Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T02:15:37.050Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary conditions for rapid granular flows: phase interfaces

Published online by Cambridge University Press:  26 April 2006

J. T. Jenkins and
E. Askari
J. T. Jenkins
Affiliation:
Department of Theoretical & Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
E. Askari
Affiliation:
Department of Theoretical & Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
Get accessRights & Permissions [Opens in a new window]

Abstract

We consider the region of agitated grains that is at rest in the neighbourhood of its interface with a dense granular flow. We suppose that this region can be modelled as an amorphous solid of nearly elastic spheres in which both momentum and energy are transferred and energy is dissipated in collisions. Making rather rough assumptions about the collision probability, we calculate the stress and energy flux in the solid and use their continuity at the interface to obtain boundary conditions on the flow. We employ them with existing kinetic theory for nearly elastic spheres to solve boundary-value problems for shearing between two such interfaces and between such an interface and a flat plate to which spheres have been rigidly attached. For the latter, we compare the predictions of the theory with the results of experiments.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991, pp. 497 - 508
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Carnahan, N. F. & Starling, K. E., 1979 Equations of state for non-attracting rigid spheres. J. Chem. Phys. 51, 635–636.Google Scholar
Chapman, S. & Cowling, T. G., 1970 The. Mathematical Theory of Nonuniform Gases, 3rd edn. Cambridge University Press.
Craig, K. C., Buckholz, R. & Domoto, G., 1986 An experimental study of the rapid flow of dry eohesionless metal powders. Trans. ASME E: J. Appl. Mech. 53, 935–952.Google Scholar
Dorfman, J. R. & Kirkpatrick, T. R., 1986 Recent results in the kinetic theory of hard sphere systems. In Molecular Dynamics Simulations of Statistical-Mechanical Systems (ed. G. Ciccotti & W. G. Hoover), pp. 260–293. North Holland.
Hanes, D. M. & Inman, D. L., 1985 Observations of rapidly flowing granular-fluid materials. J. Fluid Mech. 150, 357–380.Google Scholar
Hanes, D. M., Jenkins, J. T. & Richman, M. W., 1988 The thickness of steady plane shear flows of circular disks driven by identical boundaries. Trans. ASME E: J. Appl. Mech. 55, 969–974.Google Scholar
Jenkins, J. T.: 1987 Rapid flows of granular materials. In Non-Classical Continuum Mechanics (R. J. Knops & A. A. Lacey). pp. 213–225. Cambridge University Press.
Jenkins, J. T.: 1990 Boundary conditions for rapid granular flow: flat, frictional walls. Trans. ASME E: J. Appl. Mech (under review).Google Scholar
Jenkins, J. T. & Askari, E., 1990 Comparison of theory and experiment for rapid granular shear flow between identical boundaries. Trans. ASME E: J. Appl. Mech. (under review).Google Scholar
Jenkins, J. T. & Richman, M. W., 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic circular disks. Phys. Fluids 28, 3485–3495.Google Scholar
Jenkins, J. T. & Richman, M. W., 1986 Boundary conditions for plane flows of smooth, nearly elastic, circular disks. J. Fluid Mech. 171, 53–69.Google Scholar
Jenkins, J. T. & Savage, S. B., 1983 A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130, 187–202.Google Scholar
Johnson, P. C. & Jackson, R., 1987 Frictional-collisional constitutive relations for granular materials with application to plane shearing. J. Fluid Mech. 176, 67–93.Google Scholar
Louge, M. Y., Jenkins, J. T. & Hopkins, M. A., 1989 Computer simulation of rapid granular shear flows. Phys. Fluids A 2, 1042–1044.Google Scholar
Richman, M. W.: 1988 Boundary conditions based upon a modified Maxwellian distribution for flows of identical, smooth, nearly elastic spheres. Acta Mech. 75, 227–240.Google Scholar
Richman, M. W. & Chou, C. S., 1988 Boundary effects on granular shear flows of smooth disks. Z. Angew Math. Phys. 39, 885–901.Google Scholar
Walton, O. R.: 1990 Computer simulation of rapidly flowing granular solids. In Science on Form (ed. S. Ishizaka). KTK Scientific Publishers.
Woodcock, L. V.: 1981 Glass transition in the hard-sphere model and Kauzmann's paradox. Ann. NY Acad. Sci. 37, 274–298.Google Scholar