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International audience; In this paper, we present a new device called the Darcytron, allowing pressure-imposed rheological measurements on dense suspensions made of very small particles, like shear-thickening suspensions. The main idea is to impose and control the particle pressure using a vertical Darcy flow across the settled bed of particles. We first validate the proof of concept of the Darcytron on a standard (non shear-thickening) suspension composed of large glass particles. We then use this new device to investigate the frictional behavior of a model shear-thickening suspension composed of small silica particles. These results provide direct evidence of a transition between a frictionless and a frictional state as the particle pressure is increased, providing support to the recent frictional transition scenario for shear thickening.

Granular materials whether dry or immersed in fluid show dilation or compaction depending upon the initial conditions, solid fraction and normal stress. Here we probe the transient response of a dense granular suspension subjected to change of applied normal stress under simple shear. In this aim, normal-stress-imposed discrete element particle simulations are developed considering the contributions arising from the drag induced on the particles by fluid phase. These pressure-imposed simulations show transient behaviors of dense granular suspensions such as dilation or compaction before reaching a steady state following the µ(J) rheology. Less expectedly, the transient behavior, in particular the height of the system as a function of applied strain, can also be described by assuming that the system follows the steady µ(J) rheology at all times.

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. The way interactions at the microscopic scale influence emerging flow properties in complex fluids at the macroscopic scale is one of the core problems in soft matter physics. This work provides experimental evidence together with a theoretical explanation for ‘Oobleck waves’, an instability arising from the coupling between the flow free surface and the non-monotonic rheological laws of shear-thickening suspensions.

Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or aerial landslides. The origin of hysteresis in granular flows is still debated. However, most mechanisms put forward so far rely on the presence of inertia at the particle level. In this paper, we study the avalanche dynamics of non-Brownian suspensions in slowly rotating drums and reveal large hysteresis of the avalanche angle even in the absence of inertia. By using micro-silica particles whose interparticle friction coefficient can be turned off, we show that microscopic friction, conversely to inertia, is key to triggering hysteresis in granular suspensions. To understand this link between friction and hysteresis, we use the rotating drum as a rheometer to extract the suspension rheology close to the flow onset for both frictional and frictionless suspensions. This analysis shows that the flow rule for frictionless particles is monotonous and follows a power law of exponent $\alpha \!= \! 0.37 \pm 0.05$, in close agreement with the previous theoretical prediction, $\alpha\!=\! 0.35$. By contrast, the flow rule for frictional particles suggests a velocity-weakening behavior, thereby explaining the flow instability and the emergence of hysteresis. These findings show that hysteresis can also occur in particulate media without inertia, questioning the intimate nature of this phenomenon. By highlighting the role of microscopic friction, our results may be of interest in the geophysical context to understand the failure mechanism at the origin of undersea landslides., Comment: 10 pages, 8 figures

International audience; Flows of granular media in air or in a liquid have been a research field for physicists for several decades. Sometimes solid, sometimes liquid, these particulate materials exhibit peculiar behaviors, which have motivated many studies at the frontiers between nonlinear physics, soft matter physics and fluid mechanics. This paper presents a summary of the recent advances in the field, with a focus on the development of continuous approaches, which make it possible to treat granular media as a complex fluid and to develop a granular hydrodynamics. We also discuss how the better understanding of granular flows we have today may help to address more complex materials, such as colloidal suspensions or some biological systems. © 2018 Académie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).; Les écoulements de milieux formés de grains dans l'air ou dans un liquide intéressent les physiciens depuis plusieurs décennies. Tantôt solides, tantôt liquides, ces matériaux divisés ont des comportements singuliers qui sont au coeur de nombreuses études à la frontière entre la physique non linéaire, la physique de la matière molle et la mécanique des fluides. Cet article se propose de faire un point sur les avancées récentes dans le domaine, en se concentrant sur le développement d'approches continues qui permettent de traiter le milieu comme un fluide complexe et de développer une hydrodynamique granulaire. Nous discutons également en quoi la compréhension plus fine des écoulements granulaires que nous avons aujourd'hui permet de mieux appréhender les matériaux plus complexes comme les suspensions colloïdales, voire certains milieux biologiques.

In order to better understand the mechanism governing segregation in dense granular flows, the force experienced by a large particle embedded in a granular flow made of small particles is studied using discrete numerical simulations. Accurate force measurements have been obtained in a large range of flow parameters by trapping the large particle in a harmonic potential well to mimic an optical tweezer. Results show that positive or negative segregation lift forces (perpendicular to the shear) exist depending on the stress inhomogeneity. An empirical expression of the segregation force is proposed as a sum of a term proportional to the gradient of pressure and a term proportional to the gradient of shear stress, which both depend on the local friction and particle size ratio.

International audience; We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally , we briefly present depth-averaged methods developed for free surface granular flows.

International audience; Experiments have shown that when a horizontal cylinder rotates around the vertical axis in a granular medium, the drag force in the stationary regime becomes independent of the depth, in contradiction with the frictional picture stipulating that the drag should be proportional to the hydrostatic pressure. The goal of this study is to understand the origin of this depth independence of the granular drag. Intensive numerical simulations using the discrete element method are performed giving access to the stress distribution in the packing during the rotation of the cylinder. It is shown that the rotation induces a strong anisotropy in the stress distribution, leading to the formation of arches that screen the hydrostatic pressure in the vicinity of the cylinder and create a bubble of low pressure.

In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely measured by imposing a controlled perturbation at the entrance of the flow and measuring its evolution along the slope. The results are compared with the prediction of a linear stability analysis conducted in the framework of the depth-averaged or Saint-Venant equations. We show that when the friction law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations, the theory is able to predict quantitatively the stability threshold and the phase velocity of the waves but fails in predicting the observed cutoff frequency. The instability is shown to be of the same nature as the long wave instability observed in classical fluids but with characteristics that can dramatically differ due to the specificity of the granular rheology., Comment: 29 pages, 20 figures, to be published in Journal of Fluid Mechanics

International audience; An elastic strip is transversely clamped in a curved frame. The induced curvature decreases as the strip opens and connects to its flat natural shape. Various ribbon profiles are measured and the scaling law for the opening length validates a description where the in-plane stretching gradually relaxes the bending stress. An analytical model of the strip profile is proposed and a quantitative agreement is found with both experiments and simulations of the plates equations. This result provides a unique illustration of smooth nondevelopable solutions in thin sheets. Geometry-induced rigidity is a fundamental feature of thin structures [1], which has long been used in engineering and architecture to design stiff fuselages, hulls, roofs, and deployable structures [2–4]. It is also widely encountered in living structures, such as in plant leaves where curvature can prevent the collapse of the leaves under their own weight [5]. A simple illustration of this rigidity induced by curvature is given by a strip of paper held at one end. When the strip is flat, it is unable to sustain its own weight and bends downward under gravity. However, if the end of the paper is slightly curved transversely, the strip straightens up and becomes much stiffer. Rigidity in these systems arises because bending in one direction is coupled to the transverse curvature and cannot occur without stretching the sheet—a costly mode of deformation in thin plates in terms of elastic energy [6]. Knowing the distance over which an induced curvature spreads is thus an important issue for predicting the rigidity of thin plates and shells. In this Letter, we address the question of the persistence length of curvature in thin sheets on a minimal system: a flat elastic ribbon of thickness t, width W, and length L W, which is clamped at one end over a cylinder of radius R [Fig. 1(a)]. After what distance from the clamp does the ribbon unfold and recover its flat natural shape? This deceptively simple problem is actually not straightforward as, to unfold, the ribbon has to stretch—a forbidden mode of deformation in the inextensible limit. In thin sheets, this constraint is usually resolved by focusing the stretch in elastic defects or singularities, such as the ridges and peaks of a crumpled paper, the rest of the surface being fully developable (i.e. free of stretching) [7–14]. However, another way to obtain the stretching of a thin sheet is to consider that the curvature variation on large distances is associated with a regular stretching, i.e., without defects. Surprisingly, the first insights of this approach are found in the studies of defects such as ridges [15] and pinches [16], where both the focused-stress and the diffuse-stress are present [17]. In each of these situations, regular developable solutions exist away from the defect but they are not observed as the bending energy can be progressively released by a small in-plane stretching (see also [18,19]). The stretching over large distances is also involved in the shape of drapes [20] and curtains [21], the tearing of sheets [22], or the dynamics of curved ribbons [23,24]. Our prototypal system provides a reduced model to probe these situations and the transition between smooth and singular solutions in strained sheets. A first observation of the opening is displayed in Fig. 1(b), using an acetate elastic sheet (t ¼ 110 m, W ¼ 4.5 cm) clamped in a circular frame of radius R ¼ 2.5 cm. The strip is positioned vertically to limit the out-of-plane deflection caused by its weight. Away from the clamping, the strip opens and its curvature decreases and connects to the flat stress-free region over a finite length L p. The opening also results in a small deflection of the strip corresponding to a tilt angle θ of the centerline. The persistence length of curvature L p can be estimated from a balance between the stretching and bending elastic energies using scaling arguments similar to [15]. On one hand, the bending energy of the ribbon scales as E b ∼ EtWL p ðt=RÞ 2 , where E is the Young modulus of the medium. On the other hand, the opening of the ribbon requires the stretching of the edges of the ribbon over a length L p. This is associated with a stretching energy E s ∼ EtWL p 2 , where ∼ Z 2 =2L 2 p is the typical in-plane strain and Z ∼ W 2 =8R is the out-of-plane deflection of the ribbon at the clamp [see Fig. 1(b) inset]. The trade off between the two energies E s and E b gives L p ∼ W 2 = ffiffiffiffiffi tR p or equivalently [15] L p ∼ W ffiffiffiffiffiffiffiffi Z=t p. The persistence length of the curved region is independent of the Young modulus and increases when the thickness is reduced.

A simple model is presented for the description of steady uniform shear flow of granular material. The model is based on a stress fluctuation activated process. The basic idea is that shear between two particle layers induces fluctuations in the media that may trigger a shear at some other position. Based on this idea, a minimum model is derived and applied to different configurations of granular shear flow.

The behaviour of a granular material is closely related to the nature of the interactions between grains. In this chapter, we focus on these forces at the grain level. We first discuss solid contact, which is dominant in the case of dry granular media made of macroscopic particles (Section 2.1). The basics of Hertz elastic contact, solid friction and the rules of inelastic collisions between solid particles are given. We then discuss other kinds of interaction between grains such as electrostatic and adhesive forces, capillary cohesion and solid bridges (Section 2.2). The last part of the chapter gives a brief overview of the hydrodynamic forces produced on a particle immersed in a fluid (Section 2.3). Our aim in this chapter is to provide some background in contact physics and hydrodynamics that will be useful for our study of granular media. More detailed treatments can be found in the classical books given in the text. Solid contact forces The contact force between two dry grains is usually split into a normal force and a tangential force. The physical origin of these forces at the microscopic level involves many phenomena, such as surface roughness, local mechanical properties (elasticity, plasticity, viscoelasticity) and physical and chemical properties (the presence of electrical charge, oxidation, temperature, the presence of lubricant film). In the following, we will not consider these microscopic features in detail but rather focus on the macroscopic laws of solid contact. At the macroscopic level, these laws are dominated by elastic repulsion (Hertz contact) and solid friction (Coulomb’s law).

Publisher version: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.138303 5 pages; International audience; The drag force experienced by a horizontal cylinder rotating around the vertical axis in a granular medium under gravity is experimentally investigated. We show that for deeply buried objects, the drag force dramatically drops after half a turn, as soon as the cylinder crosses its own wake. Whereas the drag during the first half turn increases linearly with the depth, the drag after several rotations appears to be independent of depth, in contradiction with the classical frictional picture stipulating that the drag is proportional to the hydrostatic pressure. We systematically study how the saturated drag force scales with the control parameters and show that this effect may be used to drill deeply in a granular medium without developing high torques.

International audience; We describe a new spreading regime during the drop impact of model yield-stress fluids (Carbopol microgel solutions) on rough hydrophobic surfaces, in a range of parameters where classical Newtonian drops usually splash. For large surface roughness and high impact velocity, we observe that the maximal inertial spreading diameter of the drops can be as much as twice larger than on smooth surfaces in the same conditions, corresponding to apparent basal friction reductions of more than 80%. We interpret this large drag reduction using a simple energy balance model and a dynamic slip length that depends on both the surface roughness and the drop's dynamics.

International audience; Although they lack muscle, plants have evolved a remarkable range of mechanisms to create motion, from the slow growth of shoots to the rapid snapping of carnivorous plants and the explosive rupture of seed pods. Here we review the key fluid mechanics principles used by plants to achieve movements, summarizing current knowledge and recent discoveries. We begin with a brief overview of water transport and material properties in plants and emphasize that the poroelastic timescale of water diffusion through soft plant tissue imposes constraints on the possible mechanisms for motion. We then discuss movements that rely only on the transport of water, from irreversible growth to reversible swelling/shrinking due to osmotic or humidity gradients. We next show how plants use mechanical instabilities—snap buckling, cavitation, and fracture—to speed up their movements beyond the limits imposed by simple hydraulic mechanisms. Finally, we briefly discuss alternative schemes, involving capillarity or complex fluids.

We experimentally investigate how a long granular pile confined in a narrow channel destabilizes when it is inclined above the angle of repose. A uniform flow then develops, which is localized at the free surface. It first accelerates before reaching a steady uniform regime. During this process, an apparent erosion is observed and the thickness of the flowing layer increases. We precisely study the evolution of the vertical velocity profile in this transient regime. The measurements are compared with the prediction of a visco-plastic model [P. Jop, Y. Forterre and O. Pouliquen, Nature 441, 727 (2006)], Comment: 5 pages, 5 figures, to be published in Physics of Fluids

In this paper we study the steady uniform flows that develop when granular material is released from a hopper on top of a static pile in a channel. We more specifically focus on the role of side walls by carrying out experiments in setup of different widths, from narrow channels 20 particle diameters wide to channels 600 particle diameters wide. Results show that steady flows on pile are entirely controlled by side wall effects. A theoretical model, taking into account the wall friction and based on a simple local constitutive law recently proposed for other granular flow configurations (GDR MiDi 2004), gives predictions in quantitative agreement with the measurements. This result gives new insights in our understanding of free surface granular flows and strongly supports the relevance of the constitutive law proposed., a forgotten square root in Appendix B (Eq B4), and corrected coefficients in Appendix C; 25 pages, 17 figures, published in J. Fluid Mech

A simple model is presented for the description of steady uniform shear flow of granular material. The model is based on a stress fluctuation activated process. The basic idea is that shear between two particle layers induces fluctuations in the media that may trigger a shear at some other position. Based on this idea, a minimum model is derived and applied to different configurations of granular shear flow.

Published version: http://scitation.aip.org/content/aip/journal/pof2/26/4/10.1063/1.4869859; International audience; The paper presents an experimental and numerical study of the forces experienced by a cylinder moving horizontally in a granular medium under gravity. Despite the symmetry of the object, a strong lift force is measured. Whereas the drag force increases linearly with depth, the lift force is shown to saturate at depths much greater than the cylinder diameter, and to scale like the buoyancy with a large amplification factor of order 20. The origin of this high lift force is discussed based on the stress distribution measured in discrete numerical simulations. The lift force comes from the gravitational pressure gradient, which breaks the up/down symmetry and strongly modifies the flow around the obstacle compared to the case without pressure gradient.

In a recent article (Forterre, PRL, 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we have proposed an instability mechanism based on the coupling between the flow and the granular temperature in rapid granular flows. In order to investigate the relevance of the proposed mechanism, we perform in the present paper a three-dimensional linear stability analysis of steady uniform flows down inclined planes using the kinetic theory of granular flows. We show that in a wide range of parameters, steady uniform flows are unstable under transverse perturbations. The structure of the unstable modes are in qualitative agreement with the experimental observations. This theoretical analysis shows that the kinetic theory is able to capture the formation of longitudinal vortices and validates the instability mechanism., 27 pages, 13 figures, submitted to J. Fluid. Mech

The problem of the spreading of a granular mass released at the top of a rough inclined plane was investigated. We experimentally measure the evolution of the avalanche from the initiation up to the deposit using a Moir\'e image processing technique. The results are quantitatively compared with the prediction of an hydrodynamic model based on depth averaged equations. In the model, the interaction between the flowing layer and the rough bottom is described by a non trivial friction force whose expression is derived from measurements on steady uniform flows. We show that the spreading of the mass is quantitatively predicted by the model when the mass is released on a plane free of particles. When an avalanche is triggered on an initially static layer, the model fails in quantitatively predicting the propagation but qualitatively captures the evolution., Comment: 19 pages, 10 figures, to be published in J. Fluid Mech

We present a new instability observed in rapid granular flows down rough inclined planes. For high inclinations and flow rates, the free surface of the flow experiences a regular deformation in the transverse direction. Measurements of the surface velocities imply that this instability is associated with the formation of longitudinal vortices in the granular flow. From the experimental observations, we propose a mechanism for the longitudinal vortex formation based on the concept of granular temperature., Comment: 4 pages, 4 figures

International audience; Long-surface-wave instability in dense granular flows down inclined planes is analysed using recently proposed three-dimensional constitutive equations. A full linear stability analysis of the local governing equations is performed and compared to previous experimental results obtained with glass beads. We show that the proposed rheology is able to capture all the features of the instability quantitatively. In particular, it predicts well the behaviour and scaling for the cutoff frequency of the instability observed in the experiments. This result gives strong support for the three-dimensional rheology proposed and suggests new terms in the Saint-Venant equations used to describe free-surface granular flows.

International audience; The jamming transition is accompanied by a rich phenomenology such as hysteresis or nonlocal effects that is still not well understood. Here, we experimentally investigate a model frictionless granular layer flowing down an inclined plane as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis of the avalanche angle, yet the layer stability increases as it gets thinner. Steady rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting the idea that nonlocal effects are the consequence of the usual finite-size effects associated with the presence of a critical point. This collapse indicates that the so-called isostatic length l∗, the scale on which pinning a boundary freezes all remaining floppy modes, governs the effect of boundaries on flow and rules out other propositions made in the past.