Abstract
The axial dispersion of approximately monosized particles in rolling mode in rotating cylinders with bulk flow is examined using a Monte Carlo model and discrete element method (DEM) simulations. The Monte Carlo model predicts that the mean square displacement relative to the mean axial displacement of the bed undergoes oscillations in time. The nature of these oscillations depends on the fill level of the cylinder and the extent of particle mixing during avalanches. When the cylinder is half full the Monte Carlo model predicts undamped oscillations, whereas a filling fraction of 0.26 produces oscillations whose amplitude decreases with time. If mixing during avalanches is assumed to be perfect then the oscillations occur about a linear increase with time. In contrast, if it is assumed that the particles do not mix during avalanching, the oscillations occur about an increase with time which has a gradient which increases with time. There is good qualitative agreement between the Monte Carlo model with perfect mixing and the DEM when the filling fraction is 0.26. For a filling fraction of 0.5 the DEM data show oscillations about a faster than linear increase with time.
This is a preview of subscription content, access via your institution.







References
Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Rev. Mod. Phys. 68, 1259 (1996)
Hill, K.M., Khakhar, D.V., Gilchrist, J.F., McCarthy, J.J., Ottino, J.M.: Proc. Natl. Acad. Sci. 96, 11701 (1999)
Müller, C.R., Davidson, J.F., Dennis, J.S., Fennell, P.S., Gladden, L.F., Hayhurst, A.N., Mantle, M.D., Rees, A.C., Sederman, A.J.: Phys. Rev. Lett. 96, 154504 (2006)
Aranson, I.S., Tsimring, L.S.: Rev. Mod. Phys. 78, 641 (2006)
Sandnes, B., Flekkøy, E.G., Knudsen, H.A., Måløy, K.J., See, H.: Nat. Comm. 2, 288 (2011)
Seiden, G., Thomas, P.J.: Rev. Mod. Phys. 83, 1323 (2011)
Ottino, J.M., Khakhar, D.V.: Annu. Rev. Fluid Mech. 32, 55 (2000)
Fischer, R., Gondret, P., Rabaud, M.: Phys. Rev. Lett. 103, 128002 (2009)
Ristow, G.H.: Europhys. Lett. 34, 263 (1996)
Hajra, S.K., Khakhar, D.V.: Phys. Fluids 17, 013101 (2005)
Zik, O., Stavans, J.: Europhys. Lett. 16, 255 (1991)
Mellmann, J.: Powder Technol. 118, 251 (2001)
Hehl, M., Kröger, H., Helmrich, H., Schügerl, K.: Powder Technol. 20, 29 (1978)
Third, J.R., Müller, C.R.: Phys. Rev. E 86, 061314 (2012)
Hogg, R., Cahn, D.S., Healy, T.W., Fuerstenau, D.W.: Chem. Eng. Sci. 21, 1025 (1966)
Das Gupta, S., Khakhar, D.V., Bhatia, S.K.: Powder Technol. 67, 145 (1991)
Taberlet, N., Richard, P.: Phys. Rev. E 73, 041301 (2006)
Third, J.R., Scott, D.M., Scott, S.A.: Powder Technol. 203, 510 (2010)
Christov, I.C., Stone, H.A.: Proc. Natl. Acad. Sci. 109, 16012 (2012)
Pickering, R.W., Feakes, F., Fitzgerald, M.L.: J. Appl. Chem. 1, 13 (1951)
Saeman, W.C.: Chem. Eng. Prog. 47, 508 (1951)
Vàhl, L., Kingma, W.: Chem. Eng. Sci. 1, 253 (1952)
Kramers, H., Croockewit, P.: Chem. Eng. Sci. 1, 259 (1952)
Rogers, R.S.C., Gardner, R.P.: Powder Technol. 23, 159 (1979)
Rao, S.J., Bhatia, S.K., Khakhar, D.V.: Powder Technol. 67, 153 (1991)
Scott, D.M., Davidson, J.F., Lim, S.-Y., Spurling, R.J.: Powder Technol. 182, 466 (2008)
Rapaport, D.C.: Phys. Rev. E 65, 061306 (2002)
Third, J.R., Scott, D.M., Scott, S.A., Müller, C.R.: Granul. Matter 13, 75 (2011)
Gao, Y., Glasser, B.J., Ierapetritou, M.G., Cuitino, A., Muzzio, F.J., Beeckman, J.W., Fassbender, N.A., Borghard, W.G.: AIChE J. 59, 4068 (2013)
Campbell, C.S.: J. Fluid Mech. 348, 85 (1997)
Kohav, T., Richardson, J.T., Luss, D.: AIChE J. 41, 2465 (1995)
Davidson, J.F., McTait, G.E., Scott, D.M.: In: Fan, L.S., Knowlton, T. (eds.) Fluidization IX: Proceedings of the ninth engineering foundation conference on fluidization, pp. 397–414. Engineering Foundation, Durango (1998)
McTait, G.E.: Residence times and solid flows in rotary kilns. Ph.D. thesis, University of Cambridge (1998)
Li, S.Q., Yan, J.H., Li, R.D., Chi, Y., Cen, K.F.: Powder Technol. 126, 217 (2002)
Ingram, A., Seville, J.P.K., Parker, D.J., Fan, X., Forster, R.G.: Powder Technol. 158, 76 (2005)
Cundall, P.A., Strack, O.D.L.: Géotechnique 29, 47 (1979)
Carley-Macauly, K.W., Donald, M.B.: Chem. Eng. Sci. 19, 191 (1964)
Hogg, R., Fuerstenau, D.W.: Powder Technol. 6, 139 (1972)
Acknowledgments
We are grateful to the referees for helpful and constructive comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Third, J., Scott, D., Lu, G. et al. Modelling axial dispersion of granular material in inclined rotating cylinders with bulk flow. Granular Matter 17, 33–41 (2015). https://doi.org/10.1007/s10035-014-0542-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-014-0542-0
Keywords
- Axial dispersion
- Rotating cylinders