Volume 52, Number 2, October II 2000
|Page(s)||137 - 143|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||01 September 2002|
A self-similar model for shear flows in dense granular materials
The James Franck Institute, The University of Chicago
5640 South Ellis Avenue,
Chicago, IL 60637, USA
Accepted: 4 September 2000
We propose a model to describe the quasistatic shearing of dry granular materials, which notably captures the differences in velocity profiles recently observed in 2 and 3D Couette flow experiments. In our scheme, the steady-state flow is due to the intermittent motion of clusters of particles moving together with the wall. The motion of a cluster is associated with the transient formation of a fracture inside the sheared pack. The model is based on the existence of a persistence length for the fractures, which imposes a self-similar structure on the clusters. Through a probabilistic approach, we can evaluate the rate of appearance of a cluster of a given size and obtain a prediction for the average velocity profiles. We also predict the existence of large stress fluctuations at the moving wall, whose characteristics are in good agreement with experimental data.
PACS: 45.70.-n – Granular systems / 83.50.Ax – Steady shear flows / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, 2000
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