Grain Size Reduction in Granular Flows of Spheres: The Effects of Critical Impact Energy

[+] Author and Article Information
M. W. Richman

Mechanical Engineering Department, Higgins Laboratories, Worcester Polytechnic Institute, Worcester, MA 01609

A. A. Oyediran

National Research Council, Fluid Dynamics Branch, Space Science Laboratory, NASA Marshall Space Flight Center, Huntsville, AL 35812

J. Appl. Mech 59(2S), S17-S22 (Jun 01, 1992) doi:10.1115/1.2899485 History: Received December 28, 1989; Revised March 07, 1991; Online March 31, 2008


We extend methods employed to derive recent kinetic theories for rapid noncomminuting granular flows, to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles’ peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the pressure tensor and collisional rates of mass and energy lost. We improve upon the work of Richman and Chou (1989) by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction, granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.

Copyright © 1992 by The American Society of Mechanical Engineers
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