A frictional soliton controls the resistance law of shear-thickening suspensions in pipes.

Pipe flows are commonly found in nature and industry as an effective mean of transporting fluids. They are primarily characterized by their resistance law, which relates the mean flow rate to the driving pressure gradient. Since Poiseuille and Hagen, various flow regimes and fluid rheologies have been investigated, but the behavior of shear-thickening suspensions, which jam above a critical shear stress, remains poorly understood despite important applications (e.g., concrete or food processing). In this study, we build on recent advances in the physics of shear-thickening suspensions to address their flow through pipes and establish their resistance law. We find that for discontinuously shear-thickening suspensions (large particule volume fractions), the flow rate saturates at high driving stress. Local pressure and velocity measurements reveal that this saturation stems from the emergence of a frictional soliton: a unique, localized, superdissipative, and backpropagating flow structure coexisting with the laminar frictionless flow phase observed at low driving stress. We characterize the remarkably steep effective rheology of the frictional soliton and show that it sets the resistance law at the whole pipe scale. These findings offer an unusual perspective on low-Reynolds suspension flows through pipes, intriguingly reminiscent of the transition to turbulence for simple fluids. They also provide a predictive law for the transport of such suspensions in pipe systems, with implications for a wide range of applications.

Nonlocal Effects Reflect the Jamming Criticality in Frictionless Granular Flows Down Inclines.

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.

An Integrative Model of Plant Gravitropism Linking Statoliths Position and Auxin Transport.

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.

Revealing the hierarchy of processes and time-scales that control the tropic response of shoots to 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.

Brownian Granular Flows Down Heaps.

We study the avalanche dynamics of a pile of micrometer-sized silica grains in water-filled microfluidic drums. Contrary to what is expected for classical granular materials, avalanches do not stop at a finite angle of repose. After a first rapid phase during which the angle of the pile relaxes to an angle θ_{c}, a creep regime is observed where the pile slowly flows until the free surface reaches the horizontal. This relaxation is logarithmic in time and strongly depends on the ratio between the weight of the grains and the thermal agitation (gravitational Péclet number). We propose a simple one-dimensional model based on Kramers' escape rate to describe these Brownian granular avalanches, which reproduces the main observations.

Gravisensors in plant cells behave like an active granular liquid.

Plants are able to sense and respond to minute tilt from the vertical direction of the gravity, which is key to maintain their upright posture during development. However, gravisensing in plants relies on a peculiar sensor made of microsize starch-filled grains (statoliths) that sediment and form tiny granular piles at the bottom of the cell. How such a sensor can detect inclination is unclear, as granular materials like sand are known to display flow threshold and finite avalanche angle due to friction and interparticle jamming. Here, we address this issue by combining direct visualization of statolith avalanches in plant cells and experiments in biomimetic cells made of microfluidic cavities filled with a suspension of heavy Brownian particles. We show that, despite their granular nature, statoliths move and respond to the weakest angle, as a liquid clinometer would do. Comparison between the biological and biomimetic systems reveals that this liquid-like behavior comes from the cell activity, which agitates statoliths with an apparent temperature one order of magnitude larger than actual temperature. Our results shed light on the key role of active fluctuations of statoliths for explaining the remarkable sensitivity of plants to inclination. Our study also provides support to a recent scenario of gravity perception in plants, by bridging the active granular rheology of statoliths at the microscopic level to the macroscopic gravitropic response of the plant.

Revealing the frictional transition in shear-thickening suspensions.

Shear thickening in dense particulate suspensions was recently proposed to be driven by the activation of friction above an onset stress needed to overcome repulsive forces between particles. Testing this scenario represents a major challenge because classical rheological approaches do not provide access to the frictional properties of suspensions. Here we adopt a different strategy inspired by pressure-imposed configurations in granular flows that specifically gives access to this information. By investigating the quasi-static avalanche angle, compaction, and dilatancy effects in different nonbuoyant suspensions flowing under gravity, we demonstrate that particles in shear-thickening suspensions are frictionless under low confining pressure. Moreover, we show that tuning the range of the repulsive force below the particle roughness suppresses the frictionless state and also the shear-thickening behavior of the suspension. These results, which link microscopic contact physics to the suspension macroscopic rheology, provide direct evidence that the recent frictional transition scenario applies in real suspensions.

Inclination not force is sensed by plants during shoot gravitropism.

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.

Unifying Impacts in Granular Matter from Quicksand to Cornstarch.

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.

Origin of a depth-independent drag force induced by stirring in granular media.

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.

How a curved elastic strip opens.

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.

Slow, fast and furious: understanding the physics of plant movements.

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 instabilities. 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.

Giant drag reduction in complex fluid drops on rough hydrophobic surfaces.

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.

Depth-independent drag force induced by stirring in granular media.

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.

Slippery or sticky? Functional diversity in the trapping strategy of Nepenthes carnivorous plants.

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.

A non-local rheology for dense granular flows.

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.

A viscoelastic deadly fluid in carnivorous pitcher plants.

BACKGROUND: The carnivorous plants of the genus Nepenthes, widely distributed in the Asian tropics, rely mostly on nutrients derived from arthropods trapped in their pitcher-shaped leaves and digested by their enzymatic fluid. The genus exhibits a great diversity of prey and pitcher forms and its mechanism of trapping has long intrigued scientists. The slippery inner surfaces of the pitchers, which can be waxy or highly wettable, have so far been considered as the key trapping devices. However, the occurrence of species lacking such epidermal specializations but still effective at trapping insects suggests the possible implication of other mechanisms. METHODOLOGY/PRINCIPAL FINDINGS: Using a combination of insect bioassays, high-speed video and rheological measurements, we show that the digestive fluid of Nepenthes rafflesiana is highly viscoelastic and that this physical property is crucial for the retention of insects in its traps. Trapping efficiency is shown to remain strong even when the fluid is highly diluted by water, as long as the elastic relaxation time of the fluid is higher than the typical time scale of insect movements. CONCLUSIONS/SIGNIFICANCE: This finding challenges the common classification of Nepenthes pitchers as simple passive traps and is of great adaptive significance for these tropical plants, which are often submitted to high rainfalls and variations in fluid concentration. The viscoelastic trap constitutes a cryptic but potentially widespread adaptation of Nepenthes species and could be a homologous trait shared through common ancestry with the sundew (Drosera) flypaper plants. Such large production of a highly viscoelastic biopolymer fluid in permanent pools is nevertheless unique in the plant kingdom and suggests novel applications for pest control.

A constitutive law for dense granular flows.

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

How the Venus flytrap snaps.

The rapid closure of the Venus flytrap (Dionaea muscipula) leaf in about 100 ms is one of the fastest movements in the plant kingdom. This led Darwin to describe the plant as "one of the most wonderful in the world". The trap closure is initiated by the mechanical stimulation of trigger hairs. Previous studies have focused on the biochemical response of the trigger hairs to stimuli and quantified the propagation of action potentials in the leaves. Here we complement these studies by considering the post-stimulation mechanical aspects of Venus flytrap closure. Using high-speed video imaging, non-invasive microscopy techniques and a simple theoretical model, we show that the fast closure of the trap results from a snap-buckling instability, the onset of which is controlled actively by the plant. Our study identifies an ingenious solution to scaling up movements in non-muscular engines and provides a general framework for understanding nastic motion in plants.