Analytical solution of the $\mu(I)-$rheology for fully developed granular flows in simple configurations

Merline Tankeo (1) , Patrick Richard (1, 2) , Édouard Canot (3)

1 IPR - Institut de Physique de Rennes
2 IFSTTAR/MAST/GPEM - Granulats et Procédés d'Elaboration des Matériaux
3 SAGE - Simulations and Algorithms on Grids for Environment

Using the $\mu(I)$ continuum model recently proposed for dense granular flows, we study theoretically steady and fully developed granular flows in two configurations: a plane shear cell and a channel made of two parallel plates (Poiseuille configuration). In such a description, the granular medium behaves like a fluid whose viscosity is a function of the inertia. In the shear plane geometry our calculation predicts that the height of the shear bands scales with $U_0^{1/4}P_0^{1/2}$, where $U_0$ is the velocity of the moving plate and $P_0$ the pressure applied at its top. In the Poiseuille configuration, the medium is sheared between the lateral boundaries and a plug flow is located in the center of the channel. The size of the plug flow is found to increase for a decreasing pressure gradient. We show that, for small pressure gradient, the granular material behaves like a Bingham plastic fluid.

Mots clés: granular materials; shear; Poiseuille; analytical solution

Domaines: Autre [cond-mat.other]

Merline Tankeo, Patrick Richard, Édouard Canot. Analytical solution of the $\mu(I)-$rheology for fully developed granular flows in simple configurations. Granular Matter, 2013, 15 (6), pp.881-891. ⟨10.1007/s10035-013-0447-3⟩. ⟨hal-00859926⟩