Coulomb’s Model
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Coulomb’s Model θ r θ max Δθ Identified two characteristic Angles: • θ r , Angle of Repose • θ max , Maximum Stable Angle Additional material treated as a single entity.
description
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. - PowerPoint PPT Presentation
Transcript of Coulomb’s Model
Coulomb’s Model
θr
θmaxΔθ
Identified two characteristic Angles:
•θr, Angle of Repose•θmax, Maximum Stable Angle
Additional material treated as a single entity.
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.)
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.
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.
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.
A Common Experimental Setup
Avalanches
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.
Tracking Individual Particles:
Avalanches do not move particles from top to bottom in one step.
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.
Wet Granular Materials:Change in Maximum Angle
Percent Liquid Content
Ang
le (
Deg
rees
)
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.
