Publication 17-CNA-011

Normal stress effects in the gravity driven flow of granular materials

We-Tao Wu
Department of Biomedical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
weitaow@andrew.cmu.edu

Nadine Aubry
Department of Mechanical and Industrial Engineering
Northeastern University
Boston, MA 02115
n.aubry@northeastern.edu

James F. Antaki
Department of Biomedical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
antaki@cmu.edu

Mehrdad Massoudi
Center for Nonlinear Analysis
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
and
National Energy Technology Laboratory (NETL)
U.S. Department of Energy
626 Cochrans Mill Road, P.O. Box 10940
Pittsburgh, PA 15236
massoudi@netl.doe.gov

Abstract: In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined plates. We assume that the granular materials can be represented by a modified form of the second grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fraction has reached the critical/maximum packing value. The numerical results indicate that the newly proposed stress tensor has obvious and physically meaningful effects on both the velocity and the volume fraction fields.

Get the paper in its entirety as  17-CNA-011.pdf

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