The Thickness of Steady Plane Shear Flows of Circular Disks Driven by Identical Boundaries

[+] Author and Article Information
D. M. Hanes

Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149

J. T. Jenkins

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853

M. W. Richman

Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609

J. Appl. Mech 55(4), 969-974 (Dec 01, 1988) (6 pages) doi:10.1115/1.3173749 History: Received February 12, 1987; Revised April 08, 1988; Online July 21, 2009


We employ balance laws and constitutive relations for rapid, dense, plane flows of identical circular disks together with boundary conditions at a bumpy wall to analyse steady shearing flows maintained by the relative motion of two identical, parallel walls. The disks and the walls are assumed to be frictionless and nearly elastic. Given the properties of the flowing disks, those of the boundary, and the ratio of the tangential and normal tractions applied to the boundary, we determine what the distance between the walls must be for a steady solution to be possible. For these steady solutions we relate the velocity of the walls to the normal and tangential tractions applied to them. We find that in certain circumstances steady motions may be maintained even when the ratio of tangential to normal traction is much less than its value in a homogeneous simple shear. In the Appendix, the corresponding results for spheres are outlined.

Copyright © 1988 by ASME
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