# A note on Stokes' problem in dense granular media using the $\mu(I)$--rheology

@article{Jerome2018ANO,
title={A note on Stokes' problem in dense granular media using the \$\mu(I)\$--rheology},
author={J. John Soundar Jerome and Bastien Di Pierro},
journal={arXiv: Fluid Dynamics},
year={2018}
}
• Published 26 March 2018
• Physics
• arXiv: Fluid Dynamics
The classical Stokes' problem describing the fluid motion due to a steadily moving infinite wall is revisited in the context of dense granular flows of mono-dispersed beads using the recently proposed $\mu(I)$--rheology. In Newtonian fluids, molecular diffusion brings about a self-similar velocity profile and the boundary layer in which the fluid motion takes place increases indefinitely with time $t$ as $\sqrt{\nu t}$, where $\nu$ is the kinematic viscosity. For a dense granular visco-plastic…
1 Citations

## References

SHOWING 1-10 OF 56 REFERENCES

### The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a μ(I)-rheology

• Engineering
Journal of Fluid Mechanics
• 2011
Abstract There is a large amount of experimental and numerical work dealing with dry granular flows (such as sand, glass beads, etc.) that supports the so-called $\ensuremath{\mu} (I)$-rheology. The

### Well-posed and ill-posed behaviour of the ${\it\mu}(I)$ -rheology for granular flow

• Physics
Journal of Fluid Mechanics
• 2015
In light of the successes of the Navier–Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging

### Partial regularisation of the incompressible 𝜇(I)-rheology for granular flow

• Mathematics
Journal of Fluid Mechanics
• 2017
In recent years considerable progress has been made in the continuum modelling of granular flows, in particular the $\unicode[STIX]{x1D707}(I)$ -rheology, which links the local viscosity in a flow to

### A two-dimensional depth-averaged ${\it\mu}(I)$ -rheology for dense granular avalanches

• Geology
Journal of Fluid Mechanics
• 2015
Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the

### Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects

• Geology
• 2016
We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22°) and compare precisely the results with laboratory experiments. Incompressibility

### On the stability of the μ(I) rheology for granular flow

• Physics
Journal of Fluid Mechanics
• 2017
This article deals with the Hadamard instability of the so-called $\unicode[STIX]{x1D707}(I)$ model of dense rapidly sheared granular flow, as reported recently by Barker et al. (J. Fluid Mech., vol.

### A constitutive law for dense granular flows

• Geology, Engineering
Nature
• 2006
The results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

### STOKES FIRST PROBLEM FOR AN OLDROYD-B FLUID IN A POROUS HALF SPACE

• Engineering
• 2005
Based on a modified Darcy’s law for a viscoelastic fluid, Stokes’ first problem was extended to that for an Oldroyd-B fluid in a porous half space. By using Fourier sine transform, an exact solution