Simulating fluid flows in micro and nano devices: The challenge of non-equilibrium behaviour

Journal of Computational and Theoretical Nanoscience

Volumn 6, Issue 10, 2009, Pages 2061-2074

  Reese, Jason M ^a   Zhang, Yonghao ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Extended hydrodynamics; Knudsen layer; Lattice Boltzmann; Micro and nano scale flows; Microfluidics; Nanofluidics; Non equilibrium fluid dynamics; Rarefied gas dynamics; Slip flow

Indexed keywords

KNUDSEN LAYER; LATTICE BOLTZMANN; MICRO-AND NANO-SCALE FLOWS; NANO SCALE; NON EQUILIBRIUM; NON-EQUILIBRIUM FLUID DYNAMICS; RAREFIED GAS DYNAMICS; SLIP FLOW;

AERODYNAMICS; BOUNDARY CONDITIONS; DROP FORMATION; FLOW OF GASES; GASES; HYDRODYNAMICS; MICROFLUIDICS; NANOFLUIDICS; NANOSTRUCTURED MATERIALS; SIMULATORS; STANDARDIZATION;

FLUID DYNAMICS;

EID: 72749089694     PISSN: 15461955     EISSN: None     Source Type: Journal    
DOI: 10.1166/jctn.2009.1263     Document Type: Review

References (87)

1. M. Gad-el-Hak, J. Fluids Eng.-Trans. ASME 121, 5 (1999).
2. G. E. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, New York (2005).
3. E. B. Arkilic, M. A. Schmidt, and K. S. Breuer, J. MEMS 6, 167 (1997).
4. D. A. Lockerby, J. M. Reese, D. R. Emerson, and R. W. Barber, Phys. Rev. E 70, 017303 (2004).
5. M. Knudsen, Annal. Physik 28, 75 (1909).
6. S. E. Vargo, E. P. Muntz, G. R. Shiflett, and W. C. Tang, J. Vacuum Sci. Tech. A: Vacuum, Surface, Films 17, 2308 (1999).
7. R. K. Agarwal, K. Y. Yun, and R. Balakrishnan, Phys. Fluids 13, 3061 (2001).
8. F. Sharipov, L. M. G. Cumin, and D. Kalempa, Eur. J. Mech. B-Fluids 23, 899 (2004).
9. M. Kalweit and D. Drikakis, J. Comput. Theor. Nanosci. 5, 1923 (2008).
10. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, UK (1970).
11. D. A. Lockerby, J. M. Reese, and M. A. Gallis, Phys. Fluids 17, 100609 (2005).
12. D. A. Lockerby and J. M. Reese, J. Fluid Mech. 604, 235 (2008).
13. H. Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows, Springer, Heidelberg (2005).
14. D. A. Lockerby and J. M. Reese, J. Comput. Phys. 188, 333 (2003).
15. H. Grad, Comm. Pure Appl. Math. 2, 331 (1949).
16. H. Struchtrup and M. Torrilhon, Phys. Fluids, 15, 2668 (2003).
17. H. Struchtrup and M. Torrilhon, Phys. Rev. Lett. 99, 014502 (2007).
18. S. Mizzi, Extended macroscopic models for rarefied gas dynamics in micro-sized domains, Ph. D. Thesis, University of Strathclyde, UK (2008).
19. S. Mizzi, X. J. Gu, D. R. Emerson, R. W. Barber, and J. M. Reese, Int. J. Num. Meth. Fluids 56, 1433 (2008).
20. X. J. Gu and D. R. Emerson, J. Comput. Phys. 225, 263 (2007).
21. S. Mizzi, D. R. Emerson, S. K. Stefanov, R. W. Barber, and J. M. Reese, J. Comput. Theoret. Nanosci., 4, 817 (2007).
22. L. O'Hare, T. J. Scanlon, D. R. Emerson, and J. M. Reese, Int. J. Heat Mass Transf. 51, 1281 (2008).
23. R. S. Myong, J. M. Reese, R. W. Barber, and D. R. Emerson, Phys. Fluids 17, 087105 (2005).
24. R. S. Myong, D. A. Lockerby, and J. M. Reese, Int. J. Heat Mass Transf. 49, 2502 (2006).
25. J. C. Maxwell, Phil. Trans. Roy. Soc. London 170, 231 (1879).
26. R. Schamberg, The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems. Ph. D. Thesis, California Institute of Technology, USA (1947).
27. C. Cercignani, Mathematical Methods in Kinetic Theory, Plenum, New York (1969).
28. R. G. Deissler, Int. J. Heat Mass Transf. 7, 681 (1964).
29. A. K. Sreekanth, Slip flow through long circular tubes, Rarefied Gas Dynamics, 6th Symposium, Academic, New York (1969), Vol. 1.
30. Y. T. Hsia and G. A. Domoto, J. Lubrication Technol. 105, 120 (1983).
31. N. G. Hadjiconstantinou, Phys Fluids 15, 2352 (2003).
32. J. Maurer, P. Tabeling, P. Joseph, and H. Willaime, Phys. Fluids 15, 2613 (2003).
33. T. Ewart, P. Perrier, I. Graur, and J. G. Méolans, Expts. Fluids 41, 487 (2006).
34. Y. Sone, Phys. Fluids 15, 1418 (1972).
35. D. W. Stops, J. Phys. D: Appl. Phys. 3, 685 (1970).
36. Z. L. Guo, B. C. Shi, and C. G. Zheng, EPL 80, 24001 (2007).
37. M. Fichman and G. Hetsroni, Phys. Fluids 17, 123102 (2005).
38. J. M. Li, B. X. Wang, and X. F. Peng, Int. J. Heat Mass Transf. 43, 839 (2000).
39. Y. H. Sun, W. K. Chan, and N. Y. Liu, Proc. Inst. Mech. Engin., J-J. Eng. Tribology 217, 187 (2003).
40. G. Schrag and G. Wachutka, Sens. Actuators, A 97-98, 193 (2002).
41. T. Veijola, H. Kuisma, J. Lahdenperä, and T. Ryhänen, Sens. Actuators, A 48, 239 (1995).
42. S. Mizzi, R. W. Barber, D. R. Emerson, J. M. Reese, and S. K. Stefanov, Cont. Mech. Thermodyn. 19, 273 (2007).
43. L. O'Hare, D. A. Lockerby, J. M. Reese, and D. R. Emerson, Int. J. Heat Fluid Flow 28, 37 (2007).
44. J. M. Reese, Y. Zheng, and D. A. Lockerby, J. Comput. Theoret. Nanosci. 4, 807 (2007).
45. D. A. Lockerby, J. M. Reese, and M. A. Gallis, AIAAJ 43, 1391 (2005).
46. C. R. Lilley and J. E. Sader, Phys. Rev. E 76, 026315 (2007).
47. C. R. Lilley and J. E. Sader, Proc. Roy. Soc. A, 464, 2015 (2008).
48. A. J. Lofthouse, L. C. Scalabrin, and I. D. Boyd, J. Thermophys. Heat Transf. 22, 38 (2008).
49. S. Chen and G. D. Doolen, AIAA J. 30, 329 (1998).
50. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon Press, Oxford (2001).
51. R. R. Nourgaliev, T. N. Dinh, T. G. Theofanous, and D. Joseph, Int. J. Multiphase Flow 29, 117 (2003).
52. U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505 (1986).
53. G. R. McNamara and G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988).
54. Y. H. Qian, Lattice gas and lattice kinetic theory applied to the Navier-Stokes equations. Ph. D. Thesis, Université Pierre et Marie Curie, Paris, France (1990).
55. Y. H. Qian, D. d'Humières, and P. Lallemand, Europhys. Lett. 17, 479 (1992).
56. S. Chen, H. D. Chen, D. Martinez, and W. Matthaeus, Phys. Rev. Lett. 67, 3776 (1991).
57. S. Hou, Q. Zou, S. Chen, G. Doolen, and A. C. Cogley, J. Comput. Phys. 118, 329 (1995).
58. D. O. Martinez, W. H. Mattaeus, S. Chen, and D. C. Montgomery, Phys. Fluids 6, 1285 (1994).
59. X. W. Shan and H. D. Chen, Phys. Rev. E 47, 1815 (1993).
60. A. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991).
61. M. R. Swift, W. R. Osborn, and J. M. Yeomans, Phys. Rev. Lett. 75, 830 (1995).
62. X. He and L. S. Luo, Phys. Rev. E, 55, 6333 (1997).
63. T. Abe, J. Comput. Phys. 131, 241 (1997).
64. X. Nie, G. D. Doolen, and S. Chen, J. Stat. Phys. 107, 279 (2002).
65. C. Y. Lim, C. Shu, X. D. Niu, and Y. T. Chew, Phys. Fluids 14, 2299 (2002).
66. F. Toschi and S. Succi, Europhys. Lett., 69, 549 (2005).
67. Y. H. Zhang, R. S. Qin, and D. R. Emerson, Phys. Rev. E 71, 047702 (2005).
68. S. Ansumali and I. V. Karlin, Phys. Rev. E 66, 026311 (2002).
69. R. Gatignol, Phys. Fluids 20, 2022 (1977).
70. X. D. Niu, C. Shu, and Y. T. Chew, Europhys. Lett., 67, 600 (2004).
71. G. H. Tang, W. Q. Tao, and Y. L. He, Phys. Fluids 17, 058101 (2005).
72. M. Sbragaglia and S. Succi, Europhys. Lett. 73, 370 (2006).
73. G. H. Tang, Y. H. Zhang, and D. R. Emerson, Phys. Rev. E 77, 046701 (2008).
74. Y. H. Qian and Y. Zou, Phys. Rev. E 61, 2103 (2000).
75. X. W. Shan, X. F. Yuan, and H. D. Chen, J. Fluid Mech. 550, 413 (2006).
76. S. Ansumali, I. V. Karlin, S. Arcidiacono, A. Abbas, and N. I. Prasianakis, Phys. Rev. Lett. 98, 124502 (2007).
77. L. Szalmás, EPL 80, 24003 (2007).
78. A. N. Gorban and I. V. Karlin, Physlca A 360, 325 (2006).
79. R. Zhang, X. Shan, and H. Chen, Phys. Rev. E 74, 046703 (2006).
80. X. D. Niu, S. A. Hyodo, T. Munekata, and K. Suga, Phys. Rev. E 76, 036711 (2007).
81. Y. H. Zhang, X. J. Gu, R. W. Barber, and D. R. Emerson, Phys. Rev. E 74, 046704 (2006).
82. Y. H. Zhang, X. J. Gu, R. W. Barber, and D. R. Emerson, EPL 77, 30003 (2007).
83. X. Y. He, L. S. Luo, and M. Dembo, J. Comput. Phys. 129, 357 (1996).
84. S. Succi, I. V. Karlin, and H. Chen, Rev. Modern Phys. 74, 1203 (2002).
85. S. S. Chikatamarla and I. V. Karlin, Phys. Rev. Lett. 97, 190601 (2006).
86. G. H. Tang, Y. H. Zhang, X. J. Gu, and D. R. Emerson, EPL 83, 40008 (2008).
87. X. He, S. Chen, and G. D. Doolen, J. Comput. Phys. 146, 282 (1998).