Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear flows in a 2D Couette geometry. We find that self-diffusivities D are proportional to the local shear rateγ with diffusivities along the direction of the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D ≈γa 2 where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is supressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Lévy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce non-diffusive effects, on average the system appears simply diffusive.

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces a mean azimuthal flow, smooth affine deformations, and irreversible so-called nonaffine particle displacements. We find that these processes are all of comparable magnitude and depend on the local shear rate. We compute the parameter of Falk and Langer characterizing nonaffine motion, Dmin2, and find that it is reasonably well described in terms of collections of single particles making locally nearly isotropic random steps, delta ri. Distributions for single particle nonaffine displacements, delta ri, satisfy P1(delta ri) proportional, variantexp[-|delta ri/Delta r|alpha] (alpha < or approximately 2).

We report experimental results on the tip splitting dynamics of seaweed growth in directional solidification of succinonitrile alloys. Despite the random appearance of the growth, a tip splitting morphology was observed in which the tip alternately splits to the left and to the right. The tip splitting frequency f was found to be related to the growth velocity V as a power law f~V1.5. This finding is consistent with the predictions of a tip splitting model that is also presented. Small anisotropies are shown to lead to different kinds of seaweed morphologies.

Abstract. As dense granular materials are sheared, a shear band and an anisotropic force network form. The approach to steady state behavior depends on the history of the packing and the existing force and contact network. We present experiments on shearing of dense granular matter in a 2D Couette geometry in which we probe the history and evolution of shear bands by measuring particle trajectories and stresses during transients. We find that when shearing is stopped and restarted in the same direction, steady state behavior is immediately reached, in agreement with the typical assumption that the system is quasistatic. Although some relaxation of the force network is observed when shearing is stopped, quasistatic behavior is maintained because the contact network remains essentially unchanged. When the direction of shear is reversed, a transient occurs in which stresses initially decrease, changes in the force network reach further into the bulk, and particles far from the wheel become more mobile. This occurs because the force network is fragile to changes transverse to the force network established under previous shear; particles must rearrange before becoming jammed again, thereby providing resistance to shear in the reversed direction. The strong force network is reestablished after displacing the shearing surface ≈ 3d, where d is the mean grain diameter. Steady state velocity profiles are reached after a shear of 30d. Particles immediately outside of the shear band move on average less than 1 diameter before becoming jammed again. We also examine particle rotation during this transient and find that mean particle spin decreases during the transient, which is related to the fact that grains are not interlocked as strongly.

We report experimental results on quasi-two-dimensional diffusion limited growth in directionally solidified succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as a solute. Seaweed growth, or dense branching morphology, is selected by growing grains close to the [111] plane, where the in-plane surface tension is nearly isotropic. The observed growth morphologies are very sensitive to small anisotropies in surface tension caused by misorientations from the [111] plane. Different seaweed morphologies are found, including the degenerate, the stabilized, and the strongly tilted seaweeds. The degenerate seaweeds show a limited fractal scaling range and, with increased undercooling, suggests a transition from "fractal" to "compact" seaweed. Strongly tilted seaweeds demonstrate a significant twofold anisotropy. In addition, seaweed-dendrite transitions are observed in low anisotropy growth.

We present experiments on the doublon growth morphology in directional solidification. Samples used are succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as the solute. Doublons, or symmetry-broken dendrites, are generic diffusion-limited growth structures expected at large undercooling and low anisotropy. Low anisotropy growth is achieved by selecting a grain near the {111} plane leading to either seaweed (dense branching morphology) or doublon growth depending on experimental parameters. We find selection of doublons to be strongly dependent on solute concentration and sample orientation. Doublons are selected at low concentrations (low solutal undercooling) in contrast to the prediction of doublons at large thermal undercooling in pure materials. Doublons also exhibit preferred growth directions and changing the orientation of a specific doublonic grain changes the character and stability of the doublons. We observe transitions between seaweed and doublon growth with changes in concentration and sample orientation.

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We present statistics on granular avalanches in a rotating drum with and without imposed vertical vibration. The experiment consists of a quasi-two-dimensional, vertical drum containing pentagonal particles and rotated at a constant angular velocity. The drum rests on an electromagnetic shaker to allow vibration of the assembly as it rotates. We measure time series of the slope of the interface and find that the critical angle for slope failure θ(c) and the resulting angle of repose θ(r) are broadly distributed with an approximate power-law distribution of avalanches θ(c)-θ(r) for large avalanches. The faceted pentagonal grains used lead to significant interlocking with critical and repose angles (θ(c)≈45° and θ(r)≈39°) larger than experiments using spherical grains, even with vibration, and avalanche magnitudes correlated with the prior build-up and anti-correlated with the prior avalanche. We find that the stability of the assembly increases with small vibrations and is destabilized at vibration amplitudes above a dimensionless acceleration (peak acceleration divided by acceleration due to gravity) of Γ=0.2. We also study history dependence of the avalanches by periodically oscillating the drum to compare the initial avalanche upon reversal of shear to steady-state distributions for avalanches during continuous rotation. We observe history dependence as an initial decrease in critical angle upon reversal of the drum rotation direction, indicating that a texture is induced to resist continued shear such that the surface is weaker to reversals in shear direction. Memory of this history is removed by sufficient external vibration (Γ≥0.8), which leads to compaction and relaxation of the surface layer grains responsible for avalanching dynamics, as initial and steady-state avalanche distributions become indistinguishable.