Hui, K. and Haff, P. K. and Ungar, J. E. and Jackson, R. (1984) Boundary conditions for high-shear grain flows. Journal of Fluid Mechanics, 145 . pp. 223-233. ISSN 0022-1120 http://resolver.caltech.edu/CaltechAUTHORS:20120702-103050439
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Boundary conditions are developed for rapid granular flows in which the rheology is dominated by grain–grain collisions. These conditions are v_0=constdv_0/dy and u_0 = constdu_0/dy, where v and u are the thermal (fluctuation) and flow velocities respectively, and the subscript indicates that these quantities and their derivatives are to be evaluated at the wall These boundary conditions are derived from the nature of individual grain–wall collisions, so that the proportionality constants involve the appropriate coefficient of restitution ew for the thermal velocity equation, and the fraction of diffuse (i.e. non-specular) collisions in the case of the flow-velocity equation. Direct application of these boundary conditions to the problem of Couette-flow shows that as long as the channel width h is very large compared with a grain diameter d it is permissible to set v=0 at the wall and to adopt the no-slip condition. Exceptions occur where d/h is not very small, when the wall is not rough, and when the grain–wall collisions are very elastic. Similar insight into other flows can be obtained qualitatively by a dimensional analysis treatment of the boundary conditions. Finally, the more difficult problem of self-bounding fluids is discussed qualitatively.
|Additional Information:||© 1984 Cambridge University Press. Received 3 January 1984. Published online: 20 April 2006. We would like to thank R. L. Shreve for helpful discussions. This work was supported in part by the National Science Foundation (EAR 82-12372). During the course of this work R. Jackson was a Sherman Fairchild Distinguished Scholar at Caltech.|
|Official Citation:||K. Hui, P. K. Haff, J. E. Ungar and R. Jackson (1984). Boundary conditions for high-shear grain flows. Journal of Fluid Mechanics, 145 , pp 223-233 doi:10.1017/S0022112084002883|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||03 Jul 2012 15:19|
|Last Modified:||26 Dec 2012 15:27|
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