Beyond the no-slip boundary condition

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

Volumn 84, Issue 4, 2011, Pages

  Brenner, Howard ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUTIVE RELATIONS; ENERGY EQUATION; EXPERIMENTAL DATA; FLUID VELOCITIES; LINEAR CONSTITUTIVE RELATION; MACROSCOPIC APPROACH; MASS DENSITIES; MOMENTUM EQUATION; NO-SLIP BOUNDARY CONDITIONS; PRESSURE-DRIVEN; SLIP BOUNDARY CONDITIONS; SLIP VELOCITY; SOLID BOUNDARIES; SOLID SURFACE; TANGENTIAL COMPONENTS; THERMAL CREEP;

CREEP; FLUIDS;

BOUNDARY CONDITIONS;

EID: 80054942466     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.046309     Document Type: Article

References (61)

1. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Butterworth-Heinemann, Oxford, UK, 1987).
2. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, MA, 1967).
3. G. G. Stokes, Trans. Cambridge Philos. Soc. 8, 287 (1845);
4. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 8 (1850).
5. E. Lauga, M. P. Brenner, and H. A. Stone, in Handbook of Experimental Fluid Dynamics, edited by, J. Foss, C. Tropea, and, A. Yarin, (Springer, New York, 2007), Chap. 19, p. 1219.
6. C. Neto, D. R. Evans, E. Bonaccurso, H. J. Butt, and V. S. J. Craig, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/68/12/R05 68, 2859 (2005). (Pubitemid 41435120)
7. L. Bocquet and J.-L. Barrat, Soft Matter 1744-683X 10.1039/b616490k 3, 685 (2007). (Pubitemid 46794175)
8. M. Gad-el-Hak, J. Fluids Eng. JFEGA4 0098-2202 10.1115/1.2822013 121, 5 (1999);
9. E. J. Arlemark, S. K. Dadzie, and J. M. Reese, J. Heat Transfer JHTRAO 0022-1481 10.1115/1.4000877 132, 041006 (2010).
10. J. C. Maxwell, Philos. Trans. R. Soc. London PTRSAV 0261-0523 10.1098/rstl.1879.0067 170, 231 (1879).
11. H. Brenner and J. R. Bielenberg, Physica A 0378-4371 10.1016/j.physa. 2005.03.020 355, 251 (2005). (Pubitemid 40940849)
12. P. S. Epstein, Z. Phys. 1434-6001 10.1007/BF01338485 54, 537 (1929).
13. R. T. Schermer, C. C. Olson, J. P. Coleman, and F. Bucholtz, Opt. Express OPEXFF 1094-4087 10.1364/OE.19.010571 19, 10571 (2011).
14. J. R. Bielenberg and H. Brenner, J. Fluid Mech. 0022-1120 10.1017/S0022112005006920 546, 1 (2006). (Pubitemid 43135626)
15. O. Reynolds, Philos. Trans. R. Soc. London B PTRBAE 0261-0523 10.1098/rstl.1879.0078 170, 727 (1879).
16. F. Sharipov and V. Seleznev, J. Phys. Chem. Ref. Data JPCRBU 0047-2689 10.1063/1.556019 27, 657 (1998).
17. F. Sharipov and D. Kalempa, Rarefied Gas Dyn. 663, 164 (2003).
18. H. Brenner, Physica A 0378-4371 10.1016/j.physa.2009.04.029 388, 3391 (2009).
19. H. Brenner, Int. J. Eng. Sci. IJESAN 0020-7225 10.1016/j.ijengsci.2009. 05.001 47, 930 (2009);
20. H. Brenner, Physica A 0378-4371 10.1016/j.physa.2009.12.022 389, 1297 (2010).
21. H. Brenner, Int. J. Eng. Sci. IJESAN 0020-7225 10.1016/j.ijengsci.2010. 07.006 48, 1043 (2010).
22. H. Brenner, Physica A 0378-4371 10.1016/j.physa.2011.04.023 390, 3216 (2011);
23. H. Brenner, Physica A 0378-4371 10.1016/j.physa.2011.06.036 390, 3645 (2011).
24. H. B. Callen, Thermodynamics and an Introduction to Thermostatics, 2nd ed. (Wiley, New York, 1985).
25. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed. (Wiley, New York, 2002).
26. S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962).
27. R. Haase, Thermodynamics of Irreversible Processes (Dover, New York, 1990).
28. u.
29. We define a dependent field as one that is functionally expressed in terms of the independent fields by a constitutive relation. Conversely, an independent field is one that does not require a constitutive equation.
30. Equation could possibly prove to be a necessary condition, but we do not explore that possibility here.
31. D. Burnett, Proc. London Math. Soc. 0024-6115 10.1112/plms/s2-40.1.382 40, 382 (1936).
32. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd. ed. (Cambridge University Press, Cambridge, UK, 1970).
33. S. K. Dadzie, J. M. Reese, and C. R. McInnes, Physica A 0378-4371 10.1016/j.physa.2008.07.009 387, 6079 (2008).
34. S. K. Dadzie and J. M. Reese (unpublished).
35. N. Dongari, S. K. Dadzie, Y. Zhang, and J. M. Reese, Rarefied Gas Dyn. 1333, 718 (2011).
36. F. Durst, J. Gomes, and R. Sambasivam, Turbul., Heat Mass Transfer 1 10.1615/ICHMT.2006.TurbulHeatMassTransf.10 5, 3 (2006).
37. S. Chakraborty and F. Durst, Phys. Fluids PFLDAS 1070-6631 10.1063/1.2759531 19, 088104 (2007). (Pubitemid 47577623)
38. N. Dongari, A. Sharma, and F. Durst, Microfluid. Nanofluid. 1613-4982 10.1007/s10404-008-0344-y 6, 679 (2009).
39. N. Dongari, R. Sambasivam, and F. Durst, J. Fluid Sci. Technol. 10.1299/jfst.4.454 4, 454 (2009).
40. N. Dongari, F. Durst, S. Chakraborty, Microfluid. Nanofluid. 1613-4982 10.1007/s10404-010-0604-5 9, 831 (2010).
41. R. Sambasivam and F. Durst, in Handbook of Microfluids and Nanofluidics, edited by, S. Mitra, and, S. Chakraborty, (CRC/Taylor & Francis, London, 2010).
42. F. Durst, N. K. Ravichandran, D. Filimonov, R. Sambasivam, and D. Sarit (unpublished).
43. L. C. Woods, An Introduction to the Kinetic Theory of Gases and Magnetoplasmas (Oxford University Press, New York, 1993), p. 63
44. D. A. Lockerby and J. M. Reese, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.017303 70, 017303 (2004).
45. D. Einzel, P. Panzer, and M. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.2269 64, 2269 (1990);
46. D. Einzel, P. Panzer, and M. Liu, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979292001420 6, 3251 (1992).
47. K. W. Tibbs, F. Baras, and A. L. Garcia, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.56.2282 56, 2282 (1997).
48. D. Kondepudi and I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures (Wiley, Chichester, UK, 1998), p. 305.
49. H. Brenner, Phys. Fluids PFLDAS 1070-6631 10.1063/1.3139273 21, 053602 (2009).
50. K. Shida and W. G. Hoover, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.2277 67, 2277 (1998);
51. To quote the authors: "Only a rough explanation of thermal creep was available to Maxwell. Our present understanding is not much better, and remains only semiquantitative."
52. D. E. Rosner, Phys. Fluids A PFADEB 0899-8213 10.1063/1.857501 1, 1761 (1989);
53. D. H. Papadopoulos and D. E. Rosner, Phys. Fluids A PFLDAS 1070-6631 10.1063/1.868703 7, 2535 (1995);
54. D. E. Rosner and D. H. Papadopoulos, Ind. Eng. Chem. Res. IECRED 0888-5885 10.1021/ie9600351 35, 3210 (1996).
55. S = 1.17: L. Talbot, R. K. Cheng, R. W. Schefer, and D. R. Willis, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112080001905 101, 737 (1980);
56. L. Talbot, Rarefied Gas Dyn. 74, 467 (1981).
57. Y. Sone, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.21.1836 21, 1836 (1966).
58. See Table I in H. Brenner, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72.061201 72, 061201 (2005). (Pubitemid 41777624)
59. A. Maali and B. Bhushan, Phys. Rev. E 1539-3755 10.1103/PhysRevE.78. 027302 78, 027302 (2008).
60. A. Maali, T. Cohen-Bouhacina, and H. Kellay, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2840717 92, 053101 (2008). (Pubitemid 351230027)
61. H. Brenner, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.036325 82, 036325 (2010).