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Coulomb’s Model

Coulomb’s Model. Identified two characteristic Angles: θ r , Angle of Repose θ max , Maximum Stable Angle. Additional material treated as a single entity. Δθ. θ max. θ r. Strengths and Weaknesses of the Coulomb Model. Gives a mathematical model for avalanches.

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Coulomb’s Model

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  1. Coulomb’s Model • Identified two characteristic Angles: • θr, Angle of Repose • θmax, Maximum Stable Angle Additional material treated as a single entity. Δθ θmax θr

  2. Strengths and Weaknesses of the Coulomb Model • Gives a mathematical model for avalanches. • θmax and θr are observable in piles with many particles. • Only applicable to large-scale observations. (Doesn’t account well for unique surface properties.)

  3. Bak-Tang-Wiesenfield Cellular Automaton Model A highly simplified model that lends itself well to computer simulation. Represents a pile by a grid of cells: each cell may contain a grain. Grains are added to the pileone at a time.

  4. Bak-Tang-Wiesenfield Cellular Automaton Model Simulates avalanches with two rules: • The difference in height between adjacent columns must not exceed two cells. • If adding a grain would break this rule, grains are moved in pairs until an acceptable state is reached.

  5. Uses of the Bak-Tang-Wiesenfield Model • Offers a good computational model. Easy to generalize in 3-d. • Predicts a relation that gives the frequency of avalanches of a given size. • Offers a way to predict how a pile will respond to certain disturbances.

  6. A Common Experimental Setup Avalanches

  7. Tracking Individual Particles: Individual particles behave very differently from the collective avalanche. Used Positron-Emission Particle Tracking to follow the movements of individual particles in a rotating drum.

  8. Tracking Individual Particles: Avalanches do not move particles from top to bottom in one step.

  9. Wet Granular Materials • Added oil to glass beads in a rotating drum. • Amount of oil small compared to amount of beads. • Changes frictional forces, adds cohesive forces.

  10. Wet Granular Materials:Change in Maximum Angle Angle (Degrees) Percent Liquid Content

  11. References • Duran, J. (2000). Sands, powders, and grains. New York: Springer. • Lim, S. Y., Davidson, J. F., Forster, R. N., Parker, D. J., Scott, D. M., & Seville, J. K. (2003). Avalanching of granular material in a horizontal slowly rotating cylinder: PEPT studies. Powder Technology, 25‑30. • Tegzes, P., Schiffer, P., & Vicsek, T. (2002, August). Avalanche Dynamics in Wet Granular Materials. Physical Review Letters, 89(9), 094301‑1 ‑ 094301‑4.

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