Surface instabilities generated by a slider pulled across a granular bed.

We report an instability of a slider slowly dragged at the surface of a granular bed in a quasistatic regime. The boat-shaped slider sits on the granular medium under its own weight and is free to translate vertically and to rotate around the pitch axis while a constant horizontal speed is imposed. For a wide range of parameters (mass, length, shape, velocity) a regular pattern of peaks and troughs spontaneously emerges as the slider travels forward. This instability is studied through experiments using a conveyor belt and by means of two-dimensional discrete elements method simulations. We show that the wavelength and amplitude of the pattern scale as the length of the slider. We also observe that the ripples disappear for low and high masses, indicating an optimal confining pressure. The effect of the shape, more specifically the inclination of the front spatula, is studied and found to drastically influence both the wavelength and the amplitude. Finally, we show that the mechanical details (friction, cohesion) of the contact point between the slider and the pulling device is critical and remains to be fully understood.

How dirt cones form on glaciers: Field observation, laboratory experiments, and modeling.

Dirt cones are meter-scale structures encountered at the surface of glaciers, which consist of ice cones covered by a thin layer of ashes, sand, or gravel, and which form naturally from an initial patch of debris. In this article, we report field observations of cone formation in the French Alps, laboratory-scale experiments reproducing these structures in a controlled environment, and two-dimensional discrete-element-method-finite-element-method numerical simulations coupling the grain mechanics and thermal effects. We show that cone formation originates from the insulating properties of the granular layer, which reduces ice melting underneath as compared to bare ice melting. This differential ablation deforms the ice surface and induces a quasistatic flow of grains that leads to a conic shape, as the thermal length become small compared to the structure size. The cone grows until it reaches a steady state in which the insulation provided by the dirt layer exactly compensates for the heat flux coming from the increased external surface of the structure. These results allowed us to identify the key physical mechanisms at play and to develop a model able to quantitatively reproduce the various field observations and experimental findings.

Sublimation-driven morphogenesis of Zen stones on ice surfaces.

In this article, the formation of Zen stones on frozen lakes and the shape of the resulting pedestal are elucidated. Zen stones are natural structures in which a stone, initially resting on an ice surface, ends up balanced atop a narrow ice pedestal. We provide a physical explanation for their formation, sometimes believed to be caused by the melting of the ice. Instead, we show that slow surface sublimation is indeed the physical mechanism responsible for the differential ablation. Far from the stone, the sublimation rate is governed by the diffuse sunlight, while in its vicinity, the shade it creates inhibits the sublimation process. We reproduced the phenomenon in laboratory-scale experiments conducted in a lyophilizer and studied the dynamics of the morphogenesis. In this apparatus, which imposes controlled constant sublimation rate, a variety of model stones consisting of metal disks was used, which allows us to rule out the possible influence of the thermal conduction in the morphogenesis process. Instead, we show that the stone only acts as an umbrella whose shade hinders the sublimation, hence protecting the ice underneath, which leads to the formation of the pedestal. Numerical simulations, in which the local ablation rate of the surface depends solely on the visible portion of the sky, allow us to study the influence of the shape of the stone on the formation of the ice foot. Finally, we show that the far-infrared black-body irradiance of the stone itself leads to the formation of a depression surrounding the pedestal.

Onset of Glacier Tables.

A glacier table consists of a rock supported by a slender column of ice and form naturally on glaciers. We investigate the onset of their formation at a smaller scale in a controlled environment. Depending on the size and thermal conductivity of a cap, it can either form of a table standing on an ice foot, or sink into the ice block. A one-dimension conduction model shows that the differential ice melting is controlled by a competition between two effects: a geometrical amplification, and a heat flux reduction due to the higher temperature of the cap as compared to the ice. Our model captures the transition between the two regimes and identifies a dimensionless number which controls the onset of glacier tables formation.

Particle size segregation in two-dimensional circular granular aggregates.

Although many previous studies have focused on the Brazil nut effect, segregation in a self-gravitating circular aggregate remains relatively unexplored. In this paper, size segregation in a two-dimensional assembly of grains in a circular geometry is studied through discrete element method (DEM) numerical simulations. We show that radial segregation within an asteroid submitted to periodic perturbations is not limited to the surface but also occurs in its core. The characteristic time and the overall efficiency of the segregation mechanism are studied as the intensity of the perturbation, the frictional properties, and rotational freedom of individual grains are varied.

Propelled Strings: Rising from Friction.

The shape of closed strings and chains propelled at a constant velocity and launched at an angle relative to gravity is studied experimentally, theoretically, and numerically. At low velocity, strings adopt a shape close to the well-known catenary, while at high velocity, they can rise to a nearly horizontal profile. We show that the latter regime can be counterintuitively attributed to aerodynamic effects, although the ambient air exerts no lift on a string moving longitudinally along its profile. A theoretical approach along with numerical simulations confirms these observations and allows one to predict the shape of any closed string or chain. Moreover, depending of the regime, waves rising from any local perturbation along the string may travel either upstream or downstream and seem to die out at the turning point. We show that these observations can be explained by the tension profile along the string, which strongly depends on the aerodynamic effects relative to the weight, and our theoretical analysis allows us to predict the position of the wave front.

Hydrodynamics control shear-induced pattern formation in attractive suspensions.

Dilute suspensions of repulsive particles exhibit a Newtonian response to flow that can be accurately predicted by the particle volume fraction and the viscosity of the suspending fluid. However, such a description fails when the particles are weakly attractive. In a simple shear flow, suspensions of attractive particles exhibit complex, anisotropic microstructures and flow instabilities that are poorly understood and plague industrial processes. One such phenomenon, the formation of log-rolling flocs, which is ubiquitously observed in suspensions of attractive particles that are sheared while confined between parallel plates, is an exemplar of this phenomenology. Combining experiments and discrete element simulations, we demonstrate that this shear-induced structuring is driven by hydrodynamic coupling between the flocs and the confining boundaries. Clusters of particles trigger the formation of viscous eddies that are spaced periodically and whose centers act as stable regions where particles aggregate to form flocs spanning the vorticity direction. Simulation results for the wavelength of the periodic pattern of stripes formed by the logs and for the log diameter are in quantitative agreement with experimental observations on both colloidal and noncolloidal suspensions. Numerical and experimental results are successfully combined by means of rescaling in terms of a Mason number that describes the strength of the shear flow relative to the rupture force between contacting particles in the flocs. The introduction of this dimensionless group leads to a universal stability diagram for the log-rolling structures and allows for application of shear-induced structuring as a tool for assembling and patterning suspensions of attractive particles.

Stability Analysis of an Array of Magnets: When Will It Jump?

A bidimensional array of magnets whose magnetic moments share the same vertical orientation, and lying on a planar surface, can be gradually compacted. As the density reaches a threshold, the assembly becomes unstable, and the magnets violently pop out of plane. In this Letter, we investigate experimentally and theoretically the maximum packing fraction (or density) of a bidimensional planar assembly of identical cylindrical magnets. We show that the instability can be attributed to local fluctuations of the altitude of the magnets on the planar surface. The maximum density is theoretically predicted assuming dipolar interactions between the magnets and is in excellent agreement with experimental results using a variety of cylindrical magnets.

Ion pairing controls rheological properties of "processionary" polyelectrolyte hydrogels.

We demonstrated recently that polyelectrolytes with cationic moieties along the chain and a single anionic head are able to form physical hydrogels due to the reversible nature of the head-to-body ionic bond. Here we generate a variety of such polyelectrolytes with various cationic moieties and counterion combinations starting from a common polymeric platform. We show that the rheological properties (shear modulus, critical strain) of the final hydrogels can be modulated over three orders of magnitude depending on the cation/anion pair. Our data fit remarkably well within a scaling model involving a supramolecular head-to-tail single file between cross-links, akin to the behaviour of pine-processionary caterpillar. This model allows the quantitative measure of the amount of counterion condensation from standard rheology procedure.

Grains unchained: local fluidization of a granular packing by focused ultrasound.

We report experimental results on the dynamics of a granular packing submitted to high-intensity focused ultrasound. Acoustic radiation pressure is shown to remotely induce local rearrangements within a pile as well as global motion around the focal spot in an initially jammed system. We demonstrate that this fluidization process is intermittent for a range of acoustic pressures and hysteretic when the pressure is cycled. Such a first-order-like unjamming transition is reproduced in numerical simulations in which the acoustic pressure field is modeled by a localized external force. Further analysis of the simulated packings suggests that in the intermittent regime unjamming is not associated with any noticeable prior structural signature. A simple two-state model based on effective temperatures is proposed to account for these findings.

Multiple yielding processes in a colloidal gel under large amplitude oscillatory stress.

Fatigue refers to the changes in material properties caused by repeatedly applied loads. It has been widely studied for, e.g., construction materials, but much less has been done on soft materials. Here, we characterize the fatigue dynamics of a colloidal gel. Fatigue is induced by large amplitude oscillatory stress (LAOStress), and the local displacements of the gel are measured through high-frequency ultrasonic imaging. We show that fatigue eventually leads to rupture and fluidization. We evidence four successive steps associated with these dynamics: (i) the gel first remains solid, (ii) it then slides against the walls, (iii) the bulk of the sample becomes heterogeneous and displays solid-fluid coexistence, and (iv) it is finally fully fluidized. It is possible to homogeneously scale the duration of each step with respect to the stress oscillation amplitude σ0. The data are compatible with both exponential and power-law scalings with σ0, which hints at two possible interpretations of delayed yielding in terms of activated processes or of the Basquin law. Surprisingly, we find that the model parameters behave nonmonotonically as we change the oscillation frequency and/or the gel concentration.

Mediating gel formation from structurally controlled poly(electrolytes) through multiple "head-to-body" electrostatic interactions.

Tuning the chain-end functionality of a short-chain cationic homopolymer, owing to the nature of the initiator used in the atom transfer radical polymerization (ATRP) polymerization step, can be used to mediate the formation of a gel of this poly(electrolyte) in water. While a neutral end group gives a solution of low viscosity, a highly homogeneous gel is obtained with a phosphonate anionic moiety, as characterized by rheometry and diffusion nuclear magnetic resonance (NMR). This novel type of supramolecular control over poly(electrolytic) gel formation could find potential use in a variety of applications in the field of electro-active materials.

Timescales in creep and yielding of attractive gels.

The stress-induced yielding scenario of colloidal gels is investigated under rough boundary conditions by means of rheometry coupled with local velocity measurements. Under an applied shear stress σ, the fluidization of gels made of attractive carbon black particles dispersed in a mineral oil is shown to involve a previously unreported shear rate response γ dot above(t) characterized by two well-defined and separated timescales τc and τf. First γ dot above decreases as a weak power law strongly reminiscent of the primary creep observed in numerous crystalline and amorphous solids, coined the "Andrade creep". We show that the bulk deformation remains homogeneous at the micron scale, which demonstrates that whether plastic events take place or whether any shear transformation zone exists, such phenomena occur at a smaller scale. As a key result of this paper, the duration τc of this creep regime decreases as a power law of the viscous stress, defined as the difference between the applied stress and the yield stress σc, i.e. τc ∼ (σ - σc)(-ß), with ß = 2-3 depending on the gel concentration. The end of this first regime is marked by a jump of the shear rate by several orders of magnitude, while the gel slowly slides as a solid block experiencing strong wall slip at both walls, despite rough boundary conditions. Finally, a second sudden increase of the shear rate is concomitant with the full fluidization of the material which ends up being homogeneously sheared. The corresponding fluidization time τf robustly follows an exponential decay with the applied shear stress, i.e. τf = τ0 exp(-σ/σ0), as already reported for smooth boundary conditions. Varying the gel concentration C in a systematic fashion shows that the parameter σ0 and the yield stress σc exhibit similar power-law dependences with C. Finally, we highlight a few features that are common to attractive colloidal gels and to solid materials by discussing our results in the framework of theoretical approaches of solid rupture (kinetic, fiber bundle, and transient network models).

Ultrafast ultrasonic imaging coupled to rheometry: principle and illustration.

We describe a technique coupling standard rheology and ultrasonic imaging with promising applications to characterization of soft materials under shear. Plane wave imaging using an ultrafast scanner allows to follow the local dynamics of fluids sheared between two concentric cylinders with frame rates as high as 10 000 images per second, while simultaneously monitoring the shear rate, shear stress, and viscosity as a function of time. The capacities of this "rheo-ultrasound" instrument are illustrated on two examples: (i) the classical case of the Taylor-Couette instability in a simple viscous fluid and (ii) the unstable shear-banded flow of a non-Newtonian wormlike micellar solution.

Modeling a washboard road: from experimental measurements to linear stability analysis.

When submitted to the repeated passages of vehicles unpaved roads made of sand or gravel can develop a ripply pattern known as washboard or corrugated road. We propose a stability analysis based on experimental measurements of the force acting on a blade (or plow) dragged on a circular sand track and show that a linear model is sufficient to describe the instability near onset. The relation between the trajectory of the plow and the profile of the sand bed left after its passage is studied experimentally. The various terms in the expression of the lift force created by the flow of granular material on the plow are determined up to first order by imposing a sinusoidal trajectory to the blade on an initially flat sand bed, as well as by imposing a horizontal trajectory on an initially rippled sand bed. Our model recovers all the previously observed features of washboard road and accurately predicts the most unstable wavelength near onset as well as the critical velocity for the instability.

Lift and drag forces on an inclined plow moving over a granular surface.

We studied the drag and lift forces acting on an inclined plate while it is dragged on the surface of a granular media, both in experiment and in numerical simulation. In particular, we investigated the influence of the horizontal velocity of the plate and its angle of attack. We show that a steady wedge of grains is moved in front of the plow and that the lift and drag forces are proportional to the weight of this wedge. These constants of proportionality vary with the angle of attack but not (or only weakly) on the velocity. We found a universal effective friction law that accounts for the dependence on all the above-mentioned parameters. The stress and velocity fields are calculated from the numerical simulations and show the existence of a shear band under the wedge and that the pressure is nonhydrostatic. The strongest gradients in stress and shear occur at the base of the plow where the dissipation rate is therefore highest.

Scaling and dynamics of washboard roads.

Granular surfaces subjected to forces due to rolling wheels develop ripples above a critical speed. The resulting pattern, known as washboard or corrugated road, is common on dry unpaved roads. We investigated this phenomenon theoretically and experimentally using laboratory-scale apparatus and beds of dry sand. A thick layer of sand on a circular track was forced by a rolling wheel on an arm whose weight and moment of inertia could be varied. We compared the ripples made by the rolling wheel to those made using a simple inclined plow blade. We investigated the dependence of the critical speed on various parameters and described a scaling argument that leads to a dimensionless ratio, analogous to the hydrodynamic Froude number, which controls the instability. This represents the crossover between conservative dynamic forces and dissipative static forces. Above onset wheel-driven ripples move in the direction of motion of the wheel, but plow-driven ripples move in the reverse direction for a narrow range of Froude numbers.

Recent advances in simulations of grains in a rotating drum.

The discrete elements method (DEM) has been widely used in the past decade to study a wide variety of granular systems. The use of numerical simulations constitutes an interesting alternative to the experiment as they can shed new light on a phenomenon as they can overcome experimental obstacles. A lot of granular phenomena can be studied in 2D or with a limited number of grains but the peculiar phenomenon of axial segregation (or banding) is 3-dimensional by nature and requires a large number of grains. Only very recently has it been made possible to simulate 3D systems on a large scale. This highlight reviews recent work on this topic and attempts to show what knowledge is gained from DEM numerical simulations. The perspectives on the future benefit of this method as well as the challenges it faces are discussed.

Washboard road: the dynamics of granular ripples formed by rolling wheels.

We report laboratory experiments on rippled granular surfaces formed under rolling wheels. Ripples appear above a critical speed and drift slowly in the driving direction. Ripples coarsen as they saturate and exhibit ripple creation and destruction events. All of these effects are captured qualitatively by 2D soft-particle simulations in which a disk rolls over smaller disks in a periodic box. The simulations show that compaction and segregation are inessential to the ripple phenomenon. We describe a simplified scaling model which gives some insight into the mechanism of the instability.

S shape of a granular pile in a rotating drum.

The shape of a granular pile in a rotating drum is investigated. Using discrete elements method (DEM) simulations we show that the "S shape" obtained for high rotation speed can be accounted for by the friction on the end plates. A theoretical model which accounts for the effect of the end plates is presented and the equation of the shape of the free surface is derived. The model reveals a dimensionless number which quantifies the influence of the end plates on the shape of the pile. Finally, the scaling laws of the system are discussed and numerical results support our conclusions.