This work generalises the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)] to the determination of the pressure. We focus on the Bagnold regime, and provide theoretical support to the empirical $μ(\mathcal{I})$ rheology laws, that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the $μ(\mathcal{I})$ laws apply.
In this letter, we investigate the transient rheological behavior of immersed granular flows using both experiments of submerged granular column collapses and corresponding numerical simulations. The simulations are performed with the lattice-Boltzmann method (LBM) coupled with the discrete element method (DEM) and provide a significant amount of data of the stress and deformation conditions at different positions and times during the granular collapse. We derive a new dimensionless number $\mathcal{G}$ that can unify the rheology of transient granular flows in different regimes for all the si…
The Granular Integration Through Transients (GITT) formalism gives a theoretical description of the rheology of moderately dense granular flows and suspensions. In this work, we extend the GITT equations beyond the case of simple shear flows studied before. Applying this to the particular example of extensional flows, we show that the predicted behavior is somewhat different from that of the more frequently studied simple shear case, as illustrated by the possibility of non monotonous evolution of the effective friction coefficient $μ$ with the inertial number $\mathcal{I}$. By the reduction o…
We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles under pressure-imposed conditions, subject to a sudden change in shear rate or external pressure. Discrete Element Method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may strongly differ from the prediction of the Suspension Balance Model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (2009), which prescribes …
Understanding the rheology of granular assemblies is important for natural and engineering systems, but the relationship between inter-particle friction (or microscopic friction) and macroscopic friction is still not well understood. In this study, using the the discrete element method (DEM) with spherical particles and realistic contact laws, we investigate the mechanics of granular systems with a wide range of inter-particle frictional coefficients and aim to establish a friction-dependent rheology for dry granular flows. The corresponding results show that increasing inter-particle friction…
Macroscopic and microscopic properties of dense granular layers flowing down inclined planes are obtained from Discrete-Element-Method simulations for both frictionless and frictional grains. Three fundamental observations for dense granular flows are recovered, namely the occurrence of a critical stress, the Bagnold velocity profile, as well as well-defined friction and dilatancy laws. The microscopic aspects of the grain motion highlight the formation of transient clusters. From this microscopic picture, we derive a theoretical scaling model without any empirical input that explains quantita…
