Journey of an intruder through the fluidisation and jamming transitions of a dense granular media

We study experimentally the motion of an intruder dragged into an amorphous monolayer of horizontally vibrated grains at high packing fractions. This motion exhibits two transitions. The first transition separates a continuous motion regime at comparatively low packing fractions and large dragging force from an intermittent motion one at high packing fraction and low dragging force. Associated to these different motions, we observe a transition from a linear rheology to a stiffer response. We thereby call "fluidisation" this first transition. A second transition is observed within the intermittent regime, when the intruder's motion is made of intermittent bursts separated by long waiting times. We observe a peak in the relative fluctuations of the intruder's displacements and a critical scaling of the burst amplitudes distributions. This transition occurs at the jamming point characterized in a previous study and defined as the point where the static pressure (i.e. the pressure measured in the absence of vibration) vanishes. Investigating the motion of the surrounding grains, we show that below the fluidisation transition, there is a permanent wake of free volume behind the intruder. This transition is marked by the evolution of the reorganization patterns around the intruder, which evolve from compact aggregates in the flowing regime to long-range branched shapes in the intermittent regime, suggesting an increasing role of the stress fluctuations. Remarkably, the distributions of the kinetic energy of these reorganization patterns also exhibits a critical scaling at the jamming transition.Comment: 12 pages, 11 figure

The glass transition in a nutshell: a source of inspiration to describe the subcritical transition to turbulence

The starting point of the present work is the observation of possible analogies, both at the phenomenological and at the methodological level, between the subcritical transition to turbulence and the glass transition. Having recalled the phenomenology of the subcritical transition to turbulence, we review the theories of the glass transition at a very basic level, focusing on the history of their development as well as on the concepts they have elaborated. Doing so, we aim at attracting the attention on the above mentioned analogies, which we believe could inspire new developments in the theory of the subcritical transition to turbulence. We then briefly describe a model inspired by one of the simplest and most inspiring model of the glass transition, the so-called Random Energy Model, as a first step in that direction.Comment: 9 pages, 1 figure; to appear in a topical issue of Eur. Phys. J. E dedicated to Paul Mannevill

Experimental evidences of the Gardner phase in a granular glass

Analyzing the dynamics of a vibrated bi-dimensional packing of bidisperse granular discs below jamming, we provide evidences of a Gardner phase deep into the glass phase. To do so we perform several independent compression cycles within the same glass and show that the particles select different average vibrational positions at each cycle, while the neighborhood structure remains unchanged. We compute the mean square displacement as a function of the packing fraction and compare it with the average separation between the cages obtained for different compression cycles. Our results are fully compatible with recent numerical observations obtained for a mean field model of glass as well as for hard spheres in finite dimension. We also characterize the distribution of the cage order parameters. Here we note several differences from the numerical results, which could be attributed to activated processes and cage heterogeneities.Comment: 4 pages, 3 figure

Collective Motion in Active Materials: Model Experiments

In these lecture notes from the Les Houches School, we discuss collective motion in model experiments of active systems. We specifically discuss walking grains and colloidal rollers experiments. In both cases, we focus on the theoretical tools one can use to relate the knowledge of the dynamics at the particle scale to the large scale physics.Comment: 28 pages, published as Ch3 in Active Matter and Nonequilibrium Statistical Physics Lecture Notes of the Les Houches Summer School: Volume 112, September 201

Bulk elastic fingering instability in Hele-Shaw cells

We demonstrate experimentally the existence of a purely elastic fingering instability which arises when air penetrates into an elastomer confined in a Hele-Shaw cell. Fingers appear sequentially and propagate within the bulk of the material as soon as a critical strain, independent of the elastic modulus, is exceeded. Their width depends non-linearly on the distance between the confining glass plates. A key element in the driving force of the instability is the adhesion of layers of gels to the plates, which results in a considerable expense of elastic energy during the growth of the air bubble.Comment: Submitted to Physical Review letters; 5 pages; 6 figure

Collective Motion of Vibrated Polar Disks

We experimentally study a monolayer of vibrated disks with a built-in polar asymmetry which enables them to move quasi-balistically on a large persistence length. Alignment occurs during collisions as a result of self-propulsion and hard core repulsion. Varying the amplitude of the vibration, we observe the onset of large-scale collective motion and the existence of giant number fluctuations with a scaling exponent in agreement with the predicted theoretical value.Comment: 4 pages, 4 figure

Shear modulus and Dilatancy Softening in Granular Packings above Jamming

We investigate experimentally the mechanical response of a monolayer of bi-disperse frictional grains to an inhomogeneous shear perturbation across the jamming transition. We inflate an intruder inside the packing and use photo-elasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 0.001 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in : both the shear modulus and the dilatancy shear-soften at small strain until a critical strain is reached where effective linearity is recovered. The dependencies of the critical strain and the associated critical stresses on the distance from jamming are extracted via scaling analysis. We check that the constitutive laws, when applied to the equations governing mechanical equilibrium, lead to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition.Comment: 5 pages, 5 figure

Intensive thermodynamic parameters in nonequilibrium systems

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system has to satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.Comment: 17 pages, 5 figures; final version, with minor change

Two-phase flow in a chemically active porous medium

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.Comment: 13 pages, 10 figure