Dynamical flow arrest in confined gravity driven flows of soft jammed particles

Absorbing-state transitions in particulate systems under spatially varying driving

Non-equilibrium transitions into absorbing states are widespread, and amorphous materials under cyclic shear have emerged as useful model systems in which to study their properties. Recent work has focused on homogeneous driving in which the shear amplitude is uniform in space, despite most real world flows involving spatially inhomogeneous conditions that are known to produce qualitatively distinct phenomenology. Here we study the absorbing state transition under inhomogeneous driving using a modified random organization model. For smoothly varying driving the steady state results map onto the homogeneous absorbing state phase diagram, with the position of the boundary between absorbing and diffusive states being insensitive to the driving wavelength. The phenomenology is well-described by a one-dimensional generalized continuum model that we pose. For discontinuously varying driving the position of the absorbing phase boundary and the exponent characterising the fraction of active particles are altered relative to the homogeneous case.

Reentrant melting of lanes of rough circular disks

We consider binary suspension of rough, circular particles in two dimensions under athermal conditions. The suspension is subject to a time-independent external drive in response to which half of the particles are pulled along the field direction, whereas the other half is pushed in the opposite direction. Simulating the system with different magnitude of external drive in steady state, we obtain oppositely moving macroscopic lanes only for a moderate range of external drive. Below as well as above the range we obtain states with no lane. Hence we find that the no-lane state reenters along the axis of the external drive in the nonequilibrium phase diagram corresponding to the laning transition, with varying roughness of individual particles and external drive. Interparticle friction (contact dissipation) due to the roughness of the individual particle is the main player behind the reentrance of the no-lane state at high external drives.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition.

Power-Law Scaling in Granular Rheology across Flow Geometries

Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio μ by a power of dimensionless temperature Θ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model.

Poiseuille Flow of Soft Polycrystals in 2D Rough Channels

Polycrystals are partially ordered solids where crystalline order extends over mesoscopic length scales, namely, the grain size. We study the Poisuielle flow of such materials in a rough channel. In general, similar to yield stress fluids, three distinct dynamical states, namely, flowing, stick-slip, and jammed can be observed, with a yield threshold dependent on channel width. Importantly, the interplay between the finite channel width, and the intrinsic ordering scale (the grain size) leads to a new type of spatiotemporal heterogeneity. In wide channels, although the average flow profile remains pluglike, at the underlying granular level, there is vigorous grain remodeling activity resulting from the velocity heterogeneity among the grains. As the channel width approaches typical grain size, the flowing polycrystalline state breaks up into a spatially heterogeneous mixture of flowing liquid like patches and chunks of nearly static grains. Despite these static grains, the average velocity still shows a parabolic profile, dominated by the moving liquidlike patches. However, the solid-liquid front moves at nearly constant speed in the opposite direction of the external drive.

Nonlocal Effects in Inhomogeneous Flows of Soft Athermal Disks

We numerically investigate nonlocal effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave-number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with nonlocal constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.

Size-dependence of the flow threshold in dense granular materials

The flow threshold in dense granular materials is typically modeled by local, stress-based criteria. However, grain-scale cooperativity leads to size effects that cannot be captured with local conditions. In a widely studied example, flows of thin layers of grains down an inclined surface exhibit a size effect whereby thinner layers require more tilt to flow. In this paper, we consider the question of whether the size-dependence of the flow threshold observed in inclined plane flow is configurationally general. Specifically, we consider three different examples of inhomogeneous flow - planar shear flow with gravity, annular shear flow, and vertical chute flow - using two-dimensional discrete-element method calculations and show that the flow threshold is indeed size-dependent in these flow configurations, displaying additional strengthening as the system size is reduced. We then show that the nonlocal granular fluidity model - a nonlocal continuum model for dense granular flow - is capable of quantitatively capturing the observed size-dependent strengthening in all three flow configurations.

Scaling description of non-local rheology

The plastic flow of amorphous materials displays non-local effects, characterized by a cooperativity length scale ξ. We argue that these effects enter in the more general description of surface phenomena near critical points. Using this approach, we obtain a scaling relation between exponents that describe the strain rate profiles in shear driven and pressure driven flow, which we confirm both in numerical models and experimental data. We find empirically that the cooperative length follows closely the characteristic length previously extracted in homogenous bulk flows. This analysis shows that the often used mean field exponents fail to capture quantitatively the non-local effects. Our analysis also explains the unusually large finite size effects previously observed in pressure driven flows.

Structural and cooperative length scales in polymer gels

Understanding the relationship between the material structural details, the geometrical confining constraints, the local dynamical events and the global rheological response is at the core of present investigations on complex fluid properties. In the present article, this problem is addressed on a model yield stress fluid made of highly entangled polymer gels of Carbopol which follows at the macroscopic scale the well-known Herschel-Bulkley rheological law. First, performing local rheology measurements up to high shear rates ([Formula: see text] s^-1)and under confinement, we evidence unambiguously the breakdown of bulk rheology associated with cooperative processes under flow. Moreover, we show that these behaviors are fully captured with a unique cooperativity length [Formula: see text] over the whole range of experimental conditions. Second, we introduce an original optical microscopy method to access structural properties of the entangled polymer gel in the direct space. Performing image correlation spectroscopy of fluorophore-loaded gels, the characteristic size D of carbopol gels microstructure is determined as a function of preparation protocol. Combining both dynamical and structural information shows that the measured cooperative length [Formula: see text] corresponds to 2-5 times the underlying structural size D, thus providing a strong grounding to the "Shear Transformation Zones" modeling approach.

Enstrophy cascades in two-dimensional dense granular flows

Employing two-dimensional molecular dynamics simulations of dense granular materials under simple shear deformations, we investigate vortex structures of particle rearrangements. Introducing vorticity fields as a measure of local spinning motions of the particles, we observe their heterogeneous distributions, where statistics of vorticity fields exhibit the highly non-Gaussian behavior and typical domain sizes of vorticity fields significantly increase if the system is yielding under quasistatic deformations. In such dense granular flows, a power-law decay of vorticity spectra can be observed at mesoscopic scale, implying anomalous local structures of kinetic energy dissipation. We explain the power-law decay, or enstrophy cascades in dense granular materials, by a dimensional analysis, where the dependence of vorticity spectra not only on the wave number, but also on the shear rate, is well explained. From our dimensional analyses, the scaling of granular temperature and rotational kinetic energy is also predicted.

Enhancing the linear flow of fine granules through the addition of elongated particles

Sandglasses have been used to record time for thousands of years because of their constant flow rates; however, they now are drawing attention for their substantial scientific importance and extensive industrial applications. The presence of elongated particles in a binary granular system is believed to result in undesired flow because their shape implies a larger resistance to flow. However, our experiments demonstrate that the addition of elongated particles can substantially reduce the flow fluctuation of fine granules and produce a stable linear flow similar to that in an hourglass. On the basis of experimental data and previous reports of flow dynamics, we observed that the linear flow is driven by the “needle particle effect,” including flow orientation, reduced agglomeration, and local perturbation. This phenomenon is observed in several binary granular systems, including fine granules and secondary elongated particles, which demonstrates that our simple method can be widely applied to the accurate measurement of granular flows in industry.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology μ(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

Hydrodynamic segregation in a bidisperse colloidal suspension in microchannel flow: A theoretical study

Colloids in suspension exhibit shear-induced migration towards regions of low viscous shear. In dense bidisperse colloidal suspensions under pressure driven flow large particles can segregate in the center of a microchannel and the suspension partially demixes. To develop a theoretical understanding of these effects, we formulate a phenomenological model for the particle currents based on the work of Phillips et al. [Phys. Fluids 4, 30 (1992)]. We also simulate hard spheres under pressure-driven flow in two and three dimensions using the mesoscale simulation technique of multi-particle collision dynamics. Using a single fit parameter for the intrinsic diffusivity, our theory accurately reproduces the simulated density profiles across the channel. We present a detailed parameter study on how a monodisperse suspension enriches the channel center and quantitatively confirm the experimental observation that a binary colloidal mixture partially segregates into its two species. In particular, we always find a strong accumulation of large particles in the center. Qualitative differences between two and three dimensions reveal that collective diffusion is more relevant in two dimensions.

Nonlocal modeling of granular flows down inclines

Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.

Nonuniversality in the pinch-off of yield stress fluids: role of nonlocal rheology

The pinch-off behavior of yield stress fluids is investigated using droplet and liquid-bridge breakup experiments. Contrary to expectations, the neck thinning behavior depends strongly on the way the breakup experiment is carried out. This nonuniversal behavior can be explained through an analysis of the thinning dynamics as well as the shapes of the fluid necks. Recent nonlocal models for the rheology of yield stress fluids are found to be compatible with the results presented.

Poiseuille flow of soft glasses in narrow channels: from quiescence to steady state

Using numerical simulations, the onset of Poiseuille flow in a confined soft glass is investigated. Starting from the quiescent state, steady flow sets in at a time scale which increases with a decrease in applied forcing. At this onset time scale, a rapid transition occurs via the simultaneous fluidization of regions having different local stresses. In the absence of steady flow at long times, creep is observed even in regions where the local stress is larger than the bulk yielding threshold. Finally, we show that the time scale to attain steady flow depends strongly on the history of the initial state.

Nonlocal rheology of granular flows across yield conditions

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 nonlocal 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 found to diverge as the inverse square root of the distance to the yield point, on both sides of that point.

Onset of flow in a confined colloidal glass under an imposed shear stress

A confined colloidal glass, under the imposition of a uniform shear stress, is investigated using numerical simulations. Both at macro- and microscales, the consequent dynamics during the onset of flow is studied. When the imposed stress is gradually decreased, the time scale for the onset of steady flow diverges, associated with long-lived spatial heterogeneities. Near this yield-stress regime, persistent creep in the form of shear-banded structures is observed.

Eddy viscosity in dense granular flows

We present a seminal set of experiments on dense granular flows in the stadium shear geometry. The advantage of this geometry is that it produces steady shear flow over large deformations, in which the shear stress is constant. The striking result is that the velocity profiles exhibit an S shape, and are not linear as local constitutive laws would predict. We propose a model that suggests this is a result of wall perturbations which span through the system due to the nonlocal behavior of the material. The model is analogous to that of eddy viscosity in turbulent boundary layers, in which the distance to the wall is introduced to predict velocity profiles. Our findings appear pivotal in a number of experimental and practical situations involving dense granular flows next to a boundary. They could further be adapted to other similar materials such as dense suspensions, foams, or emulsions.

Spatial cooperativity in microchannel flows of soft jammed materials: a mesoscopic approach

The flow of amorphous solids results from a combination of elastic deformation and local structural rearrangements, which induce nonlocal elastic deformations. These elements are incorporated into a mechanically consistent mesoscopic model of interacting elastoplastic blocks. We investigate the specific case of channel flow with numerical simulations, paying particular attention to situations of strong confinement. We find that the simple picture of plastic events embedded in an elastic matrix successfully accounts for manifestations of spatial cooperativity. Shear rate fluctuations are observed in seemingly quiescent regions, and the velocity profiles in confined flows at high applied pressure deviate from those expected in the absence of nonlocal effects, in agreement with experimental data. However, we suggest a different physical origin for the large deviations observed when walls have rough surfaces, associated with "bumps" of the particles against the asperities of the walls.

Experimental investigation of plastic deformations before a granular avalanche

We present an experimental study of the deformation inside a granular material that is progressively tilted. We investigate the deformation before the avalanche with a spatially resolved diffusive wave spectroscopy setup. At the beginning of the inclination process, we first observe localized and isolated events in the bulk, with a density which decreases with the depth. As the angle of inclination increases, series of microfailures occur periodically in the bulk, and finally a granular avalanche takes place. The microfailures are observed only when the tilt angles are larger than a threshold angle much smaller than the granular avalanche angle. We have characterized the density of reorganizations and the localization of microfailures. We have also explored the effect of the nature of the grains, the relative humidity conditions, and the packing fraction of the sample. We discuss those observations in the framework of the plasticity of granular matter. Microfailures may then be viewed as the result of the accumulation of numerous plastic events.

A mesoscopic model for the rheology of soft amorphous solids, with application to microchannel flows

We have studied a mesoscopic model for the flow of amorphous solids. The model is based on key features identified at the microscopic level, namely periods of elastic deformation interspersed with localised rearrangements of particles that induce long-range elastic deformations. These long-range deformations are derived following a continuum mechanics approach, in the presence of solid boundaries, and are included in full in the model. Indeed, they mediate spatial cooperativity in the flow, whereby a localised rearrangement may lead a distant region to yield. In particular, we have simulated a channel flow and found manifestations of spatial cooperativity that are consistent with published experimental observations for concentrated emulsions in microchannels. Two categories of effects are distinguished. On the one hand, the coupling of regions subject to different shear rates, for instance, leads to finite shear rate fluctuations in the seemingly unsheared "plug" in the centre of the channel. On the other hand, there is convincing experimental evidence of a specific rheology near rough walls. We discuss the diverse possible physical origins for this effect, and we suggest that it may be associated with the bumps of particles into surface asperities as they slide along the wall.