Abstract
We investigate both experimentally and theoretically the apparent mass of a ferromagnetic granular assembly filling a cylindrical container and submitted to a magnetic fieldB, aligned vertically along the silo. We show that the mass of the ferromagnetic granular column depends strongly on the applied magnetic field. Notably, our measurements deviate strongly from the exponential saturation of the measured mass as a function of the true mass of the grain packing, as predicted by Janssen [H.A. Janssen, Vereins Eutscher Ingenieure Zeitschrift, 1045 (1895)]. In particular, the measured mass of tall columns decreases systematically as the amplitude of the magnetic field increases. We rationalize our experimental findings by considering the induced magnetic dipole-dipole interactions within the whole packing. We show the emergence of a global magnetic radial force along the walls of the silos, fully determined by the external magnetic field. The resulting tunable frictional interactions allows a full control of the effective mass of the ferromagnetic granular column.
Highlights
More than hundred years ago, a German engineer H.A Janssen studying the failure of silos, proposed a phenomenological model to describe the saturation of the pressure measured at the bottom of a container filled with grains [1]
Janssen’s approach of this problem is simple but transcript nicely the experimental measurements. It can be resumed as follow: (i) the grain assembly is considered as a continuous medium with a homogeneous vertical stress σz along a tube section, (ii) within the grains packing, the vertical stress is redistributed in the horizontal direction following the proportional law: σr = Kσz, with a phenomenological constant K, (iii) the frictional contact forces Fz between the grains and the cylinder wall are at the Coulomb limit Fz = μFr, with μ the friction coefficient
The even more striking effect is clearly seen for the highest amplitude of the magnetic field used, corresponding to Ψ = 35, for which from a certain packing mass m0 ≈ 70 g, the apparent mass of the packing decreases with the actual mass of the packing m0: the more added grains, the lower the apparent mass! Pushing the limits of our experimental setup, using a very tall column corresponding to a mass m0 = 190 g where the magnetic field is not as homogeneous, we could measure that the apparent mass became null for the highest amplitude of the magnetic field applied
Summary
More than hundred years ago, a German engineer H.A Janssen studying the failure of silos, proposed a phenomenological model to describe the saturation of the pressure measured at the bottom of a container filled with grains [1]. Using these three hypothesis on a column slice, Janssen could demonstrate that the apparent mass measured at the base of the silo saturates exponentially, mJ = m∞[1 − exp (−m0/m∞)] characterized by the saturation mass m∞ = (ρπR3)/(2Kμ), with R the tube radius.
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