Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session BM: Granular Flows II |
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Chair: Richard Lueptow, Northwestern University Room: Salt Palace Convention Center 251 A |
Sunday, November 18, 2007 10:34AM - 10:47AM |
BM.00001: Applications and limitations of a rheology for granular flows Chris Cawthorn, John Hinch, Herbert Huppert In order to assess the validity of the rheological law for granular flows proposed by Jop, Pouliquen and Forterre [Nature, vol. 441, pp.727-730], we present its application to a number of different problems. Whilst it works well for steady flow on a confined sandpile, or in an inclined channel, we will show that the law fails to qualitatively predict flow some simple geometries, such as annular Couette flow and vertical chute flow. In addition, we consider perturbations to 2D flow on an inclined plane and 3D flow in an inclined channel, where the effect of the confining vertical walls becomes important. Implications for the use of Jop's rheology for more complicated problems, particularly those involving dam-break or column collapse will also be addressed. [Preview Abstract] |
Sunday, November 18, 2007 10:47AM - 11:00AM |
BM.00002: The flow rule of dense granular flows on a rough incline Robert Ecke, Tamas Borzsonyi We present experimental findings on the flow rule for dense granular flows on a rough inclined plane using various materials including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring $h_s$ (the thickness at which the flow subsides) as a function of the plane inclination $\theta$ on various surfaces. Measuring the surface velocity $u$ of the flow as a function of flow thickness $h$, we find that for sand and glass beads the Pouliquen flow rule $u/\sqrt{gh} \sim \beta h/h_s$ provides reasonable collapse of the $u(h)$ curves measured for various $\theta$ and mean particle diameter $d$. Improved collapse is obtained for sand and glass beads by using a scaling recently proposed by Jenkins of the form $u/\sqrt{gh} =\beta \cdot h\ \tan^2\theta /h_s\ \tan^2\theta_1$ where $\theta_1$ is the angle at which the $h_s(\theta)$ curves diverge. Measuring the slope $\beta$ for ten different sizes of sand and glass beads, we find a systematic, strong increase of $\beta$ with the divergence angle $\theta_1$ of $h_s$. The copper materials with different shapes are not well described by either flow rule with $u \sim h^{3/2}$. [Preview Abstract] |
Sunday, November 18, 2007 11:00AM - 11:13AM |
BM.00003: The thermodynamics of dense granular flow Kevin Lu, Pirouz Kavehpour We propose a thermodynamics description of quasi-static granular flow where the partition function samples states of a potential energy landscape. The equilibrium fictive temperature $\sim$10$^{-7}$ Joules scales as material volume, where the temperature corresponds to the packing density determined by the structural relaxation time. The theory predicts that the compressibility of granular fluids and the effective viscosity are $\sim$10$^{-4}$ Pa$^{-1}$ and $\sim$1 Pa-s, respectively. These values fit the data from steady-state shear flow experiments spanning over 5 decades in velocity and 2 decades in pressure. Furthermore, we show that our equation-of-state match the Vogel-Tammann-Fulcher relation of glass-transition in an effort to reconcile the disparate amorphous systems of molecular and granular origin. [Preview Abstract] |
Sunday, November 18, 2007 11:13AM - 11:26AM |
BM.00004: Signal Propagation in Dense Granular Systems Lou Kondic, Robert Behringer The exact manner in which signals propagate through dense granular systems is still open for discussion. In this work, we present the results of discrete element simulations of the system response to space and time dependent perturbations. Fourier analysis of the system response shows that the properties of the propagating signal strongly depend on the spatial scales introduced by the perturbation itself. We concentrate particularly on the influence of shearing on the signal propagation and discuss whether continuous breaking of the particle contacts due to shear has an influence on this process. [Preview Abstract] |
Sunday, November 18, 2007 11:26AM - 11:39AM |
BM.00005: Shear induced self-diffusion in 3-D sheared dense granular flows Ashish Orpe, Arshad Kudrolli We measure the dynamics of a 3-dimensional gravity driven sheared granular flow using a fluorescent refractive index matched interstitial fluid. The particle positions are identified and tracked over long durations to obtain particle diffusivities, mean-squared displacements and probability distributions of particle displacements. The mean-squared displacements in the velocity-vorticity direction exhibit a crossover from sub-ballistic flow at short time scales (mean flow less than a particle diameter) to diffusive flow when the mean distance traveled is more than a particle diameter. The measured diffusivities show a systematic decrease with decreasing shear rates. The probability distributions at short times show fat tails compared to a Gaussian indicating large fluctuations in particle displacements and possible cage breaking. Preliminary molecular-dynamics simulations for dry dense granular flows in a similar system are in qualitative agreement with the experimental results. Further work will be carried out to measure the full diffusion tensor and to determine the dependence of the individual components on the studied shear rates. [Preview Abstract] |
Sunday, November 18, 2007 11:39AM - 11:52AM |
BM.00006: Kubo-Green Temperature Measurements in a Vibrated and Sheared Granular Material Karen E. Daniels, Robert P. Behringer We perform Kubo-Green measurements on a dense granular material which is vibrated from below and sheared from above within an annular channel. Within this driven system, we make effective temperature measurements by relating the correlations at a particular rotation rate to the response to changes in the rotation rate. These measurements are made in a regime which is either above or below the transition between solid-like (crystallized, compact) and liquid-like (disordered, dilated, flowing). We find that the short-term response of the system provides an effective temperature measurement which increases with both rotation rate and volume, and changes continuously through the phase transition. [Preview Abstract] |
Sunday, November 18, 2007 11:52AM - 12:05PM |
BM.00007: Viscous fingering in granular materials in a vertical Hele-Shaw cell Tamas Borzsonyi The dynamics of the air-granular interface has been studied in a quasi-two-dimensional vertically aligned Hele-Shaw cell experimentally. The air was pressed into the cell at the bottom through a single hole and the development of the upward propagating fingers was analyzed with the help of fast video recording. The behavior of the system was analyzed as a function of the applied air pressure, the grain size and the grain shape by using spherical glass beads or sorted sand particles. [Preview Abstract] |
Sunday, November 18, 2007 12:05PM - 12:18PM |
BM.00008: Experimental study of spinning granular jets Abraham Medina, Patrick Weidman, Rocio Chicharro In this work the nature of noncohesive granular material flowing out of a rotating vertical pipe under the influence of gravity to form a free granular jet is examined. We analyze systems with different angular velocities $\Omega$ and found that the jet radius increases with both $% \Omega $ and the downward coordinate $z$. Experiments show that a no-flow condition is achieved for a critical angular velocity, $\Omega _ {c}$. Analytical solutions for the shape of the jet and $\Omega _{c}$ are in good agreement with experiments. [Preview Abstract] |
Sunday, November 18, 2007 12:18PM - 12:31PM |
BM.00009: Relationships between Voronoi Volume Shapes and Particle Motions in a Granular material subject to Thermal Cycling Steven Slotterback, Leonard Goff, Masahiro Toiya, Wolfgang Losert We gently compact a granular pile using a temperature cycling process to expand and contract the holding vessel. We use a laser sheet scanning method to find the centers of the individual granules to within $\sim $1{\%} accuracy after each cycle. We analyze the voronoi diagrams for all the particles in each cycle. We observe that the distributions of voronoi volumes do not change significantly as the pile compacts, and they agree with distributions found by Aste et al[1]. We also observe correlations between the shapes of voronoi cells around individual particles and their subsequent motions. [1] T. Aste \textit{et al} 2007 \textit{EPL} \textbf{79} 24003 (5pp). [Preview Abstract] |
Sunday, November 18, 2007 12:31PM - 12:44PM |
BM.00010: Intermediate states in the folding of a granular polymer-like chain in water. Jeffrey Olafsen, Benjamin Bammes The dynamics of a chain of stainless steel monomers partially submerged in a thin layer of water that is vertically oscillated on a horizontal plate have been observed to be visually similar to that of polymer collapse in a poor solvent. In this experiment, the model `polymer' is composed of 25 to 250 loosely connected spheres that allows the chain to bend but also limits the smallest circle into which the chain can be folded (a persistence length). The surface tension plays the role of the long-ranged potential that is minimized during the folding process and the surface excitations of the thin, shaken fluid layer play the role of the Brownian noise that drives the system stochastically. In real polymer systems, folding often occurs via a process where the system passes through many intermediate states before finding its native configuration within the energy landscape. The dynamics in this model experimental system exhibit the same behavior of passing through local minima in the energy landscape with different relaxation rates in the intermediate states. This system is advantageous for studying polymer folding in poor solvents in the absence of many of the electrical and chemical details in real polymers. [Preview Abstract] |
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