Coherent Force Chains in Disordered Granular Materials Emerge from a Percolation of Quasilinear Clusters.

Dense granular materials and other particle aggregates transmit stress in a manner that belies their microstructural disorder. A subset of the particle contact network is strikingly coherent, wherein contacts are aligned nearly linearly and transmit large forces. Important material properties are associated with these force chains, but their origin has remained a puzzle. We classify subnetworks by their linear connectivity, and show the emergence of a percolation transition at a critical linearity at which the network is sparse, coherent, and contains the force chains. The subnetwork at critical linearity closely reflects the macroscopic stress and explains distinctive features of granular mechanics.

A dilation-driven vortex flow in sheared granular materials explains a rheometric anomaly.

Granular flows occur widely in nature and industry, yet a continuum description that captures their important features is yet not at hand. Recent experiments on granular materials sheared in a cylindrical Couette device revealed a puzzling anomaly, wherein all components of the stress rise nearly exponentially with depth. Here we show, using particle dynamics simulations and imaging experiments, that the stress anomaly arises from a remarkable vortex flow. For the entire range of fill heights explored, we observe a single toroidal vortex that spans the entire Couette cell and whose sense is opposite to the uppermost Taylor vortex in a fluid. We show that the vortex is driven by a combination of shear-induced dilation, a phenomenon that has no analogue in fluids, and gravity flow. Dilatancy is an important feature of granular mechanics, but not adequately incorporated in existing models.

Anomalous stress profile in a sheared granular column.

We present measurements of the stress as a function of vertical position in a column of granular material sheared in a cylindrical Couette device. All three components of the stress tensor on the outer cylinder were measured as a function of distance from the free surface at shear rates low enough that the material was in the dense, slow flow regime. We find that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. We argue that the anomalous stress profile is due to an anisotropic fabric caused by the combined action of gravity and shear.

Statistics of particle velocities in dense granular flows.

We present measurements of the particle velocity distribution in the slow flow of granular material through vertical channels. The velocities of particles adjacent to the smooth, transparent front face of the channel were determined by video imaging and particle tracking. We find that the mean velocity changes sharply in shear layers near the side walls, but remains constant in a substantial core. The velocity distribution is non-Gaussian, is anisotropic, and follows a power law at large velocities. Remarkably, the distribution is identical in the shear layer and the core. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.

Stress fluctuations in sheared Stokesian suspensions.

We report an analysis, using the tools of nonlinear dynamics and chaos theory, of the fluctuations in the stress determined from simulations of shear flow of Stokesian suspensions. The simulations are for shear between plane parallel walls of a suspension of rigid identical spheres in a Newtonian fluid, over a range of particle concentration. By analyzing the time series of the stress, we find that the dynamics underlying these fluctuations is deterministic, low-dimensional, and chaotic. We use the dynamic and metric invariants of the underlying dynamics as a means of characterizing suspension behavior. The dimension of the chaotic attractor increases with particle concentration, indicating the increasing influence of multiple-body interactions on the rheology of the suspension with rise in particle concentration. We use our analysis to make accurate predictions of the short-term evolution of a stress component from its preceding time series, and predict the evolution of one component of the stress using the time series of another. We comment on the physical origin of the chaotic stress fluctuations, and on the implications of our results on the relation between the microstructure and the stress.