Andreea Panaitescu

Spatial distribution functions of random packed granular spheres obtained by direct particle imaging.

We measure the two-point density correlations and Voronoi cell distributions of cyclically sheared granular spheres obtained with a fluorescence technique and compare them with random packing of frictionless spheres. We find that the radial distribution function g(r) is captured by the Percus-Yevick equation for initial volume fraction ϕ=0.59. However, small but systematic deviations are observed because of the splitting of the second peak as ϕ is increased toward random close packing. The distribution of the Voronoi free volumes deviates from postulated Γ distributions, and the orientational order metric Q6 shows local order but no long range order. Overall, these measures show significant similarity of random packing of granular and frictionless spheres, but some systematic differences as well.

Experimental Investigation of Cyclically Sheared Granular Particles with Direct Particle Tracking

We discuss experiments on dense packing of granular beads that are cyclically sheared quasi-statically between parallel walls under constant pressure boundary conditions. The particle positions inside the shear cell are tracked over several cycles in three dimensions using particle index-matching imaging technique. The total volume fraction of the particles φ in the cell is observed to increase slowly over thousands of cycles from φ ∼ 0.59 to φ ∼ 0.63, while even slower growth in volume fraction is observed in the bulk away from boundaries. We illustrate with internal images that the difference arises due to inhomogeneity of packing with ordered regions developing progressively from the boundaries. We then focus in the bulk where the packing is uniformly disordered, and find that a linear bulk strain is observed within the first half of a cycle, which is reversed in the second half of the cycle. We present analysis of the trajectories of the particles within a shear cycle as well as over several cycles. We find anisotropic fluctuations relative to shear gradient within a cycle. However, homogeneous growth of mean square displacement when fluctuations are examined average over a cycle. The rate of growth is significantly lower leading us to hypothesize that granular matter under cyclic shear show reversible as well as irreversible or plastic response for small enough strain amplitude.

Measuring geometric frustration in twisted inextensible filament bundles

We investigate with experiments and mapping the structure of a hexagonally ordered filament bundle that is held near its ends and progressively twisted around its central axis. The filaments are free to slide relative to each other and are further held under tension-free boundary conditions. Measuring the bundle packing with micro x-ray imaging, we find that the filaments develop the helical rotation Ω imposed at the boundaries. We then show that the observed structure is consistent with a mapping of the filament positions to disks packed on a dual non-Euclidean surface with a Gaussian curvature which increases with twist. We further demonstrate that the mean interfilament distance is minimal on the surface, which can be approximated by a hemisphere with an effective curvature K_{eff}=3Ω^{2}. Examining the packing on the dual surface, we analyze the geometric frustration of packing in twisted bundles and find the core to remain relatively hexagonally ordered with interfilament strains growing from the bundle center, driving the formation of defects at the exterior of highly twisted bundles.

Drag law for an intruder in granular sediments

We investigate the drag experienced by a spherical intruder moving through a medium consisting of granular hydrogels immersed in water as a function of its depth, size, and speed. The medium is observed to display a yield stress with a finite force required to move the intruder in the quasistatic regime at low speeds before rapidly increasing at high speeds. In order to understand the relevant time scales that determine drag, we estimate the inertial number I given by the ratio of the time scales required to rearrange grains due to the overburden pressure and imposed shear and the viscous number J given by the ratio of the time scales required to sediment grains in the interstitial fluid and imposed shear. We find that the effective friction μ_{e} encountered by the intruder can be parametrized by I=sqrt[ρ_{g}/P_{p}]v_{i}, where ρ_{g} is the density of the granular hydrogels, v_{i} is the intruder speed, and P_{p} is the overburden pressure due to the weight of the medium, over a wide range of I where the Stokes number St=I^{2}/J≫1. We then show that μ_{e} can be described by the function μ_{e}(I)=μ_{0}+αI^{β}, where μ_{0}, α, and β are constants that depend on the medium. This formula can be used to predict the drag experienced by an intruder of a different size at a different depth in the same medium as a function of its speed.

Headward growth and branching in subterranean channels

We investigate the erosive growth of channels in a thin subsurface sedimentary layer driven by hydrodynamic drag toward understanding subterranean networks and their relation to river networks charged by ground water. Building on a model based on experimental observations of fluid-driven evolution of bed porosity, we focus on the characteristics of the channel growth and their bifurcations in a horizontal rectangular domain subject to various fluid source and sink distributions. We find that the erosion front between low- and high-porosity regions becomes unstable, giving rise to branched channel networks, depending on the spatial fluctuations of the fluid flow near the front and the degree to which the flow is above the erodibility threshold of the medium. Focusing on the growth of a network starting from a single channel, and by identifying the channel heads and their branch points, we find that the number of branches increases sublinearly and is affected by the source distribution. The mean angles between branches are found to be systematically lower than river networks in humid climates and depend on the domain geometry.