Kinetic theory of colloid thermodiffusion

Physica A: Statistical Mechanics and its Applications

Volumn 385, Issue 1, 2007, Pages 9-24

  Bringuier, E ^a   Bourdon, A ^b  

^a UNIVERSITÉ PARIS DIDEROT   (France)

^b CNRS   (France)

Author keywords

Brownian motion; Colloid; Soret effect; Thermodiffusion; Thermophoresis

Indexed keywords

BROWNIAN MOVEMENT; DIFFUSION; KINETIC THEORY; STATISTICAL METHODS; THEOREM PROVING; THERMAL GRADIENTS; THERMOPHORESIS;

COLLOID THERMODIFFUSION; QUANTUM DYNAMICS; SORET EFFECTS; THERMOPHORETIC FORCES;

COLLOIDS;

EID: 34548499664     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.06.011     Document Type: Article

References (78)

1. Chandrasekhar S. Rev. Mod. Phys. 15 (1943) 1
2. Chandrasekhar S. Rev. Mod. Phys. 21 (1949) 383 (Reprinted in S. Chandrasekhar, Selected papers, vol. 3, University of Chicago Press, Chicago, 1989)
3. van de Ven T.G.M. Colloidal Hydrodynamics (1989), Academic Press, London
4. Byron Bird R., Stewart W.E., and Lightfoot E.N. Transport Phenomena. second ed. (2002), Wiley, New York pp. 770-774
5. Landau L.D., and Lifshitz E.M. Fluid Mechanics (1959), Pergamon, Oxford (original Russian edition, Mir, Moscow, 1954), Section 58
6. Lenglet J., Bourdon A., Bacri J.-C., and Demouchy G. Phys. Rev. E 65 (2002) 031408
7. Ludwig C. Sitz. ber. Akad. Wiss. Wien Math.-Nat. wiss. Kl. 20 (1856) 539 Reprinted in S. Wiegand, "150 Jahre Ludwig-Soret Effekt", Bunsen-Magazin (Deutsche Bunsen-Gesellschaft für Physikalische Chemie), 8(Heft 5) (2006) 130-134
8. Soret Ch. Arch. Sci. Phys. Nat. 2 (1879) 48
9. Soret Ch., and Séances C.R. Hebd. Acad. Sci. 91 (1880) 289
10. Soret Ch. Arch. Sci. Phys. Nat. 4 (1880) 209
11. Chapman S., and Cowling T.G. The Mathematical Theory of Non-Uniform Gases. third ed. (1970), Cambridge University Press, Cambridge pp. 268-280
12. Anderson J.L. Annu. Rev. Fluid Mech. 21 (1989) 61
13. Davis E.J. Thermophoresis of particles. Encyclopedia of Surface and Colloid Science vol. 4 (2002), Marcel Dekker, New York 5365-5375 [there is a misprint in the denominator of formula (7), which actually is 1+2K]
14. Zheng F. Adv. Colloid Interface Sci. 97 (2002) 255
15. Regazzetti A., Hoyos M., and Martin M. J. Phys. Chem. B 108 (2004) 15285
16. Bringuier E. Philos. Mag. 87 (2007) 873
17. Wiegand S. J. Phys.: Condens. Matter 16 (2004) R357
18. Semenov S.N. Philos. Mag. 83 (2003) 2199
19. Semenov S., and Schimpf M. Phys. Rev. E 72 (2005) 041202
20. Piazza R. J. Phys.: Condens. Matter 16 (2004) S4195
21. Nader Rasuli S. Ramin Golestanian. J. Phys.: Condens. Matter 17 (2005) S1171
22. Bielenberg J.R., and Brenner H. Physica A 356 (2005) 279
23. Brenner H. Phys. Rev. E 74 (2006) 036306
24. Dhont J.K.G. J. Chem. Phys. 120 (2004) 1632
25. Dhont J.K.G. J. Chem. Phys. 120 (2004) 1642
26. Ning H., Buitenhuis J., Dhont J.K.G., and Wiegand S. J. Chem. Phys. 125 (2006) 204911
27. van Kampen N.G. IBM J. Res. Dev. 32 (1988) 107
28. Alves S., Demouchy G., Bée A., Talbot D., Bourdon A., and Figueiredo Neto A.M. Philos. Mag. 83 (2003) 2059
29. Alves S., Bourdon A., and Figueiredo Neto A.M. J. Opt. Soc. Am. B 20 (2003) 713
30. Demouchy G., Mezulis A., Bée A., Talbot D., Bacri J.-C., and Bourdon A. J. Phys. D 37 (2004) 1417
31. Graetzel M., and Infelta P. The Bases of Chemical Thermodynamics, vol. 2 (2000), Universal Publishers, Parkland, FL (Chapter 12)
32. Deen W.M. Analysis of Transport Phenomena (1998), Oxford University Press, New York pp. 450-452
33. van Kampen N.G. J. Phys. Chem. Solids 49 (1988) 673
34. Kramers H.A. Physica 7 (1940) 284
35. van Kampen N.G. Stochastic Processes in Physics and Chemistry. second ed. (1992), North-Holland, Amsterdam (Chapters IX and X)
36. 3f is used in Ref. [47] dealing with quantum non-equilibrium statistics.
37. Lukić B., Jeney S., Tischer C., Kulik A.J., Forró L., and Florin E.-L. Phys. Rev. Lett. 95 (2005) 160601
38. Wang Chang C.S., and Uhlenbeck G.E. In: deBoer J., and Uhlenbeck G.E. (Eds). Studies in Statistical Mechanics vol. 5 (1970), North-Holland, Amsterdam 1-16
39. Balian R. From Microphysics to Macrophysics, vol. II (1992), Springer, Berlin pp. 388-391
40. Lifshitz E.M., and Pitaevskii L.P. Physical Kinetics (1981), Pergamon, Oxford (original Russian edition, Mir, Moscow, 1979), Section 12
41. O' M. Bockris J., and Reddy A.K.N. Modern Electrochemistry, vol. 1 (1970), Plenum Press, New York
42. Kizilyalli M., Corish J., and Metselaar R. Pure Appl. Chem. 71 (1999) 1307
43. Blandamer M.J., Engberts J.B.F.N., Gleeson P.T., and Reis J.C.R. Chem. Soc. Rev. 34 (2005) 440
44. Dubois E., Cabuil V., Boué F., and Perzynski R. J. Chem. Phys. 111 (1999) 7147
45. Batchelor G.K. J. Fluid Mech. 74 (1976) 1
46. Clercx H.J.H., and Schram P.P.J.M. Physica A 174 (1991) 293
47. Clercx H.J.H., and Schram P.P.J.M. Physica A 174 (1991) 325
48. Nägele G. Phys. Rep. 272 (1996) 215
49. Bringuier E., and Bourdon A. Phys. Rev. E 67 (2003) 011404
50. Dirac P.A.M. Proc. Cambridge Philos. Soc. 22 (1924) 132
51. Price P.J. Philos. Mag. 135 (1955) 1252
52. Gharibi H., Javadian S., Sohrabi B., and Behjatmanesh R. J. Colloid Interface Sci. 285 (2005) 351
53. Monchick L., and Mason E.A. Phys. Fluids 10 (1967) 1377
54. Degond P., and Lucquin-Desreux B. Math. Models Methods Appl. Sci. 6 (1996) 405
55. Bringuier E. Phys. Rev. E 61 (2000) 6351
56. S. Chapman, T.G. Cowling, in Ref. [8], p. 167.
57. Waldmann L. Z. Naturforsch. A 14 (1959) 589
58. In: Talbot L. (Ed). Rarefied Gas Dynamics (1961), Academic Press, New York 323-344
59. Fernández de la Mora J., and Mercer J.M. Phys. Rev. A 26 (1982) 2178 [ε in their formula (35) should be divided by 2]
60. Bakanov S.P. Prikl. Mat. Mekh. 68 (2004) 30
61. J. Appl. Math. Mech. 68 (2004) 25
62. Duhr S., and Braun D. Phys. Rev. Lett. 96 (2006) 168301
63. Tavernier J., and Calecki D. Introduction aux phénomènes de transport linéaires dans les semi-conducteurs (1970), Masson, Paris
64. Rode D.L. In: Willardson R.K., and Beer A.C. (Eds). Semiconductors and Semimetals vol. 10 (1975), Academic, New York 23
65. In: McNaught A.D., and Wilkinson A. (Eds). IUPAC Compendium of Chemical Terminology. second ed. (1997), Blackwell, Oxford
66. Widder M.E., and Titulaer U.M. Physica A 154 (1989) 452
67. i) vanishes. We then use D(r)=kTμ(r).
68. d=μ[F+kT grad (ln μ)], has analogues in transport theory. For example, the Drude expression of the mobility, μ=τ/m, is valid when the momentum-relaxation time τ is independent of energy. It becomes μ(E)=(τ/m)[1+(2E/3)(d ln τ/dE)] when τ is a function τ(E) of the instantaneous energy E of the particle. See E. Bringuier, Philos. Mag. B 77 (1998) 959, and references therein.
69. d=μF+ν grad μ owing to the superposition principle. ν=kT in (34). The force exerted on a non-spherical body is in general not collinear to grad T, see K. Borg and L.H. Söderholm, J. Phys. D 40 (2007) 148.
70. Bocquet L. Am. J. Phys. 65 (1997) 140
71. Ryskin G. Phys. Rev. E 56 (1997) 5123
72. Einstein A. Ann. Phys. (Leipzig) 17 (1905) 549
73. Lançon P., Batrouni G., Lobry L., and Ostrowsky N. Physica A 304 (2002) 65
74. Gardiner C.W. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. second ed. (1985), Springer, Berlin
75. Ziman J.M. Principles of the Theory of Solids. second ed. (1972), Cambridge University Press, Cambridge p. 238
76. Ehrenfest P. Z. Phys. 45 (1927) 455
77. Schiff L.I. Quantum Mechanics (1955), McGraw-Hill, New York pp. 25-27
78. i〉. For similar reasons, the second term on the right-hand side vanishes. QED.