The diversity of boundary conditions and geometries made it difficult for a long time to extract the intrinsic rheology of dense inertial flows until a unification was achieved in 2004 by the « GDR-MiDi group » in terms of a single dimensionless inertial number I, defined as the ratio of two characteristic times (relaxation vs. shear). The increase in macroscopic friction with I despite an ever-lower solid fraction is a non-negligible property that reveals a complex microstructure. In the framework of my post-doc in 2008 we extended the « inertial number paradigm » to non-spherical grain flows. Later, a major result was to illuminate the role of structural anisotropy on the increase of internal friction with the inertial number I. In the framework of an industrial project with Arcelor Mittal, on cohesive flows, we showed that a dimensionless number combining the inertial number and the cohesion index scales the shear strength and microstructure variables. This work should continue on highly polydisperse flows, as well as on the extension to submerged granular flows, i.e. counting with a fluid phase modelled by a Finite Element approach.

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