Effects of inhomogeneous partial absorption and the geometry of the boundary on population evolution of molecules diffusing in general porous media

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

Volumn 80, Issue 2, 2009, Pages

  Ryu, Seungoh ^a  

^a SCHLUMBERGER DOLL RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY DISTRIBUTION; CONTROLLED EXPERIMENT; GLASS BEAD; INHOMOGENEITIES; NORMAL MODE ANALYSIS; NUMERICAL SIMULATION; PARTIAL ABSORPTION; POPULATION EVOLUTION; PORE GEOMETRY; POROUS MEDIA; RELAXATION MODES; RELAXATION SPECTRUM; SPATIAL VARIATIONS; SPHERICAL PORES; TIME DOMAIN;

BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; HELMHOLTZ EQUATION; POROUS MATERIALS;

TIME DOMAIN ANALYSIS;

EID: 70349551731     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.026109     Document Type: Article

References (58)

1. M. Kac, Am. Math. Monthly 73, 1 (1966). 10.2307/2313748
2. C. Gordon, D. L. Webb, and S. Wolpert, Bull., New Ser., Am. Math. Soc. 27, 134 (1992). 10.1090/S0273-0979-1992-00289-6
3. S. J. Chapman, Am. Math. Monthly 102, 124 (1995). 10.2307/2975346
4. B. Sapoval, M. Filoche, K. Karamanos, and R. Brizzi, Eur. Phys. J. B 9, 739 (1999). 10.1007/s100510050819
5. D. Rocchesso, Proceedings of the 2001 International Conference on Auditory Display, Espoo, Finland, 2001 (unpublished).
6. P. G. de Gennes, Acad. Sci., Paris, C. R. 295, 1061 (1982).
7. P. P. Mitra, P. N. Sen, L. M. Schwartz, and P. Le Doussal, Phys. Rev. Lett. 68, 3555 (1992). 10.1103/PhysRevLett.68.3555
8. M. L. Metha, Random Matrices (Elsevier, Amsterdam, 2004).
9. M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller, Phys. Rev. E 56, 2496 (1997). 10.1103/PhysRevE.56.2496
10. R. A. Fisher, Proc. Annu. Symp. Eugen. Soc. 7, 355 (1937).
11. J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999). 10.1103/PhysRevLett.82.867
12. J. Fort and V. Méndez, Phys. Rev. E 60, 5894 (1999). 10.1103/PhysRevE.60.5894
13. H. Takeno, M. Muto, N. Fujimoto, and K. Hagihara, Proceedings of the Seventh International Conference on Mobile Data Management, 2006 (unpublished), p. 44.
14. D. S. Grebenkov, Rev. Mod. Phys. 79, 1077 (2007). 10.1103/RevModPhys.79. 1077
15. R. L. Kleinberg, in Encyclopedia of Nuclear Magnetic Resonance, edited by, D. M. Grant, and, R. K. Harris, (Wiley, Chichester, 1996).
16. N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev. 73, 679 (1948). 10.1103/PhysRev.73.679
17. J. M. Perez, L. Josephson, T. O'Loughlin, D. Högemann, and R. Weissleder, Nat. Biotechnol. 20, 816 (2002).
18. A. R. Kansal and S. Torquato, J. Chem. Phys. 116, 10589 (2002). 10.1063/1.1479718
19. T. R. Bryar and R. J. Knight, Geophys. Res. Lett. 29, 2197 (2002). 10.1029/2002GL016043
20. T. R. Bryar and R. J. Knight, Water Resour. Res. 44, W02401 (2008). 10.1029/2006WR005635
21. R. Blinc, G. Lahajnar, S. Zumer, and M. M. Pintar, Phys. Rev. B 38, 2873 (1988). 10.1103/PhysRevB.38.2873
22. C. Casieri, F. De Luca, and P. Fantazzini, J. Appl. Phys. 97, 043901 (2005). 10.1063/1.1833572
23. F. R. E. Fenrich, C. Beaulieu, and P. S. Allen, NMR Biomed. 14, 133 (2001). 10.1002/nbm.685
24. M. J. Bronskill, G. E. Santyr, B. Walters, and R. M. Henkelman, Magn. Reson. Med. 31, 611 (1994). 10.1002/mrm.1910310606
25. L. van der Weerd, Plant, Cell Environ. 25, 1539 (2002). 10.1046/j.1365-3040.2002.00934.x
26. M. D. Hürlimann, L. Burcaw, and Y.-Q. Song, J. Colloid Interface Sci. 297, 303 (2006). 10.1016/j.jcis.2005.10.047
27. W. E. Kenyon, Nucl. Geophys. 6, 153 (1992).
28. G. Sorland, K. Djurhuus, H. C. Wideroe, J. Lien, and A. Skauge, Diffus. Fundam. 5, 4.1 (2007).
29. M. D. Hürlimann, L. Venkataramanan, and C. Flaum, J. Chem. Phys. 117, 10223 (2002). 10.1063/1.1518959
30. D. J. Bergman and K.-J. Dunn, Phys. Rev. E 51, 3401 (1995). 10.1103/PhysRevE.51.3401
31. K. R. Brownstein and C. E. Tarr, Phys. Rev. A 19, 2446 (1979). 10.1103/PhysRevA.19.2446
32. J.-P. Korb, L. Malier, F. Cros, S. Xu, and J. Jonas, Phys. Rev. Lett. 77, 2312 (1996). 10.1103/PhysRevLett.77.2312
33. T. M. de Swiet and P. N. Sen, J. Chem. Phys. 100, 5597 (1994). 10.1063/1.467127
34. P. Gillis and S. H. Koenig, Magn. Reson. Med. 5, 323 (1987). 10.1002/mrm.1910050404
35. K.-J. Dunn, J. Magn. Reson. 156, 171 (2002). 10.1006/jmre.2002.2541
36. R. L. Kleinberg, W. E. Kenyon, and P. P. Mitra, J. Magn. Reson., Ser. A 108, 206 (1994). 10.1006/jmra.1994.1112
37. D. J. Wilkinson, D. L. Johnson, and L. M. Schwartz, Phys. Rev. B 44, 4960 (1991). 10.1103/PhysRevB.44.4960
38. A. Valfouskaya, P. M. Adler, J. F. Thovert, and M. Fleury, J. Colloid Interface Sci. 295, 188 (2006). 10.1016/j.jcis.2005.08.021
39. C. H. Arns, A. P. Sheppard, M. Saadatfar, and M. A. Knackstedt, SPWLA 47th Annual Logging Symposium, 2006 (unpublished), p. 498610GG.
40. K. S. Mendelson, Phys. Rev. B 47, 1081 (1993). 10.1103/PhysRevB.47.1081
41. S. Ryu, SPWLA Proceedings of the 49th Annual Logging Symposium, SPWLA, 2008 (unpublished), p. 737008 BB.
42. P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1958).
43. G. Arfken, Mathematical Methods for Physicists (Academic Press, New York, 1970), Chap..
44. S. Ryu, Magn. Reson. Imaging 19, 411 (2001). 10.1016/S0730-725X(01)00258- 2
45. K. R. McCall, D. L. Johnson, and R. A. Guyer, Phys. Rev. B 44, 7344 (1991). 10.1103/PhysRevB.44.7344
46. Y.-Q. Song, S. Ryu, and P. N. Sen, Nature (London) 406, 178 (2000). 10.1038/35018057
47. L. J. Zielinski, Y.-Q. Song, S. Ryu, and P. N. Sen, J. Chem. Phys. 117, 5361 (2002). 10.1063/1.1499956
48. N. V. Lisitza and Y.-Q. Song, Phys. Rev. B 65, 172406 (2002). 10.1103/PhysRevB.65.172406
49. Y.-Q. Song, L. Zielinski, and S. Ryu, Phys. Rev. Lett. 100, 248002 (2008). 10.1103/PhysRevLett.100.248002
50. D. L. Johnson, J. Koplik, and L. M. Schwartz, Phys. Rev. Lett. 57, 2564 (1986). 10.1103/PhysRevLett.57.2564
51. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
52. J. Finjord, A. Hiorth, U. Lad, and S. Skjaeveland, Transp. Porous Media 69, 33 (2007). 10.1007/s11242-006-9062-7
53. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, Mineola, NY, 1972).
54. D. S. Grebenkov, Diffus. Fundam. 5, 1.1 (2007).
55. D. L. Johnson and S. Ryu (unpublished).
56. S. Ryu and D. L. Johnson, Phys. Rev. Lett. (to be published)
57. also e-print arXiv:0903.1653.
58. As the angular variation in δρ becomes more rapid, it acts as a high-pass filter in controlling the strength of each mode with L to δ λ0,b (as indicated by the lower bounding curve of Fig. 4). In the case of the hemispherical δρ, all odd angular momenta bigger than L=1 contributes, and one would expect that the impact of this filtering would amount to suppression of some modes with L≤1 and n∼1. For a distribution with rapid angular variations, the number of such suppressed modes may increase, thereby impacting the convergence of the projection.