Nonisothermal Brownian motion: Thermophoresis as the macroscopic manifestation of thermally biased molecular motion

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

Volumn 72, Issue 6, 2005, Pages

  Brenner, Howard ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DRIFT VELOCITY; GRAVITY-FREE GASES; QUASI-LORENTZIAN GASES; TEMPERATURE GRADIENT;

CONTINUUM MECHANICS; DIFFUSION; KINEMATICS; MOLECULAR DYNAMICS; SEPARATION; THERMOPHORESIS;

BROWNIAN MOVEMENT;

EID: 28844505736     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.061201     Document Type: Article

References (50)

1. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981)
2. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984).
3. G. M. Hidy and J. R. Brock, The Dynamics of Aerocolloidal Systems (Pergamon, Oxford, 1970)
4. L. Waldmann and K. H. Schmitt, in Aerosol Science, edited by, C. N. Davies, (Academic Press, London, 1966) p. 137
5. B. V. Derjaguin and Yu. I. Yalamov, in Topics in Current Aerosol Research, edited by, G. M. Hidy, and, J. R. Brock, (Pergamon, Oxford, 1972) p. 2
6. F. Zheng, Adv. Colloid Interface Sci. ACISB9 0001-8686 97, 255 (2002).
7. H. Brenner and J. R. Bielenberg, Physica A PHYADX 0378-4371 355, 251 (2005).
8. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, England 1970).
9. J. Fernandez de la Mora and J. M. Mercer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.26.2178 26, 2178 (1982).
10. J. M. Kincaid, E. G. D. Cohen, and M. López de Haro, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.452243 86, 963 (1987).
11. J. R. Bielenberg and H. Brenner, Physica A PHYADX 0378-4371 356, 279 (2005).
12. H. Brenner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.061201 70, 061201 (2004).
13. H. Brenner, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.10.034 349, 60 (2005).
14. J. C. Maxwell, Philos. Trans. R. Soc. London PTRSAV 0370-2316 170, 231 (1879).
15. D. E. Rosner and D. H. Papadopoulos, Ind. Eng. Chem. Res. IECRED 0888-5885 10.1021/ie9600351 35, 3210 (1996).
16. J. R. Bielenberg and H. Brenner, J. Fluid Mech. JFLSA7 0022-1120 (to be published).
17. K. E. Grew and T. L. Ibbs, Thermal Diffusion in Gases (Cambridge, London, 1952).
18. A. Einstein, Ann. Phys. ANPYA2 0003-3804 17, 549 (1905)
19. reprinted (with corrections) in Investigations on the Theory of the Brownian Movement, edited by, R. Fürth, (Dover, New York, 1956).
20. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, London, 1961)
21. A. Manela and I. Frankel, Phys. Fluids PHFLE6 1070-6631 10.1063/1. 1861876 17, 036101 (2005).
22. R. F. Probstein, Physicochemical Hydrodynamics, 2nd ed. (Wiley, New York, 1994), pp. 14 and 19.
23. J. G. Kirkwood and I. Oppenheim, Chemical Thermodynamics (McGraw-Hill, New York, 1961)
24. K. G. Denbigh, The Principles of Chemical Equilibrium (Cambridge, London, 1955).
25. Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhäuser, Boston, 2002).
26. H. Brenner, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.10.033 349, 11 (2005).
27. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed. (Wiley, New York, 2002).
28. P. S. Epstein, Z. Phys. ZEPYAA 0044-3328 54, 537 (1929).
29. A. Mohan and H. Brenner, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1858431 17, 038107 (2005).
30. F. Sharipov, Eur. J. Mech. B/Fluids EJBFEV 0997-7546 10.1016/S0997-7546(03)00017-7 22, 133 (2003)
31. F. Sharipov and D. Kalempa, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1644572 16, 759 (2004)
32. F. Sharipov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.061201 69, 061201 (2004).
33. L. Talbot, R. K. Cheng, R. W. Schefer, and D. R. Willis, J. Fluid Mech. JFLSA7 0022-1120 101, 737 (1980)
34. L. Talbot, in Rarefied Gas Dynamics, edited by, S. S. Fisher, (AIAA, New York, 1981) Part 1, p. 467.
35. B. V. Derjaguin, Ya. I. Rabinovich, A. I. Storozhilova, and G. I. Shcherbina, J. Colloid Interface Sci. JCISA5 0021-9797 10.1016/0021-9797(76)90224-1 57, 451 (1976).
36. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Kluwer, Dordrecht, 1987).
37. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
38. P. Riesco-Chueca, R. Fernandez-Feria, and J. Fernandez de la Mora, Phys. Fluids PFLDAS 0031-9171 10.1063/1.866511 30, 45 (1987).
39. G. Stolovitzky, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00109-1 241, 240 (1998); see his Eqs. (10) and (1).
40. J. R. Schmidt and J. L. Skinner, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1610442 119, 8062 (2003)
41. J. R. Schmidt and J. L. Skinner, J. Phys. Chem. B JPCBFK 1089-5647 10.1021/jp037185r 108, 6767 (2004).
42. S. Chapman, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 119, 34 (1928).
43. G. Peskir, Stoch. Models SMTOBE 1532-6349 19, 383 (2003). However, this review appears to have overlooked the highly relevant contribution of de la Mora and Mercer, as well as the precursor and subsequent follow-up researches pertaining thereto.
44. J. Fernandez de la Mora, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.25.1108 25, 1108 (1981)
45. R. Fernandez-Feria and P. Riesco-Chueca, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.36.4940 36, 4940 (1987)
46. J. Fernandez de la Mora and R. Fernandez-Feria, Phys. Fluids PFLDAS 0031-9171 10.1063/1.866324 30, 740 (1987).
47. R. F. Streater, Statistical Dynamics (Imperial College Press, London, 1995).
48. R. F. Streater, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 456, 205 (2000)
49. R. F. Streater, Open Syst. Inf. Dyn. OSIDFU 1230-1612 10.1023/A:1022919224236 10, 3 (2003).
50. M. W. Tysanner and A. L. Garcia, J. Comput. Phys. JCTPAH 0021-9991 10.1016/j.jcp.2003.10.021 196, 173 (2004).