Shear-induced diffusion in non-local granular flows

We investigate the properties of self-diffusion in heterogeneous dense granular flows involving a gradient of stress and inertial number. The study is based on simulated plane shear with gravity and Poiseuille flows, in which non-local effects induce some creep flow in zones where stresses are below the yield. Results show that shear-induced diffusion is qualitatively different in zones above and below the yield. Below the yield, diffusivity is no longer governed by velocity fluctuations, and we evidenced a direct scaling between diffusivity and local shear rate. This is interpreted by analysing the grain trajectories, which exhibit a caging dynamics developing in zones below the yield. We finally introduce an explicit scaling for the profile of local inertial number in these zones, which leads to a straightforward expression of the diffusivity as a function of the stress and position in non-local flows.Comment: 7 pages, 5 figure

Internal Dynamics and Flow Properties of Dense Granular Materials

This thesis deals with the micro-mechanics of dense granular flows and how they affect the overall flow and mixing behaviours of grains. Discrete Element Simulations of dense granular flows are performed at various flow geometries, giving us insights into the internal kinematics and dynamics of flow. This allows us to connect the micro-mechanics to the effective transport properties like self-diffusivity, viscosity and non-local rheology. The thesis is comprised of three published papers. The first paper shows how the development of granular vortices gives rise to enhanced mixing of grains in dense granular flows in plane shear flow geometries involving large widths. Rate dependent nature of the average vortex size is observed, and a general scaling law in terms of the size of granular vortices is introduced which can predict the enhanced mixing behaviour. The second paper connects the existence of granular vortices to the non-local behaviours of dense granular flows. The granular vortices are found to originate from a process of multiple orthogonal shear banding. A general non-local relation is then derived by considering the spatial redistribution of vorticity induced by these granular vortices. This relation is validated on two steady granular flow geometries involving nonlocal flow behaviours. The purely kinematic nature of this derivation suggests that non-local behaviour should be expected in flows of other materials as well that involve correlated motion of particles, like foams, pastes and gels. The final paper studies the self-diffusion behaviours in nonlocal flow geometries. The nature of grain trajectories in dense granular flow is found to depend on the stress condition. In creeping layers that have stresses below the yield stress, we observe caged dynamics of the grains and breakdown of the scaling of diffusivity with the velocity fluctuations. A scaling law is introduced that allows us to predict the rate of flow and self-diffusivity with the sole knowledge of stress condition and position

Partial jamming and non-locality in dense granular flows

Dense granular flows can exhibit non-local flow behaviours that cannot be predicted by local constitutive laws alone. Such behaviour is accompanied by the existence of diverging cooperativity length. Here we show that this length can be attributed to the development of transient clusters of jammed particles within the flow. By performing DEM simulation of dense granular flows, we directly measure the size of such clusters which scales with the inertial number with a power law. We then derive a general non-local relation based on kinematic compatibility for the existence of clusters in an arbitrary non-homogenous flow. The kinematic nature of this derivation suggests that non-locality should be expected in any material regardless of their local constitutive law, as long as transient clusters exist within the flow

Partial jamming and non-locality in dense granular flows

Dense granular flows can exhibit non-local flow behaviours that cannot be predicted by local constitutive laws alone. Such behaviour is accompanied by the existence of diverging cooperativity length. Here we show that this length can be attributed to the development of transient clusters of jammed particles within the flow. By performing DEM simulation of dense granular flows, we directly measure the size of such clusters which scales with the inertial number with a power law. We then derive a general non-local relation based on kinematic compatibility for the existence of clusters in an arbitrary non-homogenous flow. The kinematic nature of this derivation suggests that non-locality should be expected in any material regardless of their local constitutive law, as long as transient clusters exist within the flow

Partial jamming and non-locality in dense granular flows

Dense granular flows can exhibit non-local flow behaviours that cannot be predicted by local constitutive laws alone. Such behaviour is accompanied by the existence of diverging cooperativity length. Here we show that this length can be attributed to the development of transient clusters of jammed particles within the flow. By performing DEM simulation of dense granular flows, we directly measure the size of such clusters which scales with the inertial number with a power law. We then derive a general non-local relation based on kinematic compatibility for the existence of clusters in an arbitrary non-homogenous flow. The kinematic nature of this derivation suggests that non-locality should be expected in any material regardless of their local constitutive law, as long as transient clusters exist within the flow

How granular vortices can help understanding rheological and mixing properties of dense granular flows

Dense granular flows exhibit fascinating kinematic patterns characterised by strong fluctuations in grain velocities. In this paper, we analyse these fluctuations and discuss their possible role on macroscopic properties such as effective viscosity, non-locality and shear-induced diffusion. The analysis is based on 2D experimental granular flows performed with the stadium shear device and DEM simulations. We first show that, when subjected to shear, grains self-organised into clusters rotating like rigid bodies. The average size of these so-called granular vortices is found to increase and diverge for lower inertial numbers, when flows decelerate and stop. We then discuss how such a microstructural entity and its associated internal length scale, possibly much larger than a grain, may be used to explain two important properties of dense granular flows: (i) the existence of shear-induced diffusion of grains characterised by a shear-rate independent diffusivity and (ii) the development of boundary layers near walls, where the viscosity is seemingly lower than the viscosity far from walls

How granular vortices can help understanding rheological and mixing properties of dense granular flows

Dense granular flows exhibit fascinating kinematic patterns characterised by strong fluctuations in grain velocities. In this paper, we analyse these fluctuations and discuss their possible role on macroscopic properties such as effective viscosity, non-locality and shear-induced diffusion. The analysis is based on 2D experimental granular flows performed with the stadium shear device and DEM simulations. We first show that, when subjected to shear, grains self-organised into clusters rotating like rigid bodies. The average size of these so-called granular vortices is found to increase and diverge for lower inertial numbers, when flows decelerate and stop. We then discuss how such a microstructural entity and its associated internal length scale, possibly much larger than a grain, may be used to explain two important properties of dense granular flows: (i) the existence of shear-induced diffusion of grains characterised by a shear-rate independent diffusivity and (ii) the development of boundary layers near walls, where the viscosity is seemingly lower than the viscosity far from walls