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

Abstract

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≤2×10−2. Turning to the analysis of grains velocity fluctuations, we compute the associated correlation length λ and show its dependence on the inertial number: λ/d∝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 ξ=d(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.