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

  • Tankeo M
  • Richard P
  • Canot É
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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 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.

Author-supplied keywords

  • analytical solution
  • granular flows
  • rheology

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Authors

  • Merline Tankeo

  • Patrick Richard

  • Édouard Canot

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