Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KJ: Granular Media: Surface and Tumbling Flows |
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Chair: Robert Behringer, Duke University Room: Hilton Chicago Williford C |
Monday, November 21, 2005 4:10PM - 4:23PM |
KJ.00001: Surface Mobility of Horizontally Vibrated Granular Layers as a Function of Depth Conor Puls, Jerry Gollub, Jim McElwaine Stimulated by studies of avalanches where the critical slope angle is a function of layer depth [1], we investigate horizontally vibrated layers of various thickness, using acceleration to simulate the effects of gravity. The rectangular cell is 20 cm long in the direction of motion, and 8 cm transverse to that direction, containing polydisperse polystyrene particles of diameter 0.7-1.2 mm, 1-20 particles deep. We measure the RMS velocity of the mobilized surface particles in the frame of reference of the oscillating box, as a function of non-dimensional acceleration and layer depth. We find a depth-dependent threshold acceleration for surface mobility. The mobility also varies with time, due possibly to structural re-arrangement of the particles. The observations are compared to numerical simulations of the same phenomena using soft particle forces with friction, and to earlier experimental studies [2]. \newline \newline [1] O. Pouliquen, Phys. Fluids 11, 542 (1999). \newline [2] G. Metcalfe et al., Phys. Rev. E 61, 031302 (2002). [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KJ.00002: Sensitivity of Granular Hopper Flows to Boundary Conditions John Wambaugh, Robert Behringer Granular hoppers provide an excellent experimental system for studying continuum descriptions of granular materials in part because there exist the well-established Jenike radial solutions. (Moreea, S. B. M. and Nedderman, R. M., Chem. Eng. Sci., 51, 3931--3942 (1996)) In the case of a perfectly symmetrical right hopper there are multiple constitutive relations that lead to the Jenike solutions. When asymmetry is introduced by tilting the hopper with respect to gravity, these constitutive relations lead to different predictions of how the granular flow will circulate. (Gremaud, P.A., Matthews, J.V. and Schaeffer, D. G., SIAM J. Appl. Math., 64, 583--600 (2003) and personnal communications) This experimental study finds that the Matsuoka-Nakai constitutive relation most accurately describes granular flow, but only for moderate tilt angles and only for a specific range of wall roughnesses. In more extreme cases, the velocity field is found to change substantially. We believe our results may allow for discrimination between different soil mechanics descriptions of dense granular flows. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KJ.00003: Surface Flow of Sloshing Granular Materials Kenneth Desmond, Wolfgang Losert, Mike Newey We studied the fluidity of the flowing layer of grains in a tumbler through gentle sideways sloshing, and how the flow of large and small particles differs. Monodisperse beads were rotated in a long partially filled drum while also being gently vibrated sinusoidal below one g along the axial direction. As a result of the motion of the drum the beads slosh slightly back and forth also with sinusoidal motion. We compared the phase difference between the motion of the drum and the particles for big and small particles. It was determined that the phase difference is directly proportional to the frequency of vibration with a proportionality constant that increased with fluidity. The proportionality constant is a measure of the fluidity of the grains, and was shown to scale with the logarithm of rotation rate and the inverse square root of the bead diameter. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KJ.00004: Granular Flow in a Tumbler Under Variable g-Levels Antje Brucks, Julio M. Ottino, Richard M. Lueptow The Froude number $\omega^2 r/g$, where $\omega$ is the rotational speed, $r$ the radius of the tumbler and $g$ the gravitational acceleration, is frequently used to characterize a granular flow. Although $g$ appears in the Froude number, little is understood about how its variation affects the nature of granular flow. Experiments were performed with $0.5mm$ glass beads in a half-full, quasi-two dimensional 45mm radius tumbler at high $g$-levels. The tumbler was mounted in a large centrifuge to provide high g-levels. At a particular tumbler rotational speed, the dynamic angle of repose decreases as the $g$-level increases from 1$g$ to 25$g$. However, the data at all g-levels collapses so that the angle of repose is independent of the $g$-level when plottet as a function of the Froude number. Furthermore, the shape of the surface of the flowing layer depends only on the Froude number, not directly on $g$. Thus, the Froude number appears to characterize the nature of the flowing layer in a tumbler when both $\omega$ and $g$ are varied. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KJ.00005: Core Precession and Erosion in a Tumbler Under Variable g-Levels Richard M. Lueptow, Tim Arndt, Antje Brucks, Julio M. Ottino The precession and erosion of a core of granular material in a rotating tumbler that is more than half full provides a measure of the slow granular motion that occurs beneath the flowing surface layer. Since the effect of gravity on the subsurface flow has not been explored, experiments were performed in a~63{\%} to 83{\%} full tumbler apparatus mounted in a large centrifuge that can provide very high g-levels. Two colors of 0.5 mm glass beads were filled side by side to mark a vertical line in the 45mm radius quasi-two dimensional tumbler. The rotation of the core with respect to the tumbler and size of the core was monitored over 250 tumbler revolutions at accelerations between 1g and 12g. The degree of core precession increases with the g-level, while the core erosion depends less on g-level. The flowing layer thickness is essentially independent of the g-level for identical Froude numbers, suggesting that the shear rate in the flowing layer must increase with increasing g-level. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KJ.00006: Endwall Flow Effects in a Tumbler Nicholas A. Pohlman, Julio M. Ottino, Richard M. Lueptow The flow of granular material in rotating tumblers is limited to the thin flowing layer at the free surface. Particle tracking velocimetry was used to measure the surface velocity for 1 mm and 2 mm glass particles and sand in cylindrical tumblers of various diameters, lengths, and rotation rates. Friction at the end walls slows the streamwise surface velocity, yet material just in from the end wall flows faster than that in the center of the tumbler. Although the axial velocity in the center of a long tumbler is negligible, a non-negligible axial velocity exists near the end walls of cylindrical tumblers. The axial flow and increase in streamwise velocity are likely a result of the conservation of mass of particles passing through the flowing layer near the endwall. Increasing the end wall friction slows particles adjacent to the end wall, further enhancing the axial flow near the end wall. Decreasing the total axial length of the cylinder to quasi-two-dimensional causes the axial flow regions near the endwalls to merge and generates an even higher streamwise velocity than for three-dimensional tumblers. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KJ.00007: Granular Surface Flows in Three Dimensional Tumblers Steven W. Meier, Nicholas A. Pohlman, Richard M. Lueptow, Julio M. Ottino Many granular flows are confined to thin layers of rapid surface flow. Therefore, a complete understanding of surface flows is the key to an accurate representation of the entire flow. Experiments were conducted measuring the surface flow in three-dimensional tumblers: cylindrical tumblers with lengths of 17.5 cm and diameters of 7.0 cm, 10.0 cm, 14.0 cm and 17.0 cm, a double-cone tumbler with a maximum diameter of 13.8 cm, and a spherical tumbler with a diameter of 13.6 cm. Surface velocity measurements for 1 mm and 2 mm glass particles were obtained using particle tracking velocimetry. Results indicate that the streamwise surface velocity at the midpoint of the flowing layer is a linear function of local flowing layer length, regardless of tumbler shape, particle size, rotation rate, and fill fraction. In addition, the axial surface velocity at the midpoint of the flowing layer is negligible. These results are key for the development of three-dimensional models of granular flows. [Supported by NSF and DOE.] [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KJ.00008: Friction and the Dynamic Angle of Repose of a Granular Material Benjamin L. Severson, Randall Q. Snurr, Julio M. Ottino, Richard M. Lueptow The angle of repose is one most common measures of the flow-ability of granular materials. Particle properties influencing the dynamic angle of repose of a granular material rotated in a cylinder are studied using particle dynamics simulations. The influence of each parameter in the force models of this commonly used simulation technique are evaluated through the use of a factorial set of designed simulation experiments. The friction coefficient is the most important parameter affecting the angle of repose. Bidisperse mixtures of particles with different friction coefficients are also studied. The angle of repose of the mixture depends on the concentration of the mixture, consistent with recent experiments, and also on how the friction coefficient for contacts between dissimilar particles is defined. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KJ.00009: Transverse Instability of Granular Avalanches Igor Aranson, Florent Malloggi, Eric Clement Recent experiments with dry and underwater avalanches revealed a surprising new phenomenon: transverse instability and fingering of avalanche front propagating on erodible granular substrate. In order to describe this phenomenon we applied order parameter model of partially fluidized granular flows which was successfully tested on downhill and triangular avalanches in thin granular layers. In the framework of our model we obtained a family of ``solitary'' front solutions with the velocity and the height of the front determined by the depth of erodible substrate, the inclination angle, and front’s total mass. We have found that the front exhibits transverse instability in the certain range of substrate depth and inclination angles, in good agreement with the experiment. The primary machanism of the transverse instability is related to the dependence of the front velocity on the mass of granular material it carries, and is not triggered by the granular size segregation [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KJ.00010: New insight on the understanding of long runout avalanches: geometric lubrication E. Linares, C. Goujon, R. Zenit The unexpected long-runout landslides have been a controversial subject of discussion. In order to provide a new insight of this phenomena, we investigate the apparent reduction of friction resulting from the presence of small beads. Results obtained by means of a 2-D soft particle numerical simulation are presented. The numerical experiments consider an avalanche of two size disks, originally placed over an inclined plane. The friction coefficient for the particle-particle and wall-particle contacts is held fixed and is equal to 0.5. The granular mass is allowed to evolve with time, until it comes back to rest. The position of the center of mass is located, such that the runout length could be measured, L/H. Many simulations were performed keeping the area of the mass constant, varying only the percentage of small disks. The results show that the runout length increases with the percentage of small beads, reaching a maximum for approximately 25\% of small disks. These results indicate that the apparent friction coefficient is reduced and affected by the percentage area of small particles. Additionally, the formation of a layer of small disks at the base of the avalanche was observed. This layer is identified as the source of ``lubrication.'' [Preview Abstract] |
Monday, November 21, 2005 6:20PM - 6:33PM |
KJ.00011: Bidisperse granular flows on inclined rough plane C. Goujon, B. Dalloz-Dubrujeaud, N. Thomas Experiments on bidiperse dry granular flows on a rough inclined plane were performed in order to investigate its rheology. Flows, created by a localised input of granular matter onto the plane, propagate and spread laterally, being unconfined by the experimental set-up. Because of size segregation, small beads are found in a layer at the bottom of the flow and larger ones at the free surface, at the borders and at the front. These lateral and vertical inhomogeneous repartitions lead to two effects: the surround effect and the interface effect. The surround effect is due to the large beads at the front and borders of the flow. It can be interpreted considering the relative frictions of the two types of beads with the rough plane. We show that a maximum of the friction exists for a particular relative roughness. Depending on the values of relative frictions, obtained for monodisperse flow, the surround effect can lead to a narrowing of the bidisperse flow, an increase of the deposit thickness. The interface effect deals with the interaction between the layers of large and small beads. Depending of the size ratio between the beads, the large beads can be ``trapped'' in the deposit of small ones, or they can increase the velocity gradient in the layer of the small beads, by an entrainment phenomenon. The combination of these two effects results in the different behavior observed for bidispersed granular deposits, compared to those observed for monodisperse flows. [Preview Abstract] |
Monday, November 21, 2005 6:33PM - 6:46PM |
KJ.00012: Failure of Granular Slopes under Vibration Greg Voth, Doug Rubin, Naomi Goldenson We report experimental measurements of the stability of a granular slope under external vibration. A 3D layer of glass beads is inclined and subjected to sinusoidal horizontal acceleration that continuously increases in amplitude. Video imaging of the upper surface of the slope provides sensitive detection of the onset of motion. For a wide range of inclination angles, even above the dynamic angle of repose, initial failure is transient: flow allows the material to find a stronger static configuration which then requires a higher acceleration to initiate the next failure. Measurements show a clear dependence of the acceleration at failure on the rate at which the acceleration increases, revealing microscopic strengthening before the onset of detectable bead motion. [Preview Abstract] |
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