Magnetic Janssen effect

L Thorens,K J Måløy,S Santucci,M Bourgoin

doi:10.1038/s41467-021-22722-y

Abstract

A pile of grains, even when at rest in a silo, can display fascinating properties. One of the most celebrated is the Janssen effect, named after the pioneering engineer who explained the pressure saturation at the bottom of a container filled with corn. This surprising behavior arises because of frictional interactions between the grains through a disordered network of contacts, and the vessel lateral walls, which partially support the weight of the column, decreasing its apparent mass. Here, we demonstrate control over frictional interactions using ferromagnetic grains and an external magnetic field. We show that the anisotropic pairwise interactions between magnetized grains result in a radial force along the walls, whose amplitude and direction is fully determined by the applied magnetic field. Such magnetic Janssen effect allows for the fine tuning of the granular column apparent mass. Our findings pave the way towards the design of functional jammed materials in confined geometries, via a further control of both their static and dynamic properties.

Highlights

A pile of grains, even when at rest in a silo, can display fascinating properties
Without any magnetic field applied, Ψ = 0, we retrieve the typical exponential saturation of the measured mass predicted by Janssen[10]
We observe a deviation from Janssen’s prediction as soon as a magnetic field is applied to the granular column

Summary

Introduction

A pile of grains, even when at rest in a silo, can display fascinating properties. One of the most celebrated is the Janssen effect, named after the pioneering engineer who explained the pressure saturation at the bottom of a container filled with corn. In order to understand and avoid the failure of silos, which is still an industrial problem nowadays, Janssen proposed in a seminal work[10] a simple continuum phenomenology to explain this puzzling behavior His model relies on three hypothesis, (i) within the grains packing, the vertical stresses σz are redistributed proportionally to the horizontal ones, σr = kσz, with a phenomenological constant k (ii) the frictional contact forces Fz between the particles and the walls are at their Coulomb threshold, Fz = μFr with μ the friction coefficient between the grains and the wall, and (iii) the grain assembly is considered as a continuous medium. Despite some criticisms and refinements[5,9,11,12,13,14], Janssen’s approach has become a “classic”, and its predictions have been shown to accurately describe experimental data, as long as the packing preparation leads to a full mobilization of the frictional forces along the container wall

Methods

Results

Conclusion