Slow kinetics of water escape from randomly folded foils

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

Volumn 83, Issue 3, 2011, Pages

  Balankin, Alexander S ^a   Gutierres, S Matías ^a   Ochoa, D Samayoa ^a   Ortiz, J Patiño ^a   Elizarraraz, B Espinoza ^a   Martinez Gonzalez C L ^a  

^a INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSED MATTER PHYSICS; PHYSICS;

ACTUAL MASS; DIFFERENT THICKNESS; FRACTAL GEOMETRY; POWER-LAW FUNCTIONS; RESIDUAL WATERS; SCALING RELATIONS; UNIVERSAL SCALING EXPONENTS; WATER DISCHARGES;

FRACTALS;

EID: 79953146612     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.036310     Document Type: Article

References (49)

1. In mathematics, Riemann used a crumpled ball of paper with bookworms to explain the hidden dimensions in non-Euclidean geometry.
2. See M. Kaku, Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 10th Dimension (Oxford University Press, New York, 1994).
3. M. S. Spector, E. Naranjo, S. Chiruvolu, and J. A. Zasadzinski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.2867 73, 2867 (1994);
4. T. Tallinen, A. Aström, P. Kekílíinen, and J. Timonen, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.105.026103 105, 026103 (2010).
5. D. L. Blair and A. Kudrolli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.166107 94, 166107 (2005); (Pubitemid 40648271)
6. E. Sultan and A. Boudaoud, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.136103 95, 136103 (2006).
7. A. S. Balankin, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.061602 74, 061602 (2006); (Pubitemid 44905757)
8. A. S. Balankin, R. C. Montes de Oca, and D. Samayoa, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.032101 76, 032101 (2007); (Pubitemid 47443140)
9. A. S. Balankin, D. Samayoa, I. A. Miguel, J. Patiño, and M. A. Martínez, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.061126 81, 061126 (2010).
10. Z. Ismat, J. Struct. Geolog. 0191-8141 10.1016/j.jsg.2008.10.006 31, 972 (2009).
11. T. A. Witten, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.79.643 79, 643 (2007). (Pubitemid 46677004)
12. K. Matan, R. B. Williams, T. A. Witten, and S. R. Nagel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.076101 88, 076101 (2002);
13. Y.-C. Lin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103. 263902 103, 263902 (2009);
14. T. Tallinen, J. A. Aström, and J. Timonen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.106101 95, 106101 (2008);
15. T. Tallinen, J. A. Aström, and J. Timonen, Nat. Mater. 1476-1122 10.1038/nmat2343 8, 25 (2009);
16. A. S. Balankin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.77.125421 77, 125421 (2008);
17. A. S. Balankin and O. Susarrey, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.051124 77, 051124 (2008). (Pubitemid 351768345)
18. M. A. F. Gomes, J. Phys. D: Appl. Phys. JPAPBE 0022-3727 10.1088/0022-3727/22/8/030 22, 1217 (1989);
19. A. S. Balankin, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.051117 75, 051117 (2007); (Pubitemid 47140192)
20. Y. C. Lin, Y. L. Wang, Y. Liu, and T. M. Hong, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.125504 101, 125504 (2008).
21. F. M. Borodich and Z. Feng, Z. Angew. Math. Phys. 0044-2275 10.1007/s00033-009-0010-6 61, 21 (2010).
22. B. Yu, J. Li, Z. Li, and M. Zou, Int. J. Multiphase Flow IJMFBP 0301-9322 10.1016/S0301-9322(03)00140-X 29, 1625 (2003); (Pubitemid 37216426)
23. G. Huang and R. Zhang, Geoderma GEDMAB 0016-7061 10.1016/j.geoderma.2004. 11.016 127, 52 (2005); (Pubitemid 40793528)
24. A. Dathea and M. Thullner, Geoderma 0016-7061 10.1016/j.geoderma.2005.01. 003 129, 279 (2005); (Pubitemid 41550349)
25. J. M. Köhne, S. Köhne, and J. Å imÅnek, J. Contam. Hydrol. JCOHE6 0169-7722 10.1016/j.jconhyd.2008.10.002 104, 4 (2009);
26. K. Li, J. Petroleum Sci. Eng. 0920-4105 10.1016/j.petrol.2010.05.002 73, 20 (2010).
27. A. S. Balankin, O. Susarrey, and J. Márquez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.096101 90, 096101 (2003);
28. A. S. Balankin, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.96.056101 96, 056101 (2006);
29. S.W. Coleman and J. C. Vassilicos, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.100.035504 100, 035504 (2008). (Pubitemid 351161797)
30. M. R. Deinert, A. Dathe, J.-Y. Parlange, and K. B. Cady, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.021203 77, 021203 (2008); (Pubitemid 351393444)
31. M. R. Deinert and J.-Y. Parlange, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.021202 79, 021202 (2009).
32. The porosity of tested balls was varied in the range 0. 802 < p (Î) < 0. 987.
33. In this way, we were able to fill with water up to 97 % of pore space of a folded ball.
34. V. P. Singh, Hydrol. Process 0885-6087 10.1002/hyp.306 16, 667 (2002). (Pubitemid 34166197)
35. α = 0. 073
36. P, where the parameter É are varied from experiment to experiment in the range 0. 003 â© É â© 0. 004.
37. Notice that the same amount of water escapes from a hollow reservoir with holes more than ten times faster than from a folded sheet with the same cross-sectional area available for water escape.
38. Strictly speaking, the best fit of all experimental data is K Â = 0. 13 Ï V P 1. 2 [see the top insert in Fig. 5(a)], whereas the data for balls with different contraction ratios are best fitted by Eq. (3) [see the bottom insert in Fig. 5(a)].
39. J. Bear, The Dynamics of Fluids in Porous Media (Dover, Mineola, NY, 1988).
40. This is possible, for example, if the height of water in a folded sheet does not decrease so far M > M r BF, or if both Î" P and Î" l decrease as M decreases, in such a way that Î" P / Î" l = const. Alternatively, we can assume that Î" P / Î" l â‰ Ï g, but this seems less probable. In any case, this point needs to be clarified in further studies.
41. R. H. Brooks and A. T. Corey, in Hydrology Papers, No. 3 (Colorado State University, Fort Collins, CO, 1964), p. 22.
42. W. Brutsaert, Adv. Water Res. 0309-1708 10.1016/S0309-1708(00)00019-1 23, 811 (2000). (Pubitemid 30398112)
43. A. G. Hunt, Adv. Water Res. 0309-1708 10.1016/j.advwatres.2004.01.002 27, 245 (2004). (Pubitemid 38473860)
44. N. Fries and M. Dreyer, J. Colloid Interface Sci. JCISA5 0021-9797 10.1016/j.jcis.2009.06.036 338, 514 (2009).
45. Of course, this statement needs to be verified by direct experiments.
46. Experimentally it was found that the mass fractal dimension of folded matter increases as Î increases [see Y.-C. Lin, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.066114 80, 066114, (2009)].
47. P (p = 0) ≡ 0.
48. S [see P. Pfeifer and D. Avnir, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.446210 79, 3558, (1983) and references therein].
49. S. If so, our finding n = α = 3 together with (7), (8) suggest that ω = 1, while ζ = 1 - χ.