Non-local rheology in dense granular flows -- Revisiting the concept of fluidity

Granular materials belong to the class of amorphous athermal systems, like foams, emulsion or suspension they can resist shear like a solid, but flow like a liquid under a sufficiently large applied shear stress. They exhibit a dynamical phase transition between static and flowing states, as for phase transitions of thermodynamic systems, this rigidity transition exhibits a diverging length scales quantifying the degree of cooperatively. Several experiments have shown that the rheology of granular materials and emulsion is non-local, namely that the stress at a given location does not depend only on the shear rate at this location but also on the degree of mobility in the surrounding region. Several constitutive relations have recently been proposed and tested successfully against numerical and experimental results. Here we use discrete elements simulation of 2D shear flows to shed light on the dynamical mechanism underlying non-locality in dense granular flows

De part et d'autre de la transition de brouillage : rhéologie et acoustique non locales en milieu granulaire sec

Les milieux granulaires, dans leur état dense, se présentent sous la forme deux régimes, un régime « solide » qui représente un état bloqué des particules et un régime fluide. La première partie de ce travail porte sur le régime fluide du milieu granulaire. Dans un premier temps, le modèle de rhéologie non-locale y est présenté et discuté au regard des modèles proposés dans la communauté. Afin de tester le modèle sur un système réel, nous présentons une expérience d’avalanche dans un canal étroit, dans lequel l’état de contrainte est hétérogène et permet ainsi de faire coexister les deux régimes. L’ajustement du modèle pose la question de la définition des conditions aux limites. Nous présentons alors une étude numérique par simulation de dynamique moléculaire en plan incliné afin d’ajuster le modèle et mesurer la condition à la surface libre. La seconde partie de la thèse porte sur le régime bloqué du milieu granulaire et plus précisément sur la mesure des modules élastiques proche de la transition. A la limite de rigidité du matériau, les propriétés élastiques disparaissent mais le module élastique en cisaillement s’annule plus vite que le module en compression. Ainsi, nous présentons une étude de propagation d’ondes acoustiques en compression permettant de mesurer les modules élastiques à des pressions de confinement évanescentes, au moyen de vols paraboliques. Nous proposons un modèle de contact inter-particulaire permettant d’expliquer la dépendance du module élastique à la pression et ainsi d’appréhender les différentes lois d’échelles évoquées dans la littérature. Enfin, nous présentons des résultats préliminaires portant sur la propagation d’ondes de cisaillement.In their dense state, granular media can either flow like fluids or behave like solids, when they are jammed. The first part of this thesis deals with the flowing regime. We begin by presenting the non-local rheology and discuss this model with respect to the other ones proposed in the community. In order to probe this model, we perform experimental measurements of the velocity profile in an avalanche flow in a narrow channel. This setup allows to observe both the fluid regime and the creep of the supposedly jammed region, in the depth of the channel. We probe the non-local model on the experimental results. The fit of the theory raises the question of the definition of the boundary conditions on such system. We therefore perform molecular dynamic simulations on an incline plane setup in order to fit the non-local model and measure the free surface boundary condition.The second part of this thesis investigates the elastic properties of jammed granular media weakly confined. Near the rigidity (jamming) transition of the medium, elastic moduli decrease and exhibit different scaling laws in their dependence on the confining pressure. We therefore perform acoustic measurements of compression waves at vanishing pressures, by the mean of parabolic flights. We then revisit the model of inter-particle contacts. This enables to predict the elastic behavior of the medium over a wide range of pressures: from evanescent to high pressures, at which the prediction from the mean field approach using the Hertz contact model has been shown to be valid. Last, we present preliminary results of shear wave propagations

De part et d'autre de la transition de brouillage : rhéologie et acoustique non locales en milieu granulaire sec

In their dense state, granular media can either flow like fluids or behave like solids, when they are jammed. The first part of this thesis deals with the flowing regime. We begin by presenting the non-local rheology and discuss this model with respect to the other ones proposed in the community. In order to probe this model, we perform experimental measurements of the velocity profile in an avalanche flow in a narrow channel. This setup allows to observe both the fluid regime and the creep of the supposedly jammed region, in the depth of the channel. We probe the non-local model on the experimental results. The fit of the theory raises the question of the definition of the boundary conditions on such system. We therefore perform molecular dynamic simulations on an incline plane setup in order to fit the non-local model and measure the free surface boundary condition.The second part of this thesis investigates the elastic properties of jammed granular media weakly confined. Near the rigidity (jamming) transition of the medium, elastic moduli decrease and exhibit different scaling laws in their dependence on the confining pressure. We therefore perform acoustic measurements of compression waves at vanishing pressures, by the mean of parabolic flights. We then revisit the model of inter-particle contacts. This enables to predict the elastic behavior of the medium over a wide range of pressures: from evanescent to high pressures, at which the prediction from the mean field approach using the Hertz contact model has been shown to be valid. Last, we present preliminary results of shear wave propagations.Les milieux granulaires, dans leur état dense, se présentent sous la forme deux régimes, un régime « solide » qui représente un état bloqué des particules et un régime fluide. La première partie de ce travail porte sur le régime fluide du milieu granulaire. Dans un premier temps, le modèle de rhéologie non-locale y est présenté et discuté au regard des modèles proposés dans la communauté. Afin de tester le modèle sur un système réel, nous présentons une expérience d’avalanche dans un canal étroit, dans lequel l’état de contrainte est hétérogène et permet ainsi de faire coexister les deux régimes. L’ajustement du modèle pose la question de la définition des conditions aux limites. Nous présentons alors une étude numérique par simulation de dynamique moléculaire en plan incliné afin d’ajuster le modèle et mesurer la condition à la surface libre. La seconde partie de la thèse porte sur le régime bloqué du milieu granulaire et plus précisément sur la mesure des modules élastiques proche de la transition. A la limite de rigidité du matériau, les propriétés élastiques disparaissent mais le module élastique en cisaillement s’annule plus vite que le module en compression. Ainsi, nous présentons une étude de propagation d’ondes acoustiques en compression permettant de mesurer les modules élastiques à des pressions de confinement évanescentes, au moyen de vols paraboliques. Nous proposons un modèle de contact inter-particulaire permettant d’expliquer la dépendance du module élastique à la pression et ainsi d’appréhender les différentes lois d’échelles évoquées dans la littérature. Enfin, nous présentons des résultats préliminaires portant sur la propagation d’ondes de cisaillement

Non-local rheology of dense granular flows

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point. We also make use of a micro-rheometer to determine the influence of a distant shear band on the local rheological behaviour. Finally, we compare various approaches based on different non-local constitutive relations and choices for the fluidity parameter. We emphasise that, to discriminate between the different approaches proposed in the literature, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics

Non-local rheology of dense granular flows

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point. We also make use of a micro-rheometer to determine the influence of a distant shear band on the local rheological behaviour. Finally, we compare various approaches based on different non-local constitutive relations and choices for the fluidity parameter. We emphasise that, to discriminate between the different approaches proposed in the literature, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics

Tunable Persistent Random Walk in Swimming Droplets

We characterize the motility of athermal swimming droplets within the framework of a persistent random walk. Just like active colloids, their trajectories can be modeled with a constant velocity V and a slow angular diffusion, but the random changes in direction are not thermally driven. Instead, V is determined by the interfacial tension gradient along the droplet surface, while reorientation of the surfactant gradient leads to changes in direction with a persistence time τ. We show that the origin of locomotion is the difference in the critical micellar concentration in the front and the back of the droplet, ΔCMC. Tuning this parameter by salt controls V from 3 to 15 diameters d/s. Surfactant concentration has little effect on speed, but leads to a dramatic decrease in τ over 4 orders of magnitude. The corresponding range of the persistence length ℓ=Vτ extends beyond the realm of synthetic or living swimmers, in which V is limited by fuel consumption and τ is set by thermal fluctuations or biological activity, respectively. Our tunable swimmers are ideal candidates for the study of the departure from equilibrium to high levels of activity. We show that their collective behavior exhibits the formation of active clusters of a well-defined size