Reverse Janssen Effect in Narrow Granular Columns

Featured in Physics
Editors' Suggestion

Reverse Janssen Effect in Narrow Granular Columns

Shivam Mahajan, Michael Tennenbaum, Sudhir N. Pathak, Devontae Baxter, Xiaochen Fan, Pablo Padilla, Caleb Anderson, Alberto Fernandez-Nieves, and Massimo Pica Ciamarra

Phys. Rev. Lett. 124, 128002 – Published 27 March 2020

See Focus story: Some Granular Columns Weigh Too Much

Abstract

When grains are added to a cylinder, the weight at the bottom is smaller than the total weight of the column, which is partially supported by the lateral walls through frictional interactions with the grains. This is known as the Janssen effect. Via a combined experimental and numerical investigation, here we demonstrate a reverse Jansen effect whereby the fraction of the weight supported by the base overcomes one. We characterize the dependence of this phenomenon on the various control parameters involved, rationalize the physical process causing the emergence of the compressional frictional forces responsible for the anomaly, and introduce a model to reproduce our findings. Contrary to prior assumptions, our results demonstrate that the constitutive relation on a material element can depend on the applied stress.

Received 2 October 2019
Revised 28 January 2020
Accepted 20 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.128002

Physics Subject Headings (PhySH)

Granular materials Granular solids Packing & jamming problems

Molecular dynamics

Polymers & Soft Matter

Focus

Some Granular Columns Weigh Too Much

Published 27 March 2020

Particles packed inside a cylinder can experience a downward force from the walls, resulting in an apparent weight increase.

See more in Physics

Authors & Affiliations

Shivam Mahajan ¹, Michael Tennenbaum², Sudhir N. Pathak¹, Devontae Baxter ², Xiaochen Fan ², Pablo Padilla², Caleb Anderson², Alberto Fernandez-Nieves^2,3,4,*, and Massimo Pica Ciamarra ^1,5,†

¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
²School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
³Department of Condensed Matter Physics, University of Barcelona, 08028 Barcelona, Spain
⁴ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
⁵CNR–SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy

^*alberto.fernandez@physics.gatech.edu
^†massimo@.ntu.edu.sg

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 124, Iss. 12 — 27 March 2020

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Experimental results for the dependence of the apparent mass, $m_{a}$ , on the added mass, $m$ , for a cylinder with diameter $D = (172.00 \pm 0.15) mm ≃ 29 σ$ , panel (a), and $D = (49.10 \pm 0.15) mm ≃ 8.2 σ$ , panel (b), with $σ$ the grain diameter. Error bars are standard deviations from the average over three different realizations. (c) Dependence of the ratio of the apparent to added mass, $m_{a} / m$ , on the filling height relative to the grain diameter, $h / σ$ , for different $D$ . Full lines are fit to the theoretical model, with $ξ ≃ 5.0 σ$ , $h_{a} ≃ 9 σ$ , $h^{*} ≃ 17 σ$ , $F_{c} = - 1.4 Mg$ , and $k$ varying in the range [0.03, 0.12]. (d) Characteristic length scales corresponding to ( $h_{a}$ ) the height where the deviation from the hydrodynamic expectation starts, ( $h^{*}$ ) the height corresponding to the maximum in $m_{a} / m$ , and ( $h_{d}$ ) the height to the right of the maximum where $m_{a} / m = 1$ .
Reuse & Permissions
Figure 2
(a) Ratio of apparent to total mass as a function of the normalized filling height, $h / σ$ , for cylinders with different diameters. Error bars are standard deviations from the average over three different realizations. Full lines are fit to the theoretical model, with $ξ ≃ 5.6 σ$ , $h_{a} ≃ 5.6 σ$ , $h^{*} ≃ 10.5 σ$ , $F_{c} = - 0.36$ Mg, and $k ≃ 0.14$ . (b) Cylinder-diameter dependence of the characteristic heights where the reverse Janssen effect appears ( $h_{a}$ ), reaches its maximum ( $h^{*}$ ), and disappears ( $h_{d}$ ). (c,d) Simulation snapshots illustrating the force network in the granular column with $D = 8 σ$ . Each segment connects the positions ( $r, h$ ) of two interacting grains, with $r$ the radial position. The color indicates the magnitude of the interaction force according to the color-scale in (c). Only the largest (5%) forces are shown in each panel. In (c), the filling height is in the anomalous region, while in (d) the filling height ( $h = 25 σ$ ) is in the saturation region. In the latter case, we only show the forces deep in the column ( $h < 13 σ$ ).
Reuse & Permissions
Figure 3
(a) Average frictional force exerted by the wall on a particle as a function of the relative depth $z / σ$ . Negative forces are compressive. (b) Numerical results for the displacements (red arrows) of a stable frictionless packing of disks induced by the addition of a new grain, the shaded one. Shown displacement vectors have an increased length relative to the actual value of $10^{5}$ . (c) Force exerted by the wall on a given particle, as a function of its depth. The depth increases as more particles are added to the column. (d) Depth dependence of the average value of the ratio between the normal and tangential forces the wall exert on each particle. The ratio exponentially approaches a constant value, with length scale $ξ ≃ 6 σ$ . In panels (a,c,d), the cylinder diameter is $D = 8 σ$ , while the friction coefficient is $μ = 0.2$ .
Reuse & Permissions
Figure 4
Experimental and numerical results for the dependence of the maximum of the reported anomaly on the cylinder diameter relative to the grain size.
Reuse & Permissions

Physical Review Letters