- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Condensed Matter Physics
Volume 2012 (2012), Article ID 906598, 8 pages
Comparison of Constitutive Relationships for Dilute Granular Flow in a Vibrofluidized Cell
Department of Mechanical Engineering, Muhammad Ali Jinnah University, Islamabad, Pakistan
Received 22 February 2012; Revised 19 April 2012; Accepted 20 April 2012
Academic Editor: Nigel Wilding
Copyright © 2012 Nadeem Ahmed Sheikh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Duran, Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials, Springer, 13th edition, 2000.
- P. Evesque, “Shaking dry powders and grains,” Contemporary Physics, vol. 33, no. 4, pp. 245–261, 1992.
- Z. Farkas, P. Tegzes, A. Vukics, and T. Vicsek, “Transitions in the horizontal transport of vertically vibrated granular layers,” Physical Review E, vol. 60, no. 6 B, pp. 7022–7031, 1999.
- C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, “Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield,” Journal of Fluid Mechanics, vol. 140, pp. 223–256, 1984.
- P. K. Haff, “Grain flow as a fluid-mechanical phenomenon,” Journal of Fluid Mechanics, vol. 134, pp. 401–430, 1983.
- J. T. Jenkins and M. W. Richman, “Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks,” Physics of Fluids, vol. 28, no. 12, pp. 3485–3494, 1985.
- V. Kumaran, “Kinetic theory for a vibro-fluidized bed,” Journal of Fluid Mechanics, vol. 364, pp. 163–185, 1998.
- J. M. Montanero, V. Garzó, A. Santos, and J. J. Brey, “Kinetic theory of simple granular shear flows of smooth hard spheres,” Journal of Fluid Mechanics, vol. 389, pp. 391–411, 1999.
- T. W. Martin, J. M. Huntley, and R. D. Wildman, “Hydrodynamic model for a vibrofluidized granular bed,” Journal of Fluid Mechanics, vol. 535, pp. 325–345, 2005.
- R. D. Wildman, T. W. Martin, J. M. Huntley et al., “Experimental investigation and kinetic-theory-based model of a rapid granular shear flow,” Journal of Fluid Mechanics, vol. 602, pp. 63–79, 2008.
- J. M. Huntley, T. W. Martin, M. D. Mantle et al., “NMR measurements and hydrodynamic simulations of phase-resolved velocity distributions within a three-dimensional vibrofluidized granular bed,” Proceedings of the Royal Society A, vol. 463, no. 2086, pp. 2519–2542, 2007.
- V. Garzó, J. W. Dufty, and C. M. Hrenya, “Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport,” Physical Review E, vol. 76, no. 3, Article ID 031303, p. 031303, 2007.
- A. Goldshtein and M. Shapiro, “Mechanics of collisional motion of granular materials—part 1. General hydrodynamic equations,” Journal of Fluid Mechanics, vol. 282, pp. 75–114, 1995.
- A. Goldshtein, M. Shapiro, L. Moldavsky, and M. Fichman, “Mechanics of collisional motion of granular materials—part 2. Wave propagation through vibrofluidized granular layers,” Journal of Fluid Mechanics, vol. 287, pp. 349–382, 1995.
- X. Yang and D. Candela, “Potential energy in a three-dimensional vibrated granular medium measured by NMR imaging,” Physical Review Letters, vol. 85, no. 2, pp. 298–301, 2000.
- S. Warr, J. M. Huntley, and G. T. H. Jacques, “Fluidization of a two-dimensional granular system: experimental study and scaling behavior,” Physical Review E, vol. 52, no. 5, pp. 5583–5595, 1995.
- R. Ramírez, D. Risso, and P. Cordero, “Thermal convection in fluidized granular systems,” Physical Review Letters, vol. 85, no. 6, pp. 1230–1233, 2000.
- A. Goldshtein, V. Kamenetsky, A. Potapov, M. Shapiro, C. Campbell, and D. Degani, “Hydrodynamics of rapid granular flow of inelastic particles into vacuum,” Granular Matter, vol. 4, no. 3, pp. 115–127, 2002.
- J. Bougie, S. J. Moon, J. B. Swift, and H. L. Swinney, “Shocks in vertically oscillated granular layers,” Physical Review E, vol. 66, no. 5, Article ID 051301, p. 051301, 2002.
- C. H. Liu and S. R. Nagel, “Sound in sand,” Physical Review Letters, vol. 68, no. 15, pp. 2301–2304, 1992.
- R. M. Nedderman, Statics and Kinematics of Granular Materials, Cambridge University Press, 1992.
- S. Serna and A. Marquina, “Capturing shock waves in inelastic granular gases,” Journal of Computational Physics, vol. 209, no. 2, pp. 787–795, 2005.
- J. T. Jenkins and M. W. Richman, “Boundary conditions for plane flows of smooth, nearly elastic, circular disks,” Journal of Fluid Mechanics, vol. 171, pp. 53–69, 1986.
- A. Goldshtein, M. Shapiro, and C. Gutfinger, “Mechanics of collisional motion of granular materials—part 4. Expansion wave,” Journal of Fluid Mechanics, vol. 327, pp. 117–138, 1996.
- N. F. Carnahan and K. E. Starling, “Equation of state for nonattracting rigid spheres,” The Journal of Chemical Physics, vol. 51, no. 2, pp. 635–636, 1969.
- S. Torquato, “Nearest-neighbor statistics for packings of hard spheres and disks,” Physical Review E, vol. 51, no. 4, pp. 3170–3182, 1995.
- V. Garzó and J. W. Dufty, “Dense fluid transport for inelastic hard spheres,” Physical Review E, vol. 59, no. 5, pp. 5895–5911, 1999.
- J. J. Brey, J. W. Dufty, and A. Santos, “Kinetic models for granular flow,” Journal of Statistical Physics, vol. 97, no. 1-2, pp. 281–322, 1999.
- J. T. Jenkins and M. Y. Louge, “On the flux of fluctuation energy in a collisional grain flow at a flat, frictional wall,” Physics of Fluids, vol. 9, no. 10, pp. 2835–2840, 1997.
- R. D. Wildman, T. W. Martin, P. E. Krouskop, J. Talbot, J. M. Huntley, and D. J. Parker, “Convection in vibrated annular granular beds,” Physical Review E, vol. 71, no. 6, Article ID 061301, p. 061301, 2005.
- H. Viswanathan, N. A. Sheikh, R. D. Wildman, and J. M. Huntley, “Convection in three-dimensional vibrofluidized granular beds,” Journal of Fluid Mechanics, vol. 682, pp. 185–212, 2011.
- C. Huan, X. Yang, D. Candela, R. W. Mair, and R. L. Walsworth, “NMR experiments on a three-dimensional vibrofluidized granular medium,” Physical Review E, vol. 69, no. 4, Article ID 041302, 13 pages, 2004.