TY - JOUR

T1 - Flow and jamming of a two-dimensional granular bed: Toward a nonlocal rheology?

AU - Staron, Lydie

AU - Lagree, Pierre-Yves

AU - Josserand, Christophe

AU - Lhuillier, Daniel

PY - 2010/11

Y1 - 2010/11

N2 - In order to test the rheology of granular flows, we performed series of numerical simulations of nearly monodisperse stationary chute flows from rapid to slow and very slow flow regime, namely, close to the jamming transition We check how existing rheological models (i e, Bagnold's model and the I-model) capture the behavior of the numerical flows, and perform an acute characterization of the structure of the flow in terms of grains velocity fluctuations close to the jamming transition The simulations show that both Bagnold's and the I-model fail to describe the data points in the slow regime, namely, when I <= 2 x 10(-2) Turning to the analysis of grains velocity fluctuations, we compute the associated correlation length lambda and show its dependence on the inertial number lambda/d proportional to I-0 32 The amplitude of the grains velocity fluctuations, namely, the granular temperature, exhibits a power-law dependence on the shear rate and allows for an efficient prediction of the shape of the velocity profiles The main result consists of a scaling merging all data points for all flow regimes onto the same master curve, and relating granular temperature, shear rate, and the variation of stress between the considered depth and the bottom wall This scaling can be written as a relation between local stress, local shear rate, and local temperature, provided the introduction of a characteristic length scale xi=d root(H-z)/z where both the distance to the surface and the distance to the bottom wall are involved This scaling strongly suggests a nonlocal behavior, valid in the flow regime and extending close to the jamming transition, and hints at granular temperature as the variable at the origin of the nonlocality (C) 2010 American Institute of Physics [doi 10 1063/1 3499353]

AB - In order to test the rheology of granular flows, we performed series of numerical simulations of nearly monodisperse stationary chute flows from rapid to slow and very slow flow regime, namely, close to the jamming transition We check how existing rheological models (i e, Bagnold's model and the I-model) capture the behavior of the numerical flows, and perform an acute characterization of the structure of the flow in terms of grains velocity fluctuations close to the jamming transition The simulations show that both Bagnold's and the I-model fail to describe the data points in the slow regime, namely, when I <= 2 x 10(-2) Turning to the analysis of grains velocity fluctuations, we compute the associated correlation length lambda and show its dependence on the inertial number lambda/d proportional to I-0 32 The amplitude of the grains velocity fluctuations, namely, the granular temperature, exhibits a power-law dependence on the shear rate and allows for an efficient prediction of the shape of the velocity profiles The main result consists of a scaling merging all data points for all flow regimes onto the same master curve, and relating granular temperature, shear rate, and the variation of stress between the considered depth and the bottom wall This scaling can be written as a relation between local stress, local shear rate, and local temperature, provided the introduction of a characteristic length scale xi=d root(H-z)/z where both the distance to the surface and the distance to the bottom wall are involved This scaling strongly suggests a nonlocal behavior, valid in the flow regime and extending close to the jamming transition, and hints at granular temperature as the variable at the origin of the nonlocality (C) 2010 American Institute of Physics [doi 10 1063/1 3499353]

U2 - 10.1063/1.3499353

DO - 10.1063/1.3499353

M3 - Article (Academic Journal)

VL - 22

SP - -

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 11

M1 - 113303

ER -