The equation of state for almost elastic, smooth, polydisperse granular gases for arbitrary density

Lecture Notes in Physics

Volumn 564, Issue , 2001, Pages 383-409

  Luding, Stefan ^a   Strauß, Oliver ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84873406650     PISSN: 00758450     EISSN: 16166361     Source Type: Book Series    
DOI: None     Document Type: Chapter

References (35)

1. S. Chapman and T. G. Cowling. The mathematical theory of nonuniform gases. Cambridge University Press, London (1960).
2. J. M. Ziman. Models of Disorder. Cambridge University Press, Cambridge (1979).
3. J. P. Hansen and I. R. McDonald. Theory of simple liquids. Academic Press Limited, London (1986).
4. L. D. Landau and E. M. Lifschitz. Physikalische Kinetik. Akademie Verlag Berlin, Berlin (1986).
5. H. J. Herrmann, J.-P. Hovi, and S. Luding, editors. Physics of dry granular media - NATO ASI Series E 350. Kluwer Academic Publishers, Dordrecht 1998.
6. P. K. Haff. Grain flow as a fluid-mechanicalphenomenon. J. Fluid Mech. 134, 401 (1983).
7. J. T. Jenkins and M. W. Richman. Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. of Fluids 28, 3485 (1985).
8. P. Sunthar and V. Kumaran. Temperature scaling in a dense vibrofluidized granular material. Phys. Rev. E 60, 1951 (1999).
9. T. P. C. van Noije and M. H. Ernst. Velocity distributions in homogeneously cooling and heated granular fluids. Granular Matter 1, 57 (1998).
10. N. Sela and I. Goldhirsch. Hydrodynamic equations for rapid flows of smooth inelastic spheres, to burnett order. J. Fluid Mech. 361, 41 (1998).
11. B. J. Alder and T. E. Wainwright. Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459 (1959).
12. R. J. Buehler, Jr. R. H. Wentorf, J. O. Hirschfelder, and C. F. Curtiss. The free volume for rigid sphere molecules. J. of Chem. Phys. 19, 61 (1951).
13. J. T. Jenkins and F. Mancini. Balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular discs. J. Appl. Mech. 54, 27 (1987).
14. B. Arnarson and J. T. Willits. Thermal diffusion in binary mixtures of smooth, nearly elastic spheres with and without gravity. Phys. Fluids 10, 1324 (1998).
15. B. Arnarson. Simplified kinetic theory of a binary mixture of nearly elastic, smooth disks, preprint (1999).
16. J. T. Willits and B. Arnarson. Kinetic theory of a binary mixture of nearly elastic disks, preprint (1999).
17. E. Dickinson. Molecular dynamics simulation of hard-disc mixtures. The equation of state. Molecular Physics 33, 1463 (1977).
18. S. Luding, O. Strauß, and S. McNamara. Segregation of polydisperse granular media in the presence of a temperature gradient. In T. Rosato, editor, IUTAM Symposium on Segregation in Granular Flows, Kluwer Academic Publishers (2000).
19. S. McNamara and S. Luding. A simple method to mix granular materials. In T. Rosato, editor, IUTAM Symposium on Segregation in Granular Flows, Kluwer Academic Publishers (2000).
20. B. D. Lubachevsky. How to simulate billards and similar systems. J. of Comp. Phys. 94, 255 (1991).
21. S. Luding and S. McNamara. How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model. Granular Matter 1, 113 (1998). cond-mat/9810009.
22. O. R. Walton and R. L Braun. Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mechanica 63, 73 (1986).
23. C. K. K. Lun. Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 233, 539 (1991).
24. A. Goldshtein and M. Shapiro. Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech. 282, 75 (1995).
25. S. Luding, M. Huthmann, S. McNamara, and A. Zippelius. Homogeneous cooling of rough dissipative particles: Theory and simulations. Phys. Rev. E 58, 3416 (1998).
26. S. Luding. Clustering instabilities, arching, and anomalous interaction probabilities as examples for cooperative phenomena in dry granular media. T.A.S.K. Quarterly, Scientific Bulletin of Academic Computer Centre of the Technical University of Gdansk 2, 417 (July 1998).
27. J. D. Goddard. Microstructuralorigins of continuum stress fields - a brief history and some unresolved issues. In D. DeKee and P. N. Kaloni, editors, Recent Developments in Structered Continua. Pitman Research Notes in Mathematics No. 143, p. 179, New York, Longman, J. Wiley (1986).
28. F. Emeriault and C. S. Chang. Interparticle forces and displacements in granular materials. Computers and Geotechnics 20, 223 (1997).
29. I. Goldhirsch. Kinetics and dynamics of rapid granular flows. In H. J. Herrmann, J.-P. Hovi, and S. Luding, editors, Physics of dry granular media - NATO ASI Series, p. 371, Dordrecht, Kluwer Academic Publishers (1998).
30. J. Zhang, R. Blaak, E. Trizac, J. A. Cuesta, and D. Frenkel. Optimal packing of polydisperse hard-sphere fluids. preprint (1999).
31. J. G. Kirkwood, E. K. Maun, and B. J. Alder. Radial distribution functions and the equation of state of a fluid composed of rigid spherical molecules. J. Chem. Phys. 18, 1040 (1950).
32. W. W. Wood. Note on the free volume equation of state for hard spheres. J. Chem. Phys. 20, 1334 (1952). Letters to the Editor.
33. J. Eggers. Sand as Maxwell’s demon. Phys. Rev. Lett. 83, 5322 (1999).
34. I. N. Bronstein and K. A. Semendjajew. Taschenbuch der Mathematik. Teubner, Leipzig (1979).
35. D. C. Hong. Fermi Statistics and Condensation, (in this volume, p. 429).