Using x-ray rheography to estimate the 3D field of inertial numbers in flowing granular media

¹ Université Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP, IGE, 38000 Grenoble, France
² School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
³ School of Computer Science and Mathematics, Liverpool John Moores University, Liverpool, L3 3AF, UK

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
^** e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
^*** e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
^**** e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
^† e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 1 December 2025

Abstract

The rheology of granular materials is commonly described using the inertial number (I) as a measure of their fluidity. As the ratio between the time of macroscopic deformation and the time of microscopic rearrangement, I depends on the shear strain rate within the medium, which can vary in space. With dry granular media being opaque, experimental measurements of the field of inertial numbers were mainly limited to twodimensional (2D) observations along transparent walls in three-dimensional (3D) systems. This work addresses this gap using dynamic x-ray rheography of continuously flowing granular materials through an open channel conveyor belt setup. The granular medium is driven towards a perpendicular wall and forms a steady heap, for which the velocity field along the belt direction is measured in 3D. When used to estimate the shear strain rate, it is shown that, under the heap, a marked 3D pattern develops in the spatial distribution of I. The experimental findings are cross-validated with discrete element method simulations.