Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity

We have studied the two-dimensional flow of balls in a small angle funnel, when either the side walls are rough or the balls are polydisperse. As in earlier work on monodisperse flows in smooth funnels, we observe the formation of kinematic shock waves/density waves. We find that for rough walls the flows are more disordered than for smooth walls and that shock waves generally propagate more slowly. For rough wall funnel flow, we show that the shock velocity and frequency obey simple scaling laws. These scaling laws are consistent with those found for smooth wall flow, but here they are cleaner since there are fewer packing-site effects and we study a wider range of parameters. For pipe flow (parallel side walls), rough walls support many shock waves, while smooth walls exhibit fewer or no shock waves. For funnel flows of balls with varying sizes, we find that flows with weak polydispersity behave qualitatively similar to monodisperse flows. For strong polydispersity, scaling breaks down and the shock waves consist of extended areas where the funnel is blocked completely.Comment: 11 pages, 15 figures; accepted for PR

Grain Dynamics in a Two-dimensional Granular Flow

We have used particle tracking methods to study the dynamics of individual balls comprising a granular flow in a small-angle two-dimensional funnel. We statistically analyze many ball trajectories to examine the mechanisms of shock propagation. In particular, we study the creation of, and interactions between, shock waves. We also investigate the role of granular temperature and draw parallels to traffic flow dynamics.Comment: 17 pages, 24 figures. To appear in Phys.Rev.E. High res./color figures etc. on http://www.nbi.dk/CATS/Granular/GrainDyn.htm

Particle dynamics in sheared granular matter

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity $V(y)$ declines strongly with distance $y$ from the moving wall, independent of the shear rate and of the shear dynamics. Local RMS velocity fluctuations $\delta V(y)$ scale with the local velocity gradient to the power $0.4 \pm 0.05$. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature $\delta V(y)^2$ and density dependent viscosity

Electronic and optical properties of lead iodide

ABSTRACT: Lead iodide (PbI2) is a very important material with a technological applicability as a room-temperature radiation detector. It is a wide-band-gap semiconductor (Eg.2 eV) with high environmental stability efficiency. The performance of the detector cannot be fully understood unless its electronic and optical properties are determined. Recently, its band-gap energy and thermal properties were determined by photoacoustic spectroscopy. A single crystal of PbI2 was grown by the Bridgman method with the c-axis oriented perpendicular to the growth axis. The purpose of this work is to obtain the electronic structure of PbI2, its dielectric functions e 1 and e 2 by ellipsometry and theoretically by full-potential linear muffin-tinorbital ~FPLMTO! method, and the temperature dependence of the measured band-gap energy by optica absorption. The obtained Eg(T) can be fitted by two different methods, leading to Eg ~0 K! and Eg ~300 K!

Thixotropy in macroscopic suspensions of spheres

An experimental study of the viscosity of a macroscopic suspension, i.e. a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density-matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown for the first time that a macroscopic suspension shows thixotropic viscosity, i.e. shear-thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10000 times larger than the viscous time scale and about 1000 times smaller than the thermodynamic time scale. The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern

Granular discharge and clogging for tilted hoppers

We measure the flux of spherical glass beads through a hole as a systematic function of both tilt angle and hole diameter, for two different size beads. The discharge increases with hole diameter in accord with the Beverloo relation for both horizontal and vertical holes, but in the latter case with a larger small-hole cutoff. For large holes the flux decreases linearly in cosine of the tilt angle, vanishing smoothly somewhat below the angle of repose. For small holes it vanishes abruptly at a smaller angle. The conditions for zero flux are discussed in the context of a {\it clogging phase diagram} of flow state vs tilt angle and ratio of hole to grain size

Self-diffusion in dense granular shear flows

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 in a 2D Couette geometry. We find that self-diffusivities are proportional to the local shear rate with diffusivities along the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D \approx \dot\gamma a^2 where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and drag at the moving boundary lead to particle displacements that can appear sub- or super-diffusive. In particular, diffusion appears 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 with 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 flow, 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 Levy flights are also observed. Although correlated motion creates velocity fields qualitatively different from Brownian motion and can introduce non-diffusive effects, on average the system appears simply diffusive.Comment: 13 pages, 20 figures (accepted to Phys. Rev. E

A Normative Model of Serum Inhibin B in Young Males

RTM is supported by a Wellcome Trust Intermediate Clinical Fellowship (Grant No: 098522).Inhibin B has been identified as a potential marker of Sertoli cell function in males. The aim of this study is to produce a normative model of serum inhibin B in males from birth to seventeen years. We used a well-defined search strategy to identify studies containing data that can contribute to a larger approximation of the healthy population. We combined data from four published studies (n = 709) and derived an internally validated model with high goodness-of-fit and normally distributed residuals. Our results show that inhibin B increases following birth to a post-natal peak of 270 pg/mL (IQR 210–335 pg/mL) and then decreases during childhood followed by a rise at around 8 years, peaking at a mean 305 pg/mL (IQR 240–445 pg/mL) at around age 17. Following this peak there is a slow decline to the standard mature adult normal range of 170 pg/mL (IQR 125–215 pg/mL). This normative model suggests that 35% of the variation in Inhibin B levels in young males is due to age alone, provides an age-specific reference range for inhibin B in the young healthy male population, and will be a powerful tool in evaluating the potential of inhibin B as a marker of Sertoli cell function in pre-pubertal boys.Publisher PDFPeer reviewe