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We experimentally revisite the flow down an inclined plane of dense granular suspensions, with particles of sizes in the micron range, for which thermal fluctuations cannot be ignored. Using confocal microscopy on a miniaturized set-up, we observe that, in contrast with standard granular rheology, the flow profiles strongly depend on the particles size. Also, suspensions composed of small enough particles flow at infinitesimal inclinations. From the velocity measurements, an effective rheology is extracted in terms of a friction coefficient as a fonction of the dimensionless shear rate (the viscous number), and of the particle pressure normalized by the thermal pressure. Inspired by a previous work [1], a phenomenological model based on the sum of a thermal contribution describing the glass transition and an athermal contribution capturing the jamming transition is developed, which reproduces well the experimental observations. The model predicts the existence of a glassy friction angle lower than the granular athermal friction angle, a signature of the glass transition in the framework of a pressure imposed rheology.

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

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.

Gravity is a major cue for the proper growth and development of plants. The response of plants to gravity implies starch-filled plastids, the statoliths, which sediments at the bottom of the gravisensing cells, the statocytes. Statoliths are assumed to modify the transport of the growth hormone, auxin, by acting on specific auxin transporters, PIN proteins. However, the complete gravitropic signaling pathway from the intracellular signal associated to statoliths to the plant bending is still not well understood. In this article, we build on recent experimental results showing that statoliths do not act as gravitational force sensor, but as position sensor, to develop a bottom-up theory of plant gravitropism. The main hypothesis of the model is that the presence of statoliths modifies PIN trafficking close to the cell membrane. This basic assumption, coupled with auxin transport and growth in an idealized tissue made of a one-dimensional array of cells, recovers several major features of the gravitropic response of plants. First, the model provides a new interpretation for the response of a plant to a steady stimulus, the so-called sine-law of plant gravitropism. Second, it predicts the existence of a gravity-independent memory process as observed recently in experiments studying the response to transient stimulus. The model suggests that the timescale of this process is associated to PIN turnover, calling for new experimental studies.

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.

We study the impact between a plate and a drop of non-colloidal solid particles suspended in a Newtonian liquid, with a specific attention to the case when the particle volume fraction, $\phi$, is close to - or even exceeds - the critical volume fraction, $\phi_c$, at which the steady effective viscosity of the suspension diverges. We use a specific concentration protocol together with an accurate determination of $\phi$ for each drop and we measure the deformation $\beta$ for different liquid viscosities, impact velocities and particle sizes. At low volume fractions, $\beta$ is found to follow closely an effective Newtonian behavior, which we determine by documenting the low deformation limit for a highly viscous Newtonian drop and characterizing the effective shear viscosity of our suspensions. By contrast, whereas the effective Newtonian approach predicts that $\beta$ vanishes at $\phi_c$, a finite deformation is observed for $\phi>\phi_c$. This finite deformation remains controlled by the suspending liquid viscosity and increases with increasing particle size, which suggests that the dilatancy of the particle phase is a key factor of the dissipation process close to and above $\phi_c$., Comment: Submitted to JFM

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

Experiments on shoot gravitropism at the plant and cell scale reveal the existence of a memory process and provide a unifying framework for predicting the bending response of shoots to arbitrary gravi-stimulations., Gravity is a major abiotic cue for plant growth. However, little is known about the responses of plants to various patterns of gravi-stimulation, with apparent contradictions being observed between the dose-like responses recorded under transient stimuli in microgravity environments and the responses under steady-state inclinations recorded on earth. Of particular importance is how the gravitropic response of an organ is affected by the temporal dynamics of downstream processes in the signalling pathway, such as statolith motion in statocytes or the redistribution of auxin transporters. Here, we used a combination of experiments on the whole-plant scale and live-cell imaging techniques on wheat coleoptiles in centrifuge devices to investigate both the kinematics of shoot-bending induced by transient inclination, and the motion of the statoliths in response to cell inclination. Unlike previous observations in microgravity, the response of shoots to transient inclinations appears to be independent of the level of gravity, with a response time much longer than the duration of statolith sedimentation. This reveals the existence of a memory process in the gravitropic signalling pathway, independent of statolith dynamics. By combining this memory process with statolith motion, a mathematical model is built that unifies the different laws found in the literature and that predicts the early bending response of shoots to arbitrary gravi-stimulations.

International audience; Shear-thickening is observed in dense particulate suspensions and consists in a severe increase of the suspension viscosity above an onset stress. This behavior, which is very useful for certain technological applications, can also be an issue in some industrial processes. Shear thickening was considered a puzzle for a long time. It can now be explained as a frictional transition thanks to a recent theoretical model. This paper presents this model and its numerical and experimental validations. Different applications which may emerge from the understanding of this phenomenon are then discussed.; Le rhéo-épaississement est un phénomène observé dans certaines suspensions denses de particules. Il consiste en une augmentation parfois brutale de leur viscosité lorsqu'elles sont soumises à une forte contrainte. Ce comportement, très utile pour certaines applications tech-nologiques, peut aussi s'avérer problématique dans certains processus industriels. Longtemps resté une énigme, le rhéo-épaississement est désormais décrit de façon cohérente par le modèle de transition frictionnelle. Cet article présente ce modèle ainsi que les études numériques et expérimentales qui le valident. Sont ensuite abordées différentes perspectives d'applications offertes par la compréhension de ce phénomène. Résumé Shear-thickening is observed in dense particulate suspensions and consists in a severe increase of the suspension viscosity above an onset stress. This behavior, which is very useful for certain technological applications, can also be an issue in some industrial processes. Shear thickening was considered a puzzle for a long time. It can now be explained as a frictio-nal transition thanks to a recent theoretical model. This paper presents this model and its numerical and experimental validations. Different applications which may emerge from the understanding of this phenomenon are then discussed.

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.

International audience; In order to better understand the mechanism governing segregation in granular flows, the force experienced by a large particle embedded in a granular flow made of small particles is studied using discrete numerical simulations. An empirical expression of the segregation force is proposed as a function of the stress distribution.

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.

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., e.g. 11 pages, 4 figures, 3 supplemetal figures, one supplemental table

ACL-11-48; International audience; The pitcher-shaped leaves of Nepenthes carnivorous plants have been considered as pitfall traps that essentially rely on slippery surfaces to capture insects. But a recent study of Nepenthes rafflesiana has shown that the viscoelasticity of the digestive fluid inside the pitchers plays a key role. Here, we investigated whether Nepenthes species exhibit diverse trapping strategies. We measured the amount of slippery wax on the pitcher walls of 23 taxa and the viscoelasticity of their digestive liquid and compared their retention efficiency on ants and flies. The amount of wax was shown to vary greatly between species. Most mountain species exhibited viscoelastic digestive fluids while water-like fluids were predominant in lowland species. Both characteristics contributed to insect trapping but wax was more efficient at trapping ants while viscoelasticity was key in trapping insects and was even more efficient than wax on flies. Trap waxiness and fluid viscoelasticity were inversely related, suggesting the possibility of an investment trade-off for the plants. Therefore Nepenthes pitcher plants do not solely employ slippery devices to trap insects but often employ a viscoelastic strategy. The entomofauna specific to the plant's habitat may exert selective pressures, favouring one trapping strategy at the expense of the other.

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.

Gravity perception plays a key role in how plants develop and adapt to environmental changes. However, more than a century after the pioneering work of Darwin, little is known on the sensing mechanism. Using a centrifugal device combined with growth kinematics imaging, we show that shoot gravitropic responses to steady levels of gravity in four representative angiosperm species is independent of gravity intensity. All gravitropic responses tested are dependent only on the angle of inclination from the direction of gravity. We thus demonstrate that shoot gravitropism is stimulated by sensing inclination not gravitational force or acceleration as previously believed. This contrasts with the otolith system in the internal ear of vertebrates and explains the robustness of the control of growth direction by plants despite perturbations like wind shaking. Our results will help retarget the search for the molecular mechanism linking shifting statoliths to signal transduction.

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.

National audience; Dépourvues de muscles, certaines plantes mettent en œuvre des mouvements dont la fulgurance est comparable à celle des animaux. Nous montrons dans cet article que beaucoup de ces mouvements, nécessités par la reproduction ou la nutrition, ont la même base physique : une instabilité mécanique qui libère de l’énergie élastique stockée. Deux grands types d’instabilités mécaniques sont utilisés par les plantes pour amplifier la vitesse de leur mouvement : les ruptures solides ou liquides (cavitation) pour la propulsion des graines ou des spores de fougères, et les instabilités de flambage élastique pour les pièges des plantes carnivores, telles que la Dionée ou l’utriculaire.

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.

Most granular flows encountered in nature and industry lie between the quasistatic and gaseous regimes seen in the previous chapters. In this intermediate ‘liquid’ regime, particles remain closely packed and interact both by collision and through long-lived contacts. Understanding and modelling the flow of dense granular media is challenging and many questions remain to be answered, despite important advances having been made during the last decade. In this chapter, we first present the basic features of dense granular flows (Section 6.1), before focusing on the rheology of this peculiar liquid (Section 6.2). A phenomenological constitutive law that is based on dimensional analysis is presented, in which the medium is described as a viscoplastic fluid with a frictional behaviour. The success and limitations of this approach are then discussed, in particular close to the solid–liquid transition where complex collective behaviours are observed. The second part of the chapter presents a hydrodynamic description of dense flows that is valid for a shallow layer flowing under gravity (the Saint-Venant equations) (Section 6.3). This depth-averaged approach enables one to gather the complex rheology into a single basal friction term and is commonly used in geophysics to describe rock avalanches and landslides. We close the chapter with a presentation of the phenomenon of size segregation, which occurs when the medium is composed of particles of different sizes. The consequences of segregation for polydisperse granular flows in various configurations are presented (Section 6.4).

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).

Sand, rice, sugar, snow, cement... Although ubiquitous in our daily lives, granular media still challenge engineers and fascinate researchers. This book provides the state-of-the-art of the physics of granular media and recent advances in the field. The book presents the fundamental properties of granular materials: interactions between grains; solid, liquid and gaseous behaviours; coupling with a fluid; and sediment transport and formation of geological structures. Descriptions of the phenomena combine qualitative and formal arguments, coming from areas as diverse as elasticity, plasticity, statistical physics, fluid mechanics and geomorphology. Many examples of the astonishing behaviours of granular media are presented, including avalanches, segregation, dune song and quicksand. This book is ideal for graduate students and researchers in physics, applied mathematics and engineering.

International audience; The ability of plants to move is central to many physiological processes from development to tropisms, from nutrition to reproduction. The movement of plants or plant parts occurs over a wide range of sizes and time scales. This review summarizes the main physical mechanisms plants use to achieve motility, highlighting recent work at the frontier of biology and physics on rapid movements. Emphasis is given to presenting in a single framework pioneering biological studies of water transport and growth with more recent physics research on poroelasticity and mechanical instabili-ties. First, the basic osmotic and hydration/dehydration motors are described that contribute to movement by growth and reversible swelling/shrinking of cells and tissues. The speeds of these water-driven movements are shown to be ultimately limited by the transport of water through the plant body. Some plant structures overcome this hydraulic limit to achieve much faster movement by using a mechanical instability. The principle is to impose an 'energy barrier' to the system, which can originate from geometrical constraint or matter cohesion, allowing elastic potential energy to be stored until the barrier is overcome, then rapidly transformed into kinetic energy. Three of these rapid motion mechanisms have been elucidated recently and are described here: the snapping traps of two carnivorous plants, the Venus flytrap and Utricularia, and the catapult of fern sporangia. Finally, movement mechanisms are reconsidered in the context of the timescale of important physiological processes at the cellular and molecular level.

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.

International audience; – NousétudionsNousétudions expérimentalement la dynamique de moussesélastiquesmoussesélastiques (mousse ouverte flexible en polyuréthane) plongées dans un fluide visqueux. La mousse est initialement comprimée dans une direction puis brutalement relâchée. Le champ de vitesse de la mousse et la pression du fluide interstitiel (pression de pore) sont mesurés au cours de la décompaction du système. Pour des petites compactions initiales, on observe que la mousse relaxe exponentiellement vers sonétatsonétat d'´ equilibre, avec une dynamique diffusive en accord quantitatif avec les théories classiques de consolidation des sols. En revanche, pour des grandes compactions initiales, la dynamique de relaxation est inhomogène et se déroulè a travers un front de décompaction. Un modèle diphasique simple permet de prédire semi-quantitativement les observations et relie l'existence du front au caractère fortement non-linéaire de la réponse mécanique de la mousse. Mots clés : Poroélasticité / matériaux cellulaires / front Abstract – On the dynamics of poroelastic foams. We experimentally investigate the dynamics of soft polyurethane open foams immersed in viscous fluids. The elastic foam is initially compressed in one direction and then suddenly released. The velocity field of the foam and the dynamic pressure of the interstitial fluid (pore pressure) are measured during the swelling of the foam. For small initial compactions, the foams relax exponentially to equilibrium with a diffusive dynamics in quantitative agreements with classical theories of soil consolidation. On the other hand, for large initial compactions, the dynamics is strongly inhomogeneous and occurs through a localized decompaction front. A simple two-fluids model semi-quantitatively predicts the observations and links the existence of a localized front to the highly non-linear mechanical response of the foam.

International audience; From a biomechanical perspective, plants offer a fascinat- ing example of living systems capable of producing non- muscular movements (Skotheim and Mahadevan 2005; Dumais and Forterre, to be published). Although most of these movements are slow, some compete in speed with those observed in the animal kingdom and are involved in essential functions such as seed/pollen dispersal, defence and nutrition. Of these spectacular examples that have long fascinated scientists, the Venus flytrap (Figure 1(a)), for which the leaves snap together in a fraction of second to capture insects, has long been a paradigm for study. Recently, we have shown that this motion involves a snap- buckling instability due to the shell-like geometry of the leaves of the trap (Forterre et al. 2005). However, the origin of the active movement used by the plant to cross the instability threshold remains unknown. More generally, the physical mechanisms involved in rapid plant movements remain poorly understood, especially at the cell and tissue scale. Two main assumptions are found in the literature: (i) a rapid flow between the cells due to changes in osmotic pressure (Hill and Findlay 1981), (ii) a rapid cell expansion due to mechanical modifications (softening) in the cell wall (Williams and Bennett 1982). In both cases, the high-water pressure inside the plant cells is believed to play a central role. Our aim in this study was to measure in real time in-vivo mechanical and hydraulic properties of Venus flytrap cells (cell wall elasticity, cell membrane per- meability and cell water pressure) and to investigate the possible mechanisms for movements at the cell scale. To this end, we use a microfluidic pressure probe device, which applies a water flux inside a single cell while measuring the cell water pressure simultaneously (Steudle 1993).

We study how a shear band in a granular medium dramatically changes the mechanical behavior of the material further in the non sheared region. To this end, we carry out a microrheology experiment, where a constant force $F$ is applied to a small rod immersed outside the shear band. In the absence of a shear band, a critical force ${F}_{c}$ is necessary to move the intruder. When a shear band exists, the intruder moves even for a force $F$ less than the critical force ${F}_{c}$. We systematically study how the creep velocity ${V}_{\mathrm{creep}}$ of the rod varies with ${F}_{c}\ensuremath{-}F$ and with the distance to the shear band, and show that the behavior can be described by an Eyring-like activated process.

International audience; A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.