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Prebifurcation enhancement of imbibition-drainage hysteresis cycles

Ido Lavi1,2, Lauren Rose3, Ramon Planet1, Jaume Casademunt1, Stéphane Santucci3, and Jordi Ortín1

  • 1Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain and UBICS (University of Barcelona Institute of Complex Systems)
  • 2Center for Computational Biology, Flatiron Institute, 162 5th Ave, New York, New York 10010, USA
  • 3Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France

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Phys. Rev. Fluids 8, 124002 – Published 20 December, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.124002

Abstract

The efficient transport of fluids through disordered media requires a thorough understanding of how the driving rate affects two-phase interface propagation. Despite our understanding of front dynamics in homogeneous environments, as well as how medium heterogeneities shape fluid interfaces at rest, little is known about the effects of localized topographical variations on large-scale interface dynamics. To gain physical insights into this problem, we study here oil-air displacements through an “imperfect” Hele-Shaw cell. Combining experiments, numerical simulations, and theory, we show that the flow rate dramatically alters the interface response to a porous constriction as one approaches the Saffman-Taylor instability, strictly under stable conditions. This gives rise to asymmetric imbibition–drainage hysteresis cycles that feature divergent extensions and nonlocal effects, all of which are aptly captured and explained by a minimal free boundary model.

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References (42)

  1. M. Sahimi, Flow and Transport in Porous Media and Fractured Rock (Wiley, New York, 2011).
  2. J. Feder, E. G. Flekkoy, and A. Hansen, Physics of Flow in Porous Media (Cambridge University Press, Cambridge, England, 2022).
  3. M. J. Blunt, Multiphase Flow in Permeable Media. a Pore-Scale Perspective (Cambridge University Press, Cambridge, England, 2017).
  4. K. Singh, M. Jung, M. Brinkmann, and R. Seemann, Capillary-dominated fluid displacement in porous media, Annu. Rev. Fluid Mech. 51, 429 (2019).
  5. R. Ababou, Capillary Flows in Heterogeneous and Random Porous Media (Wiley, New York, 2022).
  6. B. Levaché and D. Bartolo, Revisiting the saffman-taylor experiment: Imbibition patterns and liquid-entrainment transitions, Phys. Rev. Lett. 113, 044501 (2014).
  7. R. Holtzman and E. Segre, Wettability stabilizes fluid invasion into porous media via nonlocal, cooperative pore filling, Phys. Rev. Lett. 115, 164501 (2015).
  8. M. Trojer, M. L. Szulczewski, and R. Juanes, Stabilizing fluid-fluid displacements in porous media through wettability alteration, Phys. Rev. Appl. 3, 054008 (2015).
  9. B. Zhao, C. W. MacMinn, and R. Juanes, Wettability control on multiphase flow in patterned microfluidics, Proc. Natl. Acad. Sci. USA 113, 10251 (2016).
  10. B. K. Primkulov, S. Talman, K. Khaleghi, A. R. Shokri, R. Chalaturnyk, B. Zhao, C. W. Macminn, and R. Juanes, Quasistatic fluid-fluid displacement in porous media: Invasion-percolation through a wetting transition, Phys. Rev. Fluids 3, 104001 (2018).
  11. R. Lenormand, E. Touboul, and C. Zarcone, Numerical models and experiments on immiscible displacements in porous media, J. Fluid Mech. 189, 165 (1988).
  12. R. Lenormand, Liquids in porous media, J. Phys.: Condens. Matter 2, SA79 (1990).
  13. R. Hughes and M. Blunt, Pore scale modeling of rate effects in imbibition, Transp. Porous Media 40, 295 (2000).
  14. C. Odier, B. Levaché, E. Santanach-Carreras, and D. Bartolo, Forced imbibition in porous media: a fourfold scenario, Phys. Rev. Lett. 119, 208005 (2017).
  15. R. Hu, D. S. Wu, Z. Yang, and Y. F. Chen, Energy conversion reveals regime transition of imbibition in a rough fracture, Geophys. Res. Lett. 45, 8993 (2018).
  16. P. G. de Gennes, Imperfect Hele - Shaw cells, J. Phys. France 47, 1541 (1986).
  17. A. B. Thompson, A. Juel, and A. L. Hazel, Multiple finger propagation modes in Hele-Shaw channels of variable depth, J. Fluid Mech. 746, 123 (2014).
  18. R. Brandão and J. A. Miranda, Capillary and geometrically driven fingering instability in nonflat Hele-Shaw cells, Phys. Rev. E 95, 033104 (2017).
  19. H. S. Rabbani, D. Or, Y. Liu, C. Y. Lai, N. B. Lu, S. S. Datta, H. A. Stone, and N. Shokri, Suppressing viscous fingering in structured porous media, Proc. Natl. Acad. Sci. USA 115, 4833 (2018).
  20. A. Paterson, M. Fermigier, P. Jenffer, and L. Limat, Wetting on heterogeneous surfaces: Experiments in an imperfect Hele-Shaw cell, Phys. Rev. E 51, 1291 (1995).
  21. A. Paterson and M. Fermigier, Wetting of heterogeneous surfaces: Influence of defect interactions, Phys. Fluids 9, 2210 (1997).
  22. A. Gaillard, J. S. Keeler, G. Le Lay, G. Lemoult, A. B. Thompson, A. L. Hazel, and A. Juel, The life and fate of a bubble in a geometrically perturbed Hele-Shaw channel, J. Fluid Mech. 914, A34 (2021).
  23. N. Shmakova, T. Chevalier, A. Puisto, M. Alava, C. Raufaste, and S. Santucci, Quasi-two-dimensional foam flow through and around a permeable obstacle, Phys. Rev. Fluids 5, 093301 (2020).
  24. H. Schütt and H. Spetzler, Capillary crack imbibition: A theoretical and experimental study using a Hele-Shaw cell, Pure Appl. Geophys. 158, 627 (2001).
  25. X. Clotet, R. Planet, and J. Ortín, Capillary rise in Hele-Shaw models of disordered media, J. Colloid Interface Sci. 377, 387 (2012).
  26. J. Soriano, J. J. Ramasco, M. A. Rodríguez, A. Hernández-Machado, and J. Ortín, Anomalous roughening of Hele-Shaw flows with quenched disorder, Phys. Rev. Lett. 89, 026102 (2002).
  27. J. Soriano, A. Mercier, R. Planet, A. Hernández-Machado, M. A. Rodríguez, and J. Ortín, Anomalous roughening of viscous fluid fronts in spontaneous imbibition, Phys. Rev. Lett. 95, 104501 (2005).
  28. X. Clotet, J. Ortín, and S. Santucci, Experimental study of stable imbibition displacements in a model open fracture. I. Local avalanche dynamics, Phys. Rev. E 93, 012149 (2016).
  29. R. Planet, J. M. López, S. Santucci, and J. Ortín, Spatiotemporal organization of correlated local activity within global avalanches in slowly driven interfaces, Phys. Rev. Lett. 121, 034101 (2018).
  30. X. Clotet, S. Santucci, and J. Ortín, Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics, Phys. Rev. E 93, 012150 (2016).
  31. R. Planet, L. Díaz-Piola, and J. Ortín, Capillary jumps of fluid-fluid fronts across an elementary constriction in a model open fracture, Phys. Rev. Fluids 5, 044002 (2020).
  32. R. Holtzman, M. Dentz, R. Planet, and J. Ortín, The origin of hysteresis and memory of two-phase flow in disordered media, Commun. Phys. 3, 222 (2020).
  33. E. Pauné and J. Casademunt, Kinetic roughening in two-phase fluid flows through a random Hele-Shaw cell, Phys. Rev. Lett. 90, 144504 (2003).
  34. E. Álvarez-Lacalle, J. Ortín, and J. Casademunt, Relevance of dynamic wetting in viscous fingering patterns, Phys. Rev. E 74, 025302(R) (2006).
  35. F. P. Bretherton, The motion of long bubbles in tubes, J. Fluid Mech. 10, 166 (1961).
  36. C. W. Park and G. M. Homsy, Two-phase displacement in Hele Shaw cells: Theory, J. Fluid Mech. 139, 291 (1984).
  37. D. Reinelt and P. Saffman, The penetration of a finger into a viscous fluid in a channel and tube, SIAM J. Sci. Stat. Comput. 6, 542 (1985).
  38. F. Hecht, New development in freefem++, J. Numer. Math. 20, 251 (2012).
  39. I. Lavi, Physical modeling of cell motility and morphodynamics, Ph.D. thesis, Sorbonne université, 2019.
  40. I. Lavi, N. Meunier, and O. Pantz, Implicit like time discretization for the one-phase hele-shaw problem with surface tension, arXiv:2305.06180.
  41. J. F. Joanny and P.-G. de Gennes, A model for contact angle hysteresis, J. Chem. Phys. 81, 552 (1984).
  42. M. Dubé, M. Rost, K. R. Elder, M. Alava, S. Majaniemi, and T. Ala-Nissila, Liquid conservation and non-local interface dynamics in imbibition, Phys. Rev. Lett. 83, 1628 (1999).

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Phys. Rev. Fluids 8, 124002– Published 20 December, 2023
  • Received 23 April 2023
  • Accepted 27 November 2023
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