rheology of monodisperse and bidisperse emulsions with various droplet sizes (1 $μ$m -- 2 $μ$m diameter). Above a critical volume fraction $ϕ_c$, these systems exhibit solid-like behavior and a yield stress can be detected. Previous experiments suggest that for small thermal particles, rheology will see a glass transition at $ϕ_c = ϕ_g =0.58$; for large athermal systems, rheology will see a jamming transition at $ϕ_c = ϕ_J =0.64$. However, simulations point out that at the crossover of thermal and athermal regimes, the glass and jamming transitions may both be observed in the same…
We study the steady-state response to applied stress in a simple scalar model of sheared colloids. Our model is based on a schematic (F2) model of the glass transition, with a memory term that depends on both stress and shear rate. For suitable parameters, we find transitions from a fluid to a nonergodic, jammed state, showing zero flow rate in an interval of applied stress. Although the jammed state is a glass, we predict that jamming transitions have an analytical structure distinct from that of the conventional mode coupling glass transition. The static jamming transition we discuss is also…
The phase behaviour of soft colloids has attracted great attention due to the large variety of new phenomenologies emerging from their ability to pack at very high volume fractions. Here we report rheological measurements on interpenetrated polymer network microgels composed of poly(Nisopropylacrylamide) (PNIPAM) and polyacrylic acid (PAAc) at fixed PAAc content as a function of weight concentration. We found three different rheological regimes characteristic of three different states: a Newtonian shear-thinning fluid, an attractive glass characterized by a yield stress, and a jamming state. W…
We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dotγ$ is realized. The system behaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to $\dotγ^{1/δ_S}$, where $1/δ_S=0.64(2)$. It is also found that the relaxation time $τ$ and the correlation length $ξ$ of the velocity increase obeying power laws: $τ\sim\dotγ^{-β}$ and $ξ\sim\dotγ^{-α}$, where $β=0.27(3)$ and $α=0.23(3)$.
We perform numerical simulations to determine the shear stress and pressure of steady-state shear flow in a soft-disk model in two dimensions at zero temperature in the vicinity of the jamming transition ϕ_J. We use critical point scaling analyses to determine the critical behavior at jamming, and we find that it is crucial to include corrections to scaling for a reliable analysis. We find that the relative size of these corrections are much smaller for pressure than for shear stress. We furthermore find a superlinear behavior for pressure and shear stress above ϕ_J, both from the scaling anal…
The shear-jamming of dense suspensions can be strongly affected by molecular-scale interactions between particles, e.g. by chemically controlling their propensity for hydrogen bonding. However, hydrogen bonding not only enhances interparticle friction, a critical parameter for shear jamming, but also introduces (reversible) adhesion, whose interplay with friction in shear-jamming systems has so far remained unclear. Here, we present atomic force microscopy studies to assess interparticle adhesion, its relationship to friction, and how these attributes are influenced by urea, a molecule that in…
We establish that the rheological curve of dry granular media is non-monotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the non-monotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the non-monotonic flow curve governs the yielding behavior of granular media. Finally, we show that non-monotonic flow curves can be seen in at least two different flow geometries and for several granular materials.
We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined.
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 consider the rheology of soft-core frictionless disks in two dimensions in the neighborhood of the athermal jamming transition. From numerical simulations of bidisperse, overdamped, particles, we argue that the divergence of the viscosity below jamming is characteristic of the hard-core limit, independent of the particular soft-core interaction. We develop a mapping from soft-core to hard-core particles that recovers all the critical behavior found in earlier scaling analyses. Using this mapping we derive a duality relation that gives the exponent of the non-linear Herschel-Bulkley rheology…
We study, by computer simulations, the role of different dissipation forces on the rheological properties of highly-dense particle-laden flows. In particular, we are interested in the close-packing limit (jamming) and the question if "universal" observables can be identified that do not depend on the details of the dissipation model. To this end, we define a simplified lubrication force and systematically vary the range $h_c$ of this interaction. For fixed $h_c$ a cross-over is seen from a Newtonian flow regime at small strain rates to inertia-dominated flow at larger strain rates. The same cr…
We determine the form of the complex shear modulus $G^*$ in soft sphere packings near jamming. Viscoelastic response at finite frequency is closely tied to a packing's intrinsic relaxational modes, which are distinct from the vibrational modes of undamped packings. We demonstrate and explain the appearance of an anomalous excess of slowly relaxing modes near jamming, reflected in a diverging relaxational density of states. From the density of states, we derive the dependence of $G^*$ on frequency and distance to the jamming transition, which is confirmed by numerics.
When dealing with unsaturated wet granular materials, a fundamental question is: what is the effect of capillary cohesion on the bulk flow and yield behavior? We inwestigate the dense flow rheology of unsaturated granular materials through experiments and discrete element simulations of homogeneous, simple annular shear flows of frictional, cohesive, spherical particles.
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 study relaxation and rheology of dense athermal suspensions of frictionless particles close below the jamming density. Our key quantity, the relaxation time---determined from the exponential decay of the energy after the shearing has suddenly been switched off---is argued to be a determining factor behind the algebraic divergence of various quantities as the jamming density is approached from below. We also define and measure the ``dissipation time'', which is obtained directly in shearing simulations and find that it behaves similarly to the relaxation time. Comparing shear viscosity with …
Granular solid hydrodynamics, constructed to describe quasi-elastic and plastic motion of granular solid, is shown also capable of accounting for the rheology of granular dense flow. This makes it a unified, though still qualitative, hydrodynamic description, enabling one to tackle fluidization and jamming, the hysteretic transition between elasto-plastic motion and uniform dense flow.
We probe the rheology of weakly vibrated granular flows as function of flow rate, vibration strength and pressure by performing experiments in a vertically vibrated split-bottom shear cell. For slow flows, we establish the existence of a novel vibration dominated granular flow regime, where the driving stresses smoothly vanish as the driving rate is diminished. We distinguish three qualitatively different vibration dominated rheologies, most strikingly a regime where the shear stresses no longer are proportional to the pressure.
In this study we characterize the rheology of fluidized granular matter subject to secondary forcing. Our approach consists of first fluidizing granular matter in a drum half filled with grains via simple rotation, and then superimposing oscillatory shear perpendicular to the downhill flow direction. The response of the system is mostly linear, with a phase lag between the grain motion and the oscillatory forcing. The rheology of the system can be well characterize by the GDR-Midi model if the system is forced with slow oscillations. The model breaks down when the forcing timescale becomes com…
We discuss the linear and non-linear rheology of concentrated (sub)microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from…
The shear rheology of soft particles systems becomes complex at large density because crowding effects may induce a glass transition for Brownian particles, or a jamming transition for non-Brownian systems. Here we successfully explore the hypothesis that the shear stress contributions from glass and jamming physics are `additive'. We show that the experimental flow curves measured in a large variety of soft materials (colloidal hard spheres, microgel suspensions, emulsions, aqueous foams) as well as numerical flow curves obtained for soft repulsive particles in both thermal and athermal limit…
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.
For the purpose of applying laws or principles originated from thermal systems to granular athermal systems, we may need to properly define the critical temperature concept in granular powders. The conventional environmental temperature in thermal systems is too weak to drive movements of particles in granular powders and cannot function as a thermal energy indicator. For maintaining the same functionality as in thermal systems, the temperature in granular powders is defined analogously and uniformly in this article. The newly defined granular temperature is utilized to describe and explain on…
The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is foun…
We have performed a novel experiment on granular packs composed of automatically swelling particles. By analyzing the Voronoi structure of packs going through the jamming transition, we show that the local configuration of a jamming pack is strikingly similar to that of a glass-forming liquid, both in terms of their universal area distribution and the process of defect annealing. Furthermore, we demonstrate that an unambiguous structural signature of the jamming transition can be obtained from the pair correlation functions of a pack. Our study provides insights into the structural properties …
We report a transition from a disordered state to an ordered state in the flow of nearly mono-disperse granular matter flowing in an inclined channel with a bumpy base, in discrete element method simulations. For low particle-sidewall friction coefficients, the particles are disordered and the Bagnold velocity profile is obtained. However, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cro…
We numerically and theoretically investigate how the softness of particles affects the rheology of sheared dilute granular gases. We find that the kinetic theory predicts the deviation of the flow curve from the Bagnold scaling, and it works well below a certain shear rate when we compare with the simulation results. It is also found that there is no theoretical solution above this shear rate, which is because the energy loss due to inelastic collisions cannot be balanced with the energy injection by the shear.
We investigate the rheology of granular materials via molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional, noncohesive spheres. In agreement with previous results for frictionless particles, we observe three flow regimes existing in different domains of particle volume fraction and shear rate, with all stress data collapsing upon scaling by powers of the distance to the jamming point. Though this jamming point is a function of the interparticle friction coefficient, the relation between pressure and strain rate at this point is found to be independent of frict…
We introduce a class of simple models for shear thickening and/ or `jamming' in colloidal suspensions. These are based on schematic mode coupling theory (MCT) of the glass transition, having a memory term that depends on a density variable, and on both the shear stress and the shear rate. (Tensorial aspects of the rheology, such as normal stresses, are ignored for simplicity.) We calculate steady-state flow curves and correlation functions. Depending on model parameters, we find a range of rheological behaviours, including `S-shaped' flow curves, indicating discontinuous shear thickening, and …
This paper describes methods to measure flow rate and jamming onset of granules discharged through a flat-bottom cylindrical hopper with a circular orifice. The intrinsic jamming onset for ideal particles (spherical, monodisperse, smooth) is experimentally measured by two independent methods, with good agreement. For non-ideal particles, the normalized jamming onset increases with elongated granule shape, broadened size distribution and increased friction as measured by the drained angle of repose. An empirical model of the jamming onset is introduced to quantify these effects over the range o…
We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling feature…
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…
We explore the initial moments of impact between two dense granular clusters in a two-dimensional geometry. The particles are composed of solid CO$_{2}$ and are levitated on a hot surface. Upon collision, the propagation of a dynamic "jamming front" produces a distinct regime for energy dissipation in a granular gas in which the translational kinetic energy decreases by over 90%. Experiments and associated simulations show that the initial loss of kinetic energy obeys a power law in time, $ΔE=-Kt^{3/2}$, a form that can be predicted from kinetic arguments.
This paper is devoted to the basic question of what factors determine the strain field in a quasi static granular flow. It is shown that using stress - strain rate relations is not the proper way to understand quasi static rheology. An alternative approach is discussed where the local deformation is regarded as the cause of deformation in the vicinity. We suggest a continuum model where the local shear strain is proportional to its Laplacian and the proportionality factor is determined by the local stress. The predicted behavior is tested in a three dimensional shear cell by means of computer …
We study the internal dynamical processes taking place in a granular packing below yield stress. At all packing fractions and down to vanishingly low applied shear, a logarithmic creep is evidenced. The experiments are analyzed under the scope of a visco-elastic model introducing an internal "fluidity" variable. For all experiments, the creep dynamics can be rescaled onto a unique curve which displays jamming at the random-close-packing limit. At each packing fraction, a stress value is evidenced, corresponding to the onset of internal granular reorganisation leading to a slowing down the cree…
Diverging correlation lengths on either side of the jamming transition are used to formulate a rheological model of granular shear flow, based on the propagation of stress through force chain networks. The model predicts three distinct flow regimes, characterized by the shear rate dependence of the stress tensor, that have been observed in both simulations and experiments. The boundaries separating the flow regimes are quantitatively determined and testable. In the limit of jammed granular solids, the model predicts the observed anomalous scaling of the shear modulus and a new relation for the…
We carry out constant volume simulations of steady-state, shear driven, rheology in a simple model of bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We carry out a detailed critical scaling analysis of our resulting data for pressure $p$ and shear stress $σ$, in order to determine the critical exponent $β$ that describes the algebraic divergence of the Bagnold transport coefficients, as the jamming transition is approached from below. We show that it is necessary, for the strain rates considered in this work, to cons…
The steady shear rheology of granular materials is investigated in slow quasi-static states and inertial flows. The effect of the gravity field and contact stiffness, which are conventionally trivialized is the focus of this study. Series of Discrete Element Method simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various gravity fields and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate timescales describes the flow rheology, we find that a second dimensionless number, the ratio of s…
The connection between friction and jamming in granular media, molecular glasses, and complex fluids is explored. The paper first reviews the way friction is measured, the types of results that are observed, and what is known about the geometry of contacts between macroscopic surfaces. Then simple models for the origin of static friction are described. These are unable to explain the universal observation of static friction between macroscopic objects. The effects of surface roughness and chemical heterogeneity are discussed, and shown to yield exponentially weak static friction in our three d…
Shear cell simulations and experiments of weakly wetted particles (a few volume percent liquid binders) are compared, with the goal to understand their flow rheology. Application examples are cores for metal casting by core shooting made of sand and liquid binding materials. The experiments are carried out with a Couette-like rotating viscometer. The weakly wetted granular materials are made of quartz sand and small amounts of Newtonian liquids. For comparison, experiments on dry sand are also performed with a modified configuration of the viscometer. The numerical model involves spherical, mo…
Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition. Recently, SHD has been observed in confined granular packings under slow shear near the onset of jamming, bolstering speculation that the two transitions are related. Here, we report measurements of SHD in a system of air-driven granular beads, as a function of both density and effective temperature. On approach to jamming, the dynamics become progressively slower and more spatially heterogeneous. The …
We report experimental measurements on the rheology of a dry granular material under a weak level of vibration generated by sound injection. First, we measure the drag force exerted on a wire moving in the bulk. We show that when the driving vibration energy is increased, the effective rheology changes drastically: going from a non-linear dynamical friction behavior - weakly increasing with the velocity- up to a linear force-velocity regime. We present a simple heuristic model to account for the vanishing of the stress dynamical threshold at a finite vibration intensity and the onset of a line…
A systematic microscopic theory for the rheology of dense non-Brownian suspensions characterized by the volume fraction $φ$ is developed. The theory successfully derives the critical behavior in the vicinity of the jamming point (volume fraction $φ_{J}$), for both the pressure $P$ and the shear stress $σ_{xy}$, i.e. $P \sim σ_{xy} \sim \dotγη_0 δφ^{-2}$, where $\dotγ$ is the shear rate, $η_0$ is the shear viscosity of the solvent, and $δφ= φ_J - φ> 0$ is the distance from the jamming point. It also successfully describes the behavior of the stress ratio $μ= σ_{xy}/P$ with respect to the viscou…
We investigate experimentally the dynamics of an intruder dragged by a constant force in an assembly of horizontally vibrated grains close to jamming. At moderate packing fractions, the intruder moves rapidly as soon as the force is applied. Above some threshold value of the packing fraction which increases with the applied force, the intruder exhibits an intermittent creep motion with strong fluctuations reminiscent of a crackling noise signal. These fluctuations behave in a critical manner at the jamming transition unveilled in a previous study. The transition separates a regime where the in…
Jammed states of frictional granular systems can be induced by shear strain at densities below the isostatic jamming density ($ϕ_c$). It remains unclear, however, how much friction affects this so-called shear-jamming. Friction appears in two ways in this type of experiment: friction between particles, and friction between particles and the base on which they rest. Here, we study how particle-bottom friction, or basal friction, affects shear jamming in quasi-two dimensional experiments. In order to study this issue experimentally, we apply simple shear to a disordered packing of photoelastic d…
