Volume 79, Number 3, August 2007
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||13 July 2007|
A mean-field model for the rheology and the dynamical phase transitions in the flow of granular matter
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, UMR 7636 CNRS, Université Paris 7 10 rue Vauquelin, 75231 Paris Cedex 05, France
Accepted: 14 June 2007
Based on a large set of experiments and numerical simulations, it has been recently shown (GDR MiDi (collective work), Eur. Phys. J. E, 14 (2004) 341) that dense granular flows are well described by a local rheology: the ratio of the shear stress to the normal stress P is an increasing function of the properly rescaled shear rate I. We propose a mean field model for this quasi-local constitutive relation and the phase diagram of granular matter, based on the motion of single spherical grain on an array of identical grains. The model recovers a “solid-liquid” transition that is controlled by potential trapping, as well as a subcritical “liquid-gas" transition governed by the restitution coefficient. The system presents a “triple point” above which the grain directly leaves the static equilibrium to enter the gaseous regime. In the liquid regime, the relation between force and velocity is found to be almost independent of the microscopic parameters, friction and restitution coefficient. The dynamics is dominated by potential trapping and leads to a constitutive relation of the form , in close agreement with experimental and numerical results. This rheology is only quasi-local as the inertial number is redefined, introducing the effective number of grains involved in a collision: .
PACS: 45.70.Mg – Granular flow: mixing, segregation and stratification / 83.50.Ax – Steady shear flows, viscometric flow
© Europhysics Letters Association, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.