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

2013/09/09 by Tankeo, Merline, Richard, Patrick, Canot, Edouard
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Soft Condensed Matter (cond-mat.soft)

paper · doi:10.48550/arxiv.1309.2267

Abstract

Using the μ(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 U₀^1/4P₀^1/2, where U₀ is the velocity of the moving plate and P₀ 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.

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