Influence of magnetic cohesion on the stability of granular slopes

We use a molecular dynamics model to simulate the formation and evolution of a granular pile in two dimensions in order to gain a better understanding of the role of magnetic interactions in avalanche dynamics. We find that the angle of repose increases only slowly with magnetic field; the increase in angle is small even for intergrain cohesive forces many times stronger than gravity. The magnetic forces within the bulk of the pile partially cancel as a result of the anisotropic nature of the dipole-dipole interaction between grains. However, we show that this cancellation effect is not sufficiently strong to explain the discrepancy between the angle of repose in wet systems and magnetically cohesive systems. In our simulations we observe shearing deep within the pile, and we argue that it is this motion that prevents the angle of repose from increasing dramatically. We also investigate different implementations of friction with the front and back walls of the container, and conclude that the nature of the friction dramatically affects the influence of magnetic cohesion on the angle of repose.

Figure 1

A snapshot of a granular slope in the absence of a magnetic field. The diagonal line is a fit to the surface particles (darkly shaded). The lightly shaded particles adhere to the base of the container. The vertical line, a quarter of the container width from the left wall, is the position at which we evaluate the particles’ velocities and magnetic forces as a function of depth in the pile, as discussed in Sec. 4.

Figure 2

Angle of repose as a function of cohesion strength $R$ in a vertical magnetic field in a container of width of 50 particle diameters.

Figure 3

Total radial magnetic force $F_{\text{total}}$ per particle as a function of vertical position in the pile, measured at a horizontal position a quarter of the container width away from the left wall (the vertical line in Fig. 1). The horizontal line on the graph is $1.76F_v$. The particle positions are normalized so that the bottom of the pile is 0 and the top is 1.

Figure 4

The mean velocity per particle as a function of vertical position in the pile, measured at a horizontal position a quarter of the container width away from the left wall (the vertical line in Fig. 1). The particle positions are normalized so that the bottom of the pile is 0 and the top is 1. The addition of a magnetic field shifts the motion farther down into the bulk of the pile.

Figure 5

Angle of repose as a function of cohesion strength $R$ in a vertical magnetic field in a container of width of 50 particle diameters. Results are shown for different values of the friction percentage $p$.

Figure 6

The mean velocity per particle as a function of vertical position in the pile, measured at a horizontal position a quarter of the container width away from the left wall (the vertical line in Fig. 1). The particle positions are normalized so that the bottom of the pile is 0 and the top is 1. Results are shown for (a) $R=0$ and (b) $R=10$ at different values of the friction percentage $p$.

Figure 7

Angle of repose as a function of cohesion strength $R$ in a vertical magnetic field in a container of width of 50 particle diameters. Particles slide against the front and back walls of the container and are subject to a drag force $\alpha mg$ proportional to the particle weight. Results are shown for different values of the drag constant $\alpha$.