Upscaling the diffusion equations in particulate media made of highly conductive particles. I. Theoretical aspects

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

Volumn 77, Issue 1, 2008, Pages

  Vassal, J P ^a   Orgeas L ^a   Favier, D ^a   Auriault, J L ^a   Le Corre, S ^b  

^a GRENOBLE INSTITUTE OF TECHNOLOGY   (France)

^b INSTITUT DE RECHERCHE EN GÉNIE CIVIL ET MÉCANIQUE GEM   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ANALYSIS; CONDUCTIVE MATERIALS; HOMOGENIZATION METHOD; TRANSPORT PROPERTIES;

ASYMPTOTIC EXPANSIONS; TRANSIENT DIFFUSION EQUATIONS;

DIFFUSION;

EID: 40749151107     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.011302     Document Type: Article

References (35)

1. M. Kaviany, Principles of Heat Transfer in Porous Media (Springer, New York, 1991).
2. S. Torquato, Random Heterogeneous Materials (Springer-Verlag, New York, 2001).
3. G. Milton, The Theory of Composites (Cambridge University Press, Cambridge, UK, 2002).
4. M. Sahimi, Heterogeneous Materials (Springer-Verlag, New York, 2003), Vols. I and II.
5. I. Webman, J. Jornter, and M. Cohen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.11.2885 11, 2885 (1975).
6. I. Kim and S. Torquato, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.354792 74, 1844 (1993).
7. J. Carson, S. Lovatt, D. Tanner, and A. C. Cleland, Int. J. Heat Mass Transfer IJHMAK 0017-9310 10.1016/j.ijheatmasstransfer.2004.12.032 48, 2150 (2005).
8. G. Batchelor, F. O'Brien, and R. O'Brien, Proc. R. Soc. London, Ser. A 355, 313 (1977).
9. X. Cheng and A. M. Sastry, Mech. Mater. MSMSD3 0167-6636 10.1016/S0167-6636(99)00031-9 31, 765 (1999).
10. S. Kirkpatrick, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.45. 574 45, 574 (1973).
11. M. Sahimi, AIChE J. 39, 369 (1993). 0001-1541
12. M. Sahimi and T. Tsotsis, Ind. Eng. Chem. Res. IECRED 0888-5885 10.1021/ie960602k 36, 3043 (1997).
13. X. Zhuang, A. Didwana, and J. Goddard, J. Comput. Phys. JCTPAH 0021-9991 10.1016/S0021-9991(95)90187-6 121, 331 (1995).
14. M. Bartkowiak and G. D. Mahan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.10825 51, 10825 (1995).
15. C. Argento and D. Bouvard, Int. J. Heat Mass Transfer IJHMAK 0017-9310 10.1016/0017-9310(95)00257-X 39, 1343 (1996).
16. V. Favier, R. Dendievel, G. Canova, J.-Y. Cavaillé, and P. Gilormini, Acta Mater. ACMAFD 1359-6454 10.1016/S1359-6454(96)00264-9 45, 1557 (1997).
17. R. R. Sundararajakumar and D. L. Koch, J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377-0257(97)00043-8 73, 205 (1997).
18. G. Cheng, A. Yu, and P. Zulli, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/S0009-2509(99)00125-6 54, 4199 (1999).
19. L. Flandin, M. Verdier, B. Boutherin, Y. Brechet, and J.-Y. Cavaillé, J. Polym. Sci. B 37, 805 (1999). 0449-2986
20. Z. Neda, R. Florian, and Y. Brechet, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.3717 59, 3717 (1999).
21. X. Cheng, A. M. Sastry, and B. E. Layton, ASME J. Eng. Mater. Technol. JEMTA8 0094-4289 10.1115/1.1322357 123, 12 (2001).
22. W. Vargas and J. McCarthy, AIChE J. AICEAC 0001-1541 10.1002/aic. 690470511 47, 1052 (2001).
23. F. Dalmas, R. Dendievel, L. Chazeau, J.-Y. Cavaillé, and C. Gauthier, Acta Mater. ACMAFD 1359-6454 10.1016/j.actamat.2006.02.028 54, 2923 (2006).
24. L. Berhan and A. M. Sastry, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.041120 75, 041120 (2007).
25. L. Berhan and A. M. Sastry, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.041121 75, 041121 (2007).
26. A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures (North Holland, Amsterdam, 1978).
27. E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics (Springer-Verlag, Berlin, 1980).
28. J.-L. Auriault, Int. J. Eng. Sci. IJESAN 0020-7225 10.1016/0020-7225(91) 90001-J 29, 785 (1991).
29. J.-L. Auriault, Int. J. Heat Mass Transfer 26, 861 (1983).
30. J.-L. Auriault and H. I. Ene, Int. J. Heat Mass Transfer IJHMAK 0017-9310 10.1016/0017-9310(94)90342-5 37, 2885 (1994).
31. M. Lambert and L. Fletcher, J. Thermophys. Heat Transfer 11, 129 (1997).
32. J.-L. Auriault and J. Lewandowska, C. R. Acad. Sci., Ser. IIb Mec. 324, 293 (1997).
33. M. Oda, S. Nemat-Nasser, and M. Mehrabadi, Int. J. Numer. Analyt. Meth. Geomech. IJNGDZ 0363-9061 10.1002/nag.1610060106 6, 77 (1982).
34. G. K. Batchelor, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fl.06.010174.001303 6, 227 (1974).
35. J.-P. Vassal, L. Orgéas, D. Favier, J.-L. Auriault, and S. Le Corre, Phys. Rev. E PLEEE8 1063-651X 77, 011303 (2008).