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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Taylor, Kathryn Helen
Languages: English
Types: Unknown
Subjects:
This thesis presents an investigation into the influence of magnetic cohesion on the stability of granular slopes. We consider magnetic cohesion that results from the interaction between dipole moments induced in grains by a uniform magnetic field. The repose angle of spheres is known to increase much more slowly with magnetic cohesion than in experiments with liquid-bridge cohesion. To our knowledge, nowhere in the literature has anyone offered a satisfactory explanation of this discrepancy. Our two-dimensional molecular dynamics simulations of granular piles show that shear occurs deep in the pile. The addition of a magnetic field causes the motion to shift farther down into the pile, preventing the angle from increasing substantially. We investigate different models of wall friction, and discover that wall interactions have a significant influence on the rate of increase of the slope angle with magnetic cohesion. In three-dimensional simulations we observe an initial decrease in the repose angle as the cohesion is increased, contrary to expectations. We explain this effect by considering how the transverse magnetic force influences the particle distribution of the pile. In contrast, draining-crater experiments reveal that the angle of repose of diamagnetic bismuth grains increases dramatically with cohesion in a vertical field. We argue that this difference is due to the non-spherical shape of the grains, and investigate further the influence of grain shape by using non-magnetic `voids' of different shapes in a paramagnetic solution. We discover a strong positive correlation between the grain aspect ratio and the size of the effect of magnetic cohesion on the slope angle. This is because a non-spherical grain accumulates magnetic charge on sharp edges and corners, increasing the magnetic field in its immediate vicinity and leading to stronger interactions with neighbouring grains. Also, in piles of grains with larger aspect ratios, avalanches occur closer to the surface, thus increasing the stability of the pile.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 8.1 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
    • A Magnetic levitation 171
    • A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
    • A.2 Earnshaw's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
    • A.3 Stability criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
    • A.4 Effective gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
    • A.5 Levitation of permanent magnets . . . . . . . . . . . . . . . . . . . . 176
    • A.6 Magneto-Archimedes effect . . . . . . . . . . . . . . . . . . . . . . . . 176
    • A.6.1 Literature review of the magneto-Archimedes effect and non-
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    • horizontal field 180
    • B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
    • B.2 Slope angles of bismuth grains in manganese chloride solution . . . . 181
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