Dense shearing flows of soft, frictional cylinders.

We perform discrete numerical simulations at a constant volume of dense, steady, homogeneous flows of true cylinders interacting via Hertzian contacts, with and without friction, in the absence of preferential alignment. We determine the critical values of the solid volume fraction and the average number of contacts per particle above which rate-independent components of the stresses develop, along with a sharp increase in the fluctuations of angular velocity. We show that kinetic theory, extended to account for a velocity correlation at solid volume fractions larger than 0.49, can quantitatively predict the measured fluctuations of translational velocity, at least for sufficiently rigid cylinders, for any value of the cylinder aspect ratio and friction investigated here. The measured pressure above and below the critical solid volume fraction is in agreement with a recent theory originally intended for spheres that conjugates extended kinetic theory, the finite duration of collisions between soft particles and the development of an elastic network of long-lasting contacts responsible for the rate-independency of the flows in the supercritical regime. Finally, we find that, for sufficiently rigid cylinders, the ratio of shear stress to pressure in the subcritical regime is a linear function of the ratio of the shear rate to a suitable measure of the fluctuations of translational velocity, in qualitative accordance with kinetic theory, with an intercept that increases with friction. A decrease in the particle stiffness gives rise to nonlinear effects that greatly diminishes the stress ratio.

A heavy intruder in a locally-shaken granular solid.

We experimentally investigate the gravitational-driven motion of a heavy object inside a vertical 2D assembly of identical, plastic cylinders arranged in a regular, triangular lattice. The bottom of the assembly is in contact with a rough plate whose horizontal, sinusoidal motion induces the formation of shear bands in the granular solid, aligned with the edges of the lattice. The intruder sinks when the width of the shear band is as large as its size and halts once the regular configuration of the grains is recovered. The resulting vertical motion of the intruder is random and intermittent, as in disordered granular or colloidal systems near jamming, with alternate flows and blockades. We show, in analogy with earthquakes, that the relation between the size and the duration of the flowing events follows a power-law with an exponent larger than one, and that the statistics of their size is compatible with the Gutenberg-Richter law. We also show that the probability density function of times between flowing events is similar to the Omori law governing the distribution of aftershock sequences following large earthquakes. Finally, the analysis of the velocity fluctuations of the intruder points to a transition from a strong to a weak contact network in the ordered granular assembly, similar to the transition from jammed to fragile states in disordered systems.

Erodible, granular beds are fragile.

Geophysical flows that involve the transport of grains and the shearing of colloids and non-Brownian suspensions often take place above a substrate composed of the same particles that can be incorporated into the flow. Despite the importance of understanding such erodible beds to the phrasing of appropriate boundary conditions for the solution of continuum models, a rigorous definition of the erodible bed and the constitutive relations for the stresses within it are still lacking. Here, we use discrete-element simulations to show that the intense, intermittent forming and breaking of contact chains marks the transition to the erodible bed at a critical solid volume fraction, as in shear jamming of steady, homogeneous flows. However, the compressible, collisional flow that confines the bed is not strong enough to insure the stability of the contact network, resulting in a bulk stiffness that is three orders of magnitude less than in shear jamming.

Collisional dissipation rate in shearing flows of granular liquid crystals.

We make use of discrete-element-method numerical simulations of inelastic frictionless cylinders in simple shearing at different length-to-diameter ratios and solid volume fractions to analyze the rate of collisional dissipation of the fluctuation kinetic energy. We show that the nonspherical geometry of the particles is responsible, by inducing rotation, for increasing the dissipation rate of the fluctuation kinetic energy with respect to that for frictionless spheres. We also suggest that the partial alignment of the cylinders induced by shearing concurs with the particle inelasticity in generating correlation in the velocity fluctuations and thus affecting the collisional dissipation rate as the solid volume fraction increases. Finally, we propose simple phenomenological modifications to the expression of the collisional dissipation rate of kinetic theory of granular gases to take into account our findings.

Erosion and deposition in depth-averaged models of dense, dry, inclined, granular flows.

We derive expressions for the rates of erosion and deposition at the interface between a dense, dry, inclined granular flow and an erodible bed. In obtaining these, we assume that the interface between the flowing grains and the bed moves with the speed of a pressure wave in the flow, for deposition, or with the speed of a disturbance through the contacting particles in the bed, for erosion. We employ the expressions for the rates of erosion and deposition to show that after an abrupt change in the angle of inclination of the bed the characteristic time for the motion of the interface is much shorter than the characteristic time of the flow. This eliminates the need for introducing models of erosion and deposition rate in the mass balance; and the instantaneous value of the particle flux is the same function of the instantaneous value of the flow depth as in a steady, uniform flow.

Stresses and orientational order in shearing flows of granular liquid crystals.

We perform discrete element simulations of homogeneous shearing of frictionless cylinders and show that the particles are characterized by orientational order and form a granular liquid crystal. For elongated and flat cylinders, the alignment is in the plane of shearing, while cylinders having an aspect ratio equal to 1 and 0.8 show no orientational order. We show that the particle pressure is insensitive to the cylinder aspect ratio and well predicted by the kinetic theory of granular gases, with a singularity in the radial distribution function at contact different from that for frictionless spheres. The numerical results quantitatively agree with physical experiments on different geometries. The particle shear stress is affected by orientational anisotropy. We postulate that, for frictionless cylinders, the viscosity is roughly due to the motion of the orientationally disordered fraction of the particles, and show that it is proportional, through the order parameter, to the expression of kinetic theory. Finally, we suggest that the orientational order is the result of the competing effects of the shear rate, which induces alignment, and the granular temperature, which ramdomizes.

Turbulence Locality and Granularlike Fluid Shear Viscosity in Collisional Suspensions.

We reanalyze previous experimental measurements of solid volume fraction, mean velocity, and velocity fluctuations in collisional suspensions of plastic cylinders and water flowing over inclined, erodible beds. We show that the particle pressure scales with the granular temperature, as predicted by kinetic theory of granular gases. The assumption that the particle shear stress is also well predicted by kinetic theory permits us to determine the fluid shear stress and the effective fluid viscosity from the experiments. The fluid viscosity can be decomposed into turbulent and granularlike components: the turbulent viscosity can be modeled using a mixing length, which is a decreasing function of the local volume fraction and does not depend upon the distance from the bed; the granularlike viscosity, associated with the transfer of momentum due to the conjugate motion of the fluid mass added to the particles, can be modeled by replacing the particle density with the density of the added fluid mass in the viscosity of kinetic theory.

Steady shearing flows of deformable, inelastic spheres.

We extend models for granular flows based on the kinetic theory beyond the critical volume fraction at which a rate-independent contribution to the stresses develops. This involves the incorporation of a measure of the duration of the particle interaction before and after this volume fraction. At volume fractions less than the critical, the stress components contain contributions from momentum exchanged in collisions that are influenced by the particle elasticity. At volume fractions greater than the critical, the stress components contain both static contributions from particle elasticity and dynamic contributions from the momentum transfer associated with the release of elastic energy by the breaking of force chains. A simple expression for the duration of a collision before and after the critical volume fraction permits a smooth transition between the two regimes and predictions for the components of the stress in steady, homogeneous shearing that are in good agreement with the results of numerical simulations. Application of the theory to steady, inhomogeneous flows reproduces the features of such flows seen in numerical simulations and physical experiments.

Approximate analytical solutions in a model for highly concentrated granular-fluid flows.

We extend a simple two-phase model for a steady fully developed flow of particles and water over an erodible inclined bed to situations in which the water and particles do not have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that satisfactorily reproduce those measured in experiments.