Mass transport subject to time-dependent flow with nonuniform sorption in porous media

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

Volumn 80, Issue 5, 2009, Pages

  Néel, Marie Christine ^a   Zoia, Andrea ^b   Joelson, Maminirina ^a  

^a UAPV   (France)

^b CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BREAK THROUGH CURVE; CONCENTRATION OF; GOVERNING EQUATIONS; MASS TRANSPORT; MOBILE-IMMOBILE MODELS; MONTE CARLO PARTICLES; NONUNIFORM; POROUS MEDIA; SMALL-SCALE MODELS; SORPTION RATE; TIME-DEPENDENT FLOW; TRACER-PARTICLE TRAJECTORIES; TRACKING SIMULATION; TRANSPORT EQUATION;

POROUS MATERIALS; SORPTION;

SIMULATORS;

EID: 70449674354     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.056301     Document Type: Article

References (64)

1. B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Rev. Geophys. 44, RG2003 (2006). 10.1029/2005RG000178
2. M. Sahimi, Flow and Transport in Porous Media and Fractured Rock (VCH, Weinheim, 1995).
3. H. Scher, G. Margolin, and B. Berkowitz, Chem. Phys. 284, 349 (2002). 10.1016/S0301-0104(02)00558-X
4. A. Cortis and B. Berkowitz, Soil Sci. Soc. Am. J. 68, 1539 (2004).
5. B. Berkowitz and H. Scher, Phys. Rev. Lett. 79, 4038 (1997). 10.1103/PhysRevLett.79.4038
6. M. Levy and B. Berkowitz, J. Contam. Hydrol. 64, 203 (2003). 10.1016/S0169-7722(02)00204-8
7. J. W. Kirchner, X. Feng, and C. Neal, Nature (London) 403, 524 (2000). 10.1038/35000537
8. A. Zoia, Y. Kantor, and M. Kardar, Europhys. Lett. 80, 40006 (2007). 10.1209/0295-5075/80/40006
9. M. Bromly and C. Hinz, Water Resour. Res. 40, W07402 (2004). 10.1029/2003WR002579
10. B. Berkowitz, S. Emmanuel, and H. Scher, Water Resour. Res. 44, W03402 (2008). 10.1029/2007WR005906
11. N. Tufenkji and M. Elimelech, Environ. Sci. Technol. 39, 3620 (2005). 10.1021/es048289y
12. A. Zoia, C. Latrille, and A. Cartalade, Phys. Rev. E 79, 041125 (2009). 10.1103/PhysRevE.79.041125
13. A. Zoia, A. Rosso, and S. N. Majumdar, Phys. Rev. Lett. 102, 120602 (2009). 10.1103/PhysRevLett.102.120602
14. R. Haggerty and S. M. Gorelick, Water Resour. Res. 31, 2383 (1995). 10.1029/95WR01583
15. R. Schumer, D. A. Benson, M. M. Meerschaert, and B. Bauemer, Water Resour. Res. 39, 1296 (2003). 10.1029/2003WR002141
16. F. Boano, J. P. Packman, A. Cortis, R. Pardelle, and C. Ridolfi, Water Resour. Res. 43, W10425 (2007). 10.1029/2007WR006062
17. D. A. Benson and M. M. Meerschaert, Adv. Water Resour. 32, 532 (2009). 10.1016/j.advwatres.2009.01.002
18. Y. Zhang, D. A. Benson, and B. Bauemer, Water Resour. Res. 44, W04424 (2008). 10.1029/2007WR006291
19. E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi, Phys. Rev. Lett. 99, 120602 (2007). 10.1103/PhysRevLett.99.120602
20. B. Maryshev, M. Joelson, D. Lyubimov, T. Lyubimova, and M. C. Néel, J. Phys. A: Math. Theor. 42, 115001 (2009). 10.1088/1751-8113/42/ 11/115001
21. G. Zaslavsky, Physica D 76, 110 (1994). 10.1016/0167-2789(94)90254-2
22. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E 61, 132 (2000). 10.1103/PhysRevE.61.132
23. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E 75, 016708 (2007). 10.1103/PhysRevE.75.016708
24. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
25. M. T. Van Genuchten and P. J. Wierenga, Soil Sci. Soc. Am. J. 40, 473 (1976).
26. E. Barkai, Phys. Rev. E 63, 046118 (2001). 10.1103/PhysRevE.63.046118
27. R. Gorenflo, F. Mainardi, and A. Vivoli, Chaos, Solitons Fractals 34, 87 (2007). 10.1016/j.chaos.2007.01.052
28. A. Piryatinska, A. I. Saichev, and W. A. Woyczynski, Physica A 349, 375 (2005). 10.1016/j.physa.2004.11.003
29. M. Magdziarz, A. Weron, and J. Klafter, Phys. Rev. Lett. 101, 210601 (2008). 10.1103/PhysRevLett.101.210601
30. A. Weron, M. Magdziarz, and K. Weron, Phys. Rev. E 77, 036704 (2008). 10.1103/PhysRevE.77.036704
31. H. Risken, The Fokker-Planck Equation, Methods of Solution and Applications, Springer Series in Synergetics, 2nd ed. (Springer-Verlag, New York, 1989).
32. F. Delay, P. Ackerer, and C. Danquigny, Vadose Zone J. 4, 360 (2005). 10.2136/vzj2004.0125
33. B. D. Hughes, Random Walks in Random and Complex Environments (Oxford Science Publications/Clarendon Press, Oxford, 1995), Vol. 1.
34. M. Marseguerra and A. Zoia, Physica A 387, 2668 (2008).
35. I. V. Zaliapin, Y. Y. Kagan, and F. P. Schoenberg, Pure Appl. Geophys. 162, 1187 (2005). 10.1007/s00024-004-2666-3
36. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970), Vol. II.
37. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Variables (Addison-Wesley, Reading, MA, 1968).
38. P. Lévy, Théorie de l'Addition des Variables Aléatoires (Gauthier-Villars, Paris, 1937).
39. M. M. Meerschaert and H. P. Scheffler, Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice (Wiley, New York, 2000).
40. F. Mainardi, in Fractals and Fractional Calculus in Continuum Mechanics, CISM Courses and Lectures Vol. 378, edited by, A. Carpinteri, and, F. Mainardi, (Springer, New York, 1997), pp. 291-348.
41. F. Mainardi and R. Gorenflo, J. Comput. Appl. Math. 118, 283 (2000). 10.1016/S0377-0427(00)00294-6
42. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies Vol. 204 (Jan van Mill, Amsterdam, 2006).
43. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach, New York, 1993).
44. K. Diethelm, N. J. Ford, A. D. Freed, and Y. Luchko, Comput. Methods Appl. Mech. Eng. 194, 743 (2005). 10.1016/j.cma.2004.06.006
45. R. Gorenflo and E. A. Abdel-Rehim, J. Comput. Appl. Math. 205, 871 (2007). 10.1016/j.cam.2005.12.043
46. I. M. Sokolov and J. Klafter, Phys. Rev. Lett. 97, 140602 (2006). 10.1103/PhysRevLett.97.140602
47. B. Berkowitz, A. Cortis, I. Dror, and H. Scher, Water Resour. Res. 45, W02201 (2009). 10.1029/2008WR007342
48. M. Marseguerra and A. Zoia, Ann. Nucl. Energy 33, 1396 (2006). 10.1016/j.anucene.2006.09.012
49. M. Marseguerra and A. Zoia, Physica A 377, 448 (2007). 10.1016/j.physa.2006.11.083
50. G. Hornung, B. Berkowitz, and N. Barkai, Phys. Rev. E 72, 041916 (2005). 10.1103/PhysRevE.72.041916
51. A. Cortis and A. Zoia, Phys. Rev. E 80, 011122 (2009). 10.1103/PhysRevE.80.011122
52. J. F. Lutsko and J. P. Boon, Phys. Rev. E 77, 051103 (2008). 10.1103/PhysRevE.77.051103
53. A. V. Chechkin, V. Y. Gonchar, R. Gorenflo, N. Korabel, and I. M. Sokolov, Phys. Rev. E 78, 021111 (2008). 10.1103/PhysRevE.78.021111
54. P. Billingsley, Convergence of Probability Measures, Wiley Series in Probability and Statistics, 2nd ed. (Wiley, New York, 1999).
55. B. Rubin, Fractional Integrals and Potentials (Longman, Harlow, 1996).
56. W. Arendt, C. J. K. Batty, M. Hieber, and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics Vol. 96 (Birkhäuser, Basel, 2001).
57. W. Rudin, Real and Complex Analysis, 3rd ed. (McGraw-Hill, New York, 1987).
58. M. M. Meerschaert and H. P. Scheffler, Fractional Calculus Appl. Anal. 5, 27 (2002).
59. N. G. Samko and S. G. Samko, Fractional Calculus Appl. Anal. 2, 329 (1999).
60. S. G. Samko, Fractional Calculus Appl. Anal. 1, 225 (1998).
61. M. C. Néel, A. Abdennadher, and J. Solofoniania, Physica A 387, 2750 (2008). 10.1016/j.physa.2008.01.090
62. M. C. Néel, A. Abdennadher, and M. Joelson, J. Phys. A: Math. Theor. 40, 8299 (2007). 10.1088/1751-8113/40/29/007
63. A. Zoia, A. Rosso, and M. Kardar, Phys. Rev. E 76, 021116 (2007). 10.1103/PhysRevE.76.021116
64. M. Magdziarz, J. Stat. Phys. 135, 763 (2009). 10.1007/s10955-009-9751-z