Green-Kubo relation for viscosity tested using experimental data for a two-dimensional dusty plasma

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 4, 2011, Pages

  Feng, Yan ^a   Goree, J ^a   Liu, Bin ^a   Cohen, E G D ^a,b  

^a UNIVERSITY OF IOWA   (United States)

^b ROCKEFELLER UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARGON GAS; AUTOCORRELATION FUNCTIONS; DIRECT MEASUREMENT; DUST PARTICLE; DUSTY PLASMAS; ELECTRIC REPULSION; EXPERIMENTAL DATA; GREEN-KUBO RELATIONS; INTERPARTICLE POTENTIAL; IONIZED ARGON; LIQUID PHASE; NON-EQUILIBRIUM STEADY STATE; OFF-DIAGONAL ELEMENTS; SHEARING MOTION; SINGLE LAYER; STRESS TENSORS; TIME AUTOCORRELATION FUNCTIONS; WIGNER CRYSTALS;

ARGON; ARGON LASERS; AUTOCORRELATION; DUST; EXPERIMENTS; HEATING; IONIZATION OF GASES; LASER HEATING; NAVIER STOKES EQUATIONS; PLASMA THEORY; REGRESSION ANALYSIS; SEMICONDUCTOR PLASMAS; TIME SERIES;

VISCOSITY;

EID: 80155137491     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.046412     Document Type: Article

References (70)

1. C. A. Murray, W. O. Sprenger, and R. A. Wenk, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.42.688 42, 688 (1990).
2. P. M. Reis, R. A. Ingale, and M. D. Shattuck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.258001 96, 258001 (2006). (Pubitemid 43955938)
3. C. C. Grimes and G. Adams, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.42.795 42, 795 (1979).
4. T. B. Mitchell, J. J. Bollinger, X.-P. Huang, W. M. Itano, and D. H. E. Dubin, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.873433 6, 1751 (1999).
5. P. K. Shukla and A. A. Mamun, Introduction to Dusty Plasma Physics (Institute of Physics, Bristol, 2002).
6. G. E. Morfill and A. V. Ivlev, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.1353 81, 1353 (2009).
7. A. Piel, Plasma Physics (Springer, Heidelberg, 2010).
8. Y. Feng, J. Goree, and B. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.025002 105, 025002 (2010).
9. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).
10. M. S. Murillo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85. 2514 85, 2514 (2000).
11. G. Salin, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.2759881 14, 082316 (2007). (Pubitemid 47352639)
12. P. K. Kaw and A. Sen, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.873073 5, 3552 (1998).
13. M. S. Green, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1700722 20, 1281 (1952);
14. M. S. Green, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1740082 22, 398 (1954).
15. R. Kubo, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.12.570 12, 570 (1957).
16. J. P. Hansen and I. R. McDonald, The Theory of Simple Liquids, 2nd ed. (Elsevier Academic, Amsterdam, 1986).
17. Z. Donkó, P. Hartmann, and J. Goree, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984907013948 21, 1357 (2007).
18. R. Pal, J. Colloid Interface Sci. JCISA5 0021-9797 10.1006/jcis.2000.6776 225, 359 (2000). (Pubitemid 30313913)
19. T. G. Mason and D. A. Weitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1250 74, 1250 (1995).
20. J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 85.888 85, 888 (2000).
21. B. J. Alder and T. E. Wainwright, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.18.988 18, 988 (1967);
22. B. J. Alder and T. E. Wainwright, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.1.18 1, 18 (1970).
23. M. H. Ernst, E. H. Hauge, and J. M. J. van Leeuwen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.25.1254 25, 1254 (1970);
24. J. R. Dorfman and E. G. D. Cohen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.25.1257 25, 1257 (1970).
25. C. K. Goertz, Rev. Geophys. REGEEP 8755-1209 10.1029/RG027i002p00271 27, 271 (1989).
26. D. Samsonov, J. Goree, H. M. Thomas, and G. E. Morfill, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.5557 61, 5557 (2000).
27. Y. Feng, J. Goree, and B. Liu, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.3560584 18, 057301 (2011).
28. X. Wang, A. Bhattacharjee, and S. Hu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2569 86, 2569 (2001). (Pubitemid 32286705)
29. G. Joyce, M. Lampe, and G. Ganguli, IEEE Trans. Plasma Sci. ITPSBD 0093-3813 10.1109/27.923701 29, 238 (2001). (Pubitemid 32514179)
30. L. Bonsall and A. A. Maradudin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.15.1959 15, 1959 (1977).
31. V. Nosenko, J. Goree, and A. Piel, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.2182207 13, 032106 (2006).
32. The different roles of the dust particles and the neutral gas in determining the transfer of momentum can be illustrated by comparing a dusty plasma to a dilute colloidal suspension. The latter consists of two components: solid particles and a liquid solvent such as water, which have comparable mass densities. If the solid particles are sufficiently small, they are dragged along in the flow of the solvent, so that the local velocities of the solid particles and solvent are nearly the same (G. K. Batchelor, Ref. [9]). Then, the two components of a dilute colloidal suspension can be considered to be moving as one, which has an effective viscosity that is slightly larger than that of the pure solvent according to Einstein's result [A. Einstein, Ann. Phys. 339, 591 (1911)]. A dusty plasma is different because instead of a liquid solvent, there is a rarefied gas, which is many orders of magnitude less dense. Then the dust particles can flow with a velocity that is different from that of the rarefied gas as a whole. This difference in velocity between a dust particle and the gas as a whole leads to a friction between them, which is different from the viscous friction due to collisions among the dust particles via their electrical repulsion.
33. W.-T. Juan, M.-H. Chen, and L. I, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.016402 64, 016402 (2001).
34. V. Nosenko and J. Goree, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.155004 93, 155004 (2004).
35. A. Gavrikov, I. Shakhova, A. Ivanov, O. Petrov, N. Vorona, and V. Fortov, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.12.075 336, 378 (2005). (Pubitemid 40249986)
36. N. A. Vorona, A. V. Gavrikov, A. S. Ivanov, O. F. Petrov, V. E. Fortov, and I. A. Shakhova, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/ S1063776107100172 105, 824 (2007). (Pubitemid 350165530)
37. B. Liu and J. Goree, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.185002 94, 185002 (2005). (Pubitemid 41493058)
38. Z. Donkó, J. Goree, P. Hartmann, and K. Kutasi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.145003 96, 145003 (2006).
39. Z. Donkó, J. Goree, P. Hartmann, and B. Liu, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.026401 79, 026401 (2009).
40. D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1976).
41. O. S. Vaulina, X. G. Adamovich, O. F. Petrov, and V. E. Fortov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.066404 77, 066404 (2008).
42. O. S. Vaulina, K. G. Adamovich, O. F. Petrov, and V. E. Fortov, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/S1063776108080153 107, 313 (2008).
43. R. A. L. Jones, Soft Condensed Matter (Oxford University Press, Auckland, 2003).
44. B. Liu, J. Goree, and O. S. Vaulina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.015005 96, 015005 (2006). (Pubitemid 43248363)
45. G. J. Kalman, P. Hartmann, Z. Donkó, and M. Rosenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.065001 92, 065001 (2004).
46. S. Ichimaru, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.54.1017 54, 1017 (1982).
47. Y. Feng, J. Goree, and B. Liu, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.2735920 78, 053704 (2007). (Pubitemid 46878463)
48. Y. Feng, J. Goree, and B. Liu, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.3589267 82, 053707 (2011).
49. M. Wolter and A. Melzer, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.036414 71, 036414 (2005). (Pubitemid 40619871)
50. A. Melzer, S. Nunomura, D. Samsonov, Z. W. Ma, and J. Goree, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.62.4162 62, 4162 (2000).
51. B. Liu and J. Goree, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.055003 100, 055003 (2008). (Pubitemid 351222592)
52. Y. Feng, J. Goree, and B. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.205007 100, 205007 (2008). (Pubitemid 351752931)
53. U. Konopka, G. E. Morfill, and L. Ratke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.891 84, 891 (2000).
54. O. S. Vaulina, E. A. Lisin, A. V. Gavrikov, O. F. Petrov, and V. E. Fortov, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/S1063776110040138 110, 662 (2010).
55. Nonisotropic models have been developed to take into account the effects of ion wakes, which arise from a flow of ions that is driven by the same vertical electric field that levitates the dust particles. Examples include V. A. Schweigert, I. V. Schweigert, A. Melzer, A. Homann, and A. Piel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5345 80, 5345 (1998);
56. M. Lampe, G. Joyce, G. Ganguli, and V. Gavrishchaka, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1288910 7, 3851 (2000);
57. R. Kompaneets, U. Konopka, A. V. Ivlev, U. Tsytovich, and G. Morfill, Phys. Plasmas 1070-664X 10.1063/1.2730498 14, 052108 (2007). (Pubitemid 46872440)
58. M. S. Murillo, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.62.4115 62, 4115 (2000).
59. T. Saigo and S. Hamaguchi, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1459708 9, 1210 (2002). (Pubitemid 34435404)
60. G. Salin and J.-M. Caillol, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1566749 10, 1220 (2003).
61. G. Faussurier, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.066402 69, 066402 (2004).
62. S. Nunomura, J. Goree, S. Hu, X. Wang, A. Bhattacharjee, and K. Avinash, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.035001 89, 035001 (2002).
63. S. Nunomura, S. Zhdanov, D. Samsonov, and G. Morfill, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.045001 94, 045001 (2005). (Pubitemid 40618411)
64. D.
65. Z. Donkó, J. Goree, and P. Hartmann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.056404 81, 056404 (2010).
66. F. Reif, Fundamentals of Statistical and Thermal Physics, Chap. 15 (McGraw Hill, New York, 1965).
67. W. F. van Gunsteren and H. J. C. Berendsen, Mol. Phys. MOPHAM 0026-8976 10.1080/00268978200100491 45, 637 (1982).
68. T. Ott and M. Bonitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.195001 103, 195001 (2009).
69. B. Liu, J. Goree, V. Nosenko, and L. Boufendi, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1526701 10, 9 (2003).
70. U. de Angelis, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1357219 8, 1751 (2001).