Skip to main content Accessibility help
×
Home

A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes

  • K. G. Anderson (a1) and R. Jackson (a1)

Abstract

In the past few years kinetic theory has been used to derive equations of motion for rapidly shearing granular materials, and there have been empirical extensions of these to take into account stress transmitted by sustained sliding and rolling contacts between particles. The equations are complicated and solutions have been generated only for very simple flows. In this paper three forms for the equations of motion are considered; one representing interaction by collisions only, one which is a high-density asymptotic form of this, and a third which includes terms representing the ‘frictional’ stresses associated with the sustained contacts referred to above. Solutions are found for fully developed flow under gravity down an inclined plane, and it is shown that the relation between the flow rate and the depth of the flowing layer predicted by the first two sets of equations is not in accord with observations. The third form appears to eliminate much of the discrepancy, but its predictions have not been explored over the whole parameter space. It is emphasized that the form of the solutions should be studied over a wide range of operating conditions in order to assess the usefulness of proposed equations.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes
      Available formats
      ×

Copyright

References

Hide All
Campbell C. S. 1990 Rapid granular flows. Ann. Rev. Fluid Mech. 22, 5792.
Campbell, C. S. & Brennen C. E. 1985 Chute flows of granular material: some computer simulations. Trans. ASME E: J. Appl. Mech. 52, 172178.
Campbell C. S., Brennen, C. E. & Sabersky R. H. 1985 Flow regimes in open-channel flows of granular materials. Powder Tech. 41, 7782.
Haff P. K. 1983 Grain flow as a fluid mechanical phenomenon. J. Fluid Mech. 134, 401430.
Johnson, P. C. & Jackson R. 1987 Frictional-collisional constitutive relations for granular materials, with applications to plane shearing. J. Fluid Mech. 176, 6793.
Johnson P. C., Nott, P. & Jackson R. 1990 Frictional–collisional equations of motion for particulate flows and their applications to chutes. J. Fluid Mech. 210, 501535.
Lun C. K. K., Savage S. B., Jeffrey, D. J. & Chepurniy N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223256.
Nott, P. & Jackson R. 1992 Frictional–collisional equations of motion for granular materials and their application to flow in aerated chutes. J. Fluid Mech. 241, 125144
Savage S. B. 1983 Granular flows down rough inclines - review and extension. In Proc. US–Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials (ed. J. T. Jenkins & M. Satake). Elsevier.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes

  • K. G. Anderson (a1) and R. Jackson (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed