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A constitutive law for dense granular flows

2006; Nature Portfolio; Volume: 441; Issue: 7094 Linguagem: Inglês

10.1038/nature04801

1476-4687

Pierre Jop, Yoël Forterre, Olivier Pouliquen,

Soil and Unsaturated Flow

Equations describing how granular materials move under shear are still a matter of debate. Jop et al. now propose a new model for dense granular flows in three dimensions, inspired by the behaviour of visco-plastic fluids such as toothpaste. The results could serve as a basic tool for modelling complex flows in geophysical or industrial applications. A new model is proposed for dense granular flows in three dimensions, inspired by the behaviour of visco-plastic fluids such as toothpaste — the results could serve as a basic tool for modelling complex flows in geophysical or industrial applications. A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate1,2,3,4,5,6,7,8,9,10. One difficulty is that grains can behave11 like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows12, and soil mechanics for slow plastic flows13. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade14. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical15,16 and experimental work17,18,19. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our 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.