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Depinning and creeplike motion of wetting fronts in weakly vibrated granular media

Alexander S. Balankin1,*, E. García Otamendi1, D. Samayoa1, J. Patiño1, and M. A. Rodríguez2

  • 1Grupo “Mecánica Fractal,” Instituto Politécnico Nacional, México D.F., México 07738
  • 2Instituto de Física de Cantabria (IFCA), CSIC–UC, E-39005 Santander, Spain

  • *abalankin@ipn.mx
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Phys. Rev. E 85, 036313 – Published 23 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.036313

Abstract

We study the effect of weak vibrations on the imbibition of water in granular media. In our experiments, we have observed that as soon as the vibration is applied, an initially pinned wetting front advances in the direction of imbibition. We found that the front motion is governed by the avalanches of localized intermittent advances directed at 45∘ to the imbibition direction. When the rescaled gravitational acceleration of vertical vibrations is in the range of 0.81⩽G⩽0.95, we observed an almost steady motion of wetting front with a constant velocity vcr(G)∝exp−1/G during more than 20 min, whereas at lower accelerations (0.5⩽G⩽0.8) the front velocity decreases in time as v∝t−δ. We suggest that the steady motion of an imbibition front in a weakly vibrated granular medium can be treated as a creep motion associated with nonthermal temporal fluctuations of packing density in a weakly vibrated granular medium.

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References (67)

  1. M. Alava, M. Dubé, and M. Rost, Adv. Phys. 53, 83 (2004).
  2. Th. Delker, D. B. Pengra, and P. Wong, Phys. Rev. Lett. 76, 2902 (1996).
  3. M. Dubé, M. Rost, and M. Alava, Eur. Phys. J. B 76, 691 (2000).
  4. Ch.-H. Lam and V. K. Horváth, Phys. Rev. Lett. 85, 1238 (2000); D. Geromichalos, F. Mugele, and St. Herminghaus, ibid. 89, 104503 (2002); S. Supple and N. Quirke, ibid. 90, 214501 (2003); Y. Mélean, D. Broseta, A. Hasmy, and R. Blossey, Europhys. Lett. 62, 505 (2003).
  5. Y. Méheust, G. Løvoll, K. J. Måløy, and J. Schmittbuhl, Phys. Rev. E 66, 051603 (2002).
  6. A. S. Balankin, A. Bravo-Ortega, and D. Morales, Philos. Mag. Lett. 80, 503 (2000); A. S. Balankin, O. Susarrey, and J. M. Gonzáles, Phys. Rev. Lett. 90, 096101 (2003); E. N. de Azevedo, L. R. Alme, M. Engelsberg, J. O. Fossum, and P. Dommersnes, Phys. Rev. E 78, 066317 (2008); A. M. Miranda, I. L. Menezes-Sobrinho, and M. S. Couto, Phys. Rev. Lett. 104, 086101 (2010).
  7. M. Dubé, S. Majaniemi, M. Rost, M. J. Alava, K. R. Elder, and T. Ala-Nissila, Phys. Rev. E 64, 051605 (2004).
  8. J. Soriano, A. Mercier, R. Planet, A. Hernández-Machado, M. A. Rodríguez, and J. Ortín, Phys. Rev. Lett. 95, 104501 (2005); S. Santucci, R. Planet, K. Jørgen Måløy, and J. Ortín, Europhys. Lett. 94, 46005 (2011).
  9. M. Sánchez, A. Medina, and A. Rojano, Rev. Mex. Fis. 51, 349 (2005).
  10. A. S. Balankin, R. Paredes, O. Susarrey, D. Morales, and F. Castrejon, Phys. Rev. Lett. 96, 056101 (2006).
  11. S. S. Le Guen and A. R. Kovscek, Transp. Porous Media 63, 127 (2006).
  12. M. Pradas, J. M. López, and A. Hernández-Machado, Phys. Rev. E 76, 010102R (2007).
  13. M. Pradas and A. Hernández-Machado, Phys. Rev. E 74, 041608 (2006); R. Planet, M. Pradas, A. Hernández-Machado, and J. Ortín, ibid. 77, 056312 (2007); M. Pradas, A. Hernández-Machado, and M. A. Rodríguez, ibid. 77, 056305 (2008).
  14. M. Pradas, J. M. López, and A. Hernández-Machado, Phys. Rev. E 80, 050101(R) (2009).
  15. J. M. López, M. Pradas, and A. Hernández-Machado, Phys. Rev. E 82, 031127 (2010).
  16. R. Planet, St. Santucci, and J. Ortín, Phys. Rev. Lett. 102, 094502 (2009); 105, 029402 (2010); J. Contam. Hydrol. 120–121, 157 (2011); G. Pruessner, Phys. Rev. Lett. 105, 029401 (2010).
  17. M. Dubé, B. Chabot, C. Daneault, and M. Alava, Pulp Pap. Can. 169, 24 (2005).
  18. M. Rost, L. Laurson, M. Dubé, and M. Alava, Phys. Rev. Lett. 98, 054502 (2007); M. Dubé, C. Daneault, V. Vuorinen, M. Alava, and M. Rost, Eur. Phys. J. B 56, 15 (2007).
  19. Z. T. Karpyn and M. Piri, Phys. Rev. E 76, 016315 (2007); 76, 016316 (2007); B. Aminzadeh and D. A. DiCarlo, Vadose Zone J. 9, 588 (2010).
  20. C. Ulas Hatiboglu and T. Babadagli, Phys. Rev. E 77, 066311 (2008).
  21. C. Jian-Chao, Y. Bo-Mingand, M. Mao-Fei, and L. Liang, Chin. Phys. Lett. 27, 054701 (2010); J. Cai, B. Yu, M. Zou, and L. Luo, Energy Fuels 24, 1860 (2010); D. Ch. Standnes, ibid. 24, 2980 (2010); Chem. Eng. Sci. 65, 5178 (2010).
  22. S. Gruener and P. Huber, Phys. Rev. Lett. 103, 174501 (2009); S. Gruener, T. Hofmann, D. Wallacher, A. V. Kityk, and P. Huber, Phys. Rev. E 79, 067301 (2009); P. Gaillard, Y. Saito, and O. Pierre-Louis, Phys. Rev. Lett. 106, 195501 (2011).
  23. M. Lago and M. Araujo, Physica A 289, 1 (2001).
  24. N. Fries and M. Dreyer, J. Colloid Interface Sci. 338, 514 (2009).
  25. L. A. N. Amaral, A.-L. Barabási, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 72, 641 (1994).
  26. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
  27. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Rev. Mod. Phys. 81, 739 (2009).
  28. L. A. N. Amaral, A.-L. Barabási, S. V. Buldyrev, S. T. Harrington, S. Havlin, R. Sadr-Lahijany, and H. E. Stanley, Phys. Rev. E 51, 4655 (1995).
  29. A. Dougherty and N. Carle, Phys. Rev. E 58, 2889 (1998).
  30. L. A. N. Amaral, A.-L. Barabási, H. A. Makse, and H. E. Stanley, Phys. Rev. E 52, 4087 (1995).
  31. P. Chauve, T. Giamarchi, and P. Le Doussal, Phys. Rev. B 62, 6241 (2000).
  32. A. B. Kolton, A. Rosso, and T. Giamarchi, Phys. Rev. Lett. 94, 047002 (2005).
  33. F. Caysol, D. Ravelosona, C. Chappert, J. Ferré, and J. P. Jamet, Phys. Rev. Lett. 92, 107202 (2004).
  34. A. Petković and T. Nattermann, Phys. Rev. Lett. 101, 267005 (2008).
  35. J. Kierfeld, H. Nordborg, and V. M. Vinokur, Phys. Rev. Lett. 85, 4948 (2000).
  36. A. B. Kolton, A. Rosso, T. Giamarchi, and W. Krauth, Phys. Rev. B 79, 184207 (2009).
  37. D. A. Gorokhov, D. S. Fisher, and G. Blatter, Phys. Rev. B 66, 214203 (2002).
  38. J. R. Thompson, J. G. Ossandon, L. Krusin-Elbaum, K. J. Song, D. K. Christen, and J. L. Ullmann, Appl. Phys. Lett. 74, 3699 (1999).
  39. M. Schröter, D. I. Goldman, and H. L. Swinney, Phys. Rev. E 71, 030301(R) (2005).
  40. E. R. Nowak, J. B. Knight, E. Ben-Naim, H. M. Jaeger, and S. R. Nagel, Phys. Rev. E 57, 1971 (1998).
  41. M. Nicodemi, A. Coniglio, and H. J. Herrmann, Phys. Rev. E 59, 6830 (1999).
  42. A. Janda, D. Maza, A. Garcimartín, E. Kolb, J. Lanuza, and E. Clément, Europhys. Lett. 87, 24002 (2009).
  43. A. Garcimartín, I. Zuriguel, L. A. Pugnaloni, and A. Janda, Phys. Rev. E 82, 031306 (2010).
  44. T. Hamida and T. Babadagli, in SPE Asia Pacific Oil and Gas Conference and Exhibition, 5–7 April 2005, Jakarta, Indonesia (Society of Petroleum Engineers, Allen, TX, 2005), 10.2118/92124-MS.
  45. T. Hamida and T. Babadagli, Transp. Porous Media 70, 231 (2007).
  46. T. Hamida and T. Babadagli, Colloids Surf., A 316, 176 (2008).
  47. T. Hamida and T. Babadagli, Ultrason. Sonochem. 15, 274 (2008).
  48. K. Naderi and T. Babadagli, Ultrason. Sonochem., 17, 500 (2010).
  49. H. L. Chen, L. R. Lucas, L. A. D. Nogaret, H. D. Yang, and D. E. Kenyon, SPE Reservoir Eval. Eng. 3, 16 (2001); H. Karimaie, O. Torsaeter, M. R. Esfahani, M. Dadashpour, and S. M. Hashemi, J. Pet. Sci. Eng. 52, 297 (2006); D. Ch. Standnes, Energy Fuels 24, 2980 (2010); R. Meher, M. N. Mehta, and S. K. Meher, Int. J. Appl. Math. Mech. 7, 29 (2011).
  50. M. M. Kohonena, D. Geromichalosb, M. Scheelb, C. Schierb, and S. Herminghaus, Physica A 339, 7 (2004); Y. G. Tselishchev, V. A. Valtsifer, and O. G. Vasileva, Russ. J. Appl. Chem. 79, 1924 (2006); H. M. Scheel, R. Seemann, M. Brinkmann, M. D. Michiel, A. Sheppard, B. Breidenbach, and S. Herminghaus, Nat. Mater. 7, 189 (2008).
  51. H. Abou-Chakra, J. Baxter, and U. Tuzun, Adv. Powder Technol. 15, 63 (2004); M. Gan, N. Gopinathan, X. Jia, and R. A. Williams, KONA 22, 82 (2004).
  52. The overhangs were neglected.
  53. O. Chapuis and M. Prat, Phys. Rev. E 75, 046311 (2007).
  54. In some experiments, the highest parts of the moving wetting front achieve the top of the cell after 25 min, such that the water escapes from the cell through the top gap.
  55. [http://www.trusoft-international.com] (benoit1.3, 2011); W. Seffens, Science 285, 1228 (1999).
  56. A. Arnéodo, E. Bacry, P. V. Graves, and J. F. Muzy, Phys. Rev. Lett. 74 3293 (1995); I. Simonsen, A. Hansen, and O. M. Nes, Phys. Rev. E 58, 2779 (1998); W. Lui, Int. Manage. Rev. 3, 33 (2001); A. Chamoli, Earth Sci. India 12, 258 (2008).
  57. J. J. Ramasco, J. M. López, and M. A. Rodríguez, Phys. Rev. Lett. 54, 2199 (2000).
  58. S. V. Buldyrev, A.-L. Barabási, S. Havlin, J. Kenész, H. E. Stanley, and H. S. Xenias, Physica A 191, 220 (1992).
  59. We noted that the process of grain rearrangement in a weakly vibrated medium is very slow (weeks or months) and so we assume that the equilibrium height of the wetting front cannot be achieved in our experiments due to the laboratory restrictions.
  60. R. C. Acharya, S. E. A. T. M. van der Zee, and A. Leijnse, Adv. Water Res. 27, 707 (2004); M. Gladkikh and S. Bryant, J. Colloid Interface Sci. 288, 526 (2005); Adv. Water Res. 30, 249 (2007); M. Gladkikh and S. L. Bryant, J. Pet. Sci. Eng. 52, 19 (2006); J. J. Milczarek, I. F. Kirejczyk, and J. Zoladek, Acta Phys. Polonica A 113, 1245 (2008).
  61. D. S. Fisher, Phys. Rev. Lett. 56, 1964 (1986).
  62. P. Philippe and D. Bideau, Europhys. Lett. 60, 677 (2002).
  63. P. Richard, M. Nicodemi, R. Delannay, P. Ribière, and D. Bideau, Nat. Mater. 4, 121 (2005).
  64. M. Mitarai and F. Nori, Adv. Phys. 55, 1 (2006).
  65. While for a specific system, a more appropriate control parameter could be Γ=Gω (J. A. Dijksman and M. van Hecke, Europhys. Lett. 88, 44001 2009); or the dimensionless energy E, injected in the granular system at lift-off (F. Ludewig, S. Dorbolo, T. Gilet, and N. Vandewalle, 84, 44001, 2008), we have no matter to discuss the most appropriate control parameter associated with Teff, because of the small range of gravitational acceleration explored in this work.
  66. S. F. Edwards and R. B. S. Oakeshott, Physica A 157, 1080 (1989); A. Mehta and S. F. Edwards, ibid. 157, 1091 (1989); S. F. Edwards and C. C. Mounfield, ibid. 210, 290 (1994); S. F. Edwards, J. Stat. Phys. 116, 29 (2004).
  67. A. Barrat, J. Kurchan, V. Loreto, and M. Sellitto, Phys. Rev. E 63, 051301 (2001); V. Colizza, A. Barrat, and V. Loreto, ibid. 65, 050301R (2002).

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Phys. Rev. E 85, 036313– Published 23 March, 2012
  • Received 10 October 2011

©2012 American Physical Society

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