Limitations and generalizations of the classical phenomenological model for diffusion in fluids

Molecular Physics

Volumn 105, Issue 8, 2007, Pages 1085-1093

  Aranovich, G L ^a   Donohue, M D ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; EQUATIONS OF STATE; FINITE ELEMENT METHOD; PROBLEM SOLVING; VELOCITY MEASUREMENT;

DIFFUSION EQUATION; DIFFUSION PARADIGM; PHENOMENOLOGICAL MODEL;

DIFFUSERS (FLUID);

EID: 34250344490     PISSN: 00268976     EISSN: 13623028     Source Type: Journal    
DOI: 10.1080/00268970701348758     Document Type: Article

References (46)

1. A. Fick, Philos. Mag. 10, 30 (1855).
2. A. Einstein, Annalen der Physik (Leipzig) 322(8), 549 (1905)
3. (English transl. Investigations on the Theory of the Brownian Movement, Dover, New York, 1956).
4. L. Boltzmann, Lectures on Gas Theory, Part I, paragraph 11 'Basic Equation for the Transport of Any Quantity by the Molecular Motion' (University of California Press, Berkeley & Los Angeles, 1964).
5. R. E. Cunningham and R. J. J. Williams, Diffusion in Gases and Porous Solids (Plenum Press, New York, 1980).
6. H. J. V. Tyrrell and K. R. Harris, Diffusion in Liquids: Theoretical and Experimental Study (Butterworth, Boston, 1984).
7. E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems (Cambridge University Press, Cambridge, 1997).
8. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (John Wiley, New York, 2002).
9. Seizo Ito, Diffusion Equations (American Mathematical Society, Providence, 1992).
10. R.F. Bass, Diffusions and Elliptic Operators (Springer, New York, 1998).
11. R. D. Present, Kinetic Theory of Gases, section 3.3 (McGraw-Hill, New York, 1958).
12. G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930).
13. L. Boltzmann, Annalen der Physik und Chemie 53, 959 (1894)
14. C. Cattaneo, Atti. Sem. Mat. Fis. Univ. Modena 3, 83 (1948).
15. I. Muller, Z. Phys. 198, 329 (1967).
16. W. Israel, Ann. Phys. 100, 310 (1976).
17. W. Israel and J. Stewart, Ann. Phys. 118, 341 (1979).
18. I. S. Liu, I. Muller, and T. Ruggeri, Ann. Phys. 169, 191 (1986).
19. R. Geroch and L. Lindblom, Ann. Phys. 207, 394 (1991).
20. P. Kostadt and M. Liu, Phys. Rev. D 62, 023003 (2000).
21. D. Jou, J. Casas-Vazquez and G. Lebon, Rep. Prog. Phys. 51, 1105 (1988);
22. 62, 1035 (1999).
23. A. Muronga, Phys. Rev. Lett. 88, 062302 (2002);
24. 89, 159901 (2002).
25. A. Muronga, Phys. Rev. C 69, 034903 (2004).
26. V. A. Cimmelli, J. Non-Equilib. Thermodyn. 29, 125 (2004).
27. T. Koide, Phys. Rev. E 72, 026135 (2005).
28. J. Masoliver and G. H. Weiss, Eur. J. Phys. 17, 190 (1996).
29. M. A. Aziz and S. Gavin, Phys. Rev. C 70, 034905 (2004).
30. W. L. Kath, Physica D 12, 375 (1984).
31. G. L. Aranovich and M. D. Donohue, Physica A 373, 119 (2007).
32. G. L. Aranovich and M. D. Donohue, Computers Chem. 22, 428 (1998).
33. G. L. Aranovich and M. D. Donohue, Phys. Rev. E 60, 5552 (1999).
34. G. L. Aranovich and M. D. Donohue, Physica A 242, 409 (1997).
35. J. S. Erickson, G. L. Aranovich, and M. D. Donohue, Molecular Physics 100, 2121 (2002).
36. J.S. Erickson, G.L. Aranovich, and M.D. Donohue, Molecular Simulation 30, 507 (2004).
37. G. L. Aranovich and M. D. Donohue, J. Phys. Chem. 109, 16062 (2005).
38. D. Matuszak, G. L. Aranovich, and M. D. Donohue, J. Chem. Phys. 121, 426 (2004).
39. D. Matuszak, G. L. Aranovich, and M. D. Donohue, Physical Chemistry Chemical Physics (PCCP) 8, 1663 (2006).
40. J. Crank, The Mathematics of Diffusion (Oxford University Press, Oxford, 1956).
41. D. Freedman, Brownian Motion and Diffusion (Halden-Day Inc., San Francisco, 1971).
42. M. Nagasawa, Schrodinger Equations and Diffusion Theory (Birkhauser Verlag, Basel, 1993).
43. A. N. Tychonov and A. A. Samarski, Partial Differential Equations of Mathematical Physics (Holden-Day, Inc., San Francisco, 1964), Vol. 1.
44. S. Abe and S. Thurner, Physica A 356, (2005) 403;
45. A. Abe and A.K. Rajagopal, Physica A, in press.
46. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993).