Abstract
Direct numerical simulations are presented for a porous media model consisting of two immiscible fluids, an invading and defending phase, in a two-dimensional micro-geometry filled with randomly sized and randomly distributed cylinders. First, interface instability and penetration modes are studied when varying the wetting features of a single pore in the porous medium. It is found that the displacement patterns not only change with the capillary number, as previously observed, but also are a function of the contact angle, even for a viscosity ratio of unity. This is an important conclusion suggesting that capillary number and viscosity ratio alone cannot completely describe the pore-scale displacement. Second, rapid pore-scale displacement is considered, where the displacements are accompanied by sudden interface jumps from one site to another, known as Haines jumps. The characteristic time and length scales of a Haines jump are examined to better understand the transient dynamics of the jump. We then focus on analyzing the Haines jump in a simple pore configuration where cylinders of equal size are placed at the vertices of equilateral triangles. We use this geometry to provide more insight into the effect of the contact angle at which the Haines jump is predicted.
Similar content being viewed by others
References
A. Perazzo, G. Tomaiuolo, V. Preziosi, S. Guido, Adv. Colloid Interface Sci. 256, 305 (2018)
R. Lenormand, J. Phys.: Condens. Matter 2, SA79 (1990)
M.J. Blunt, H. Scher, Phys. Rev. E 52, 6387 (1995)
K. Singh, B. Bijeljic, M.J. Blunt, Water Resour. Res. 52, 1716 (2016)
K. Singh, M. Jung, M. Brinkmann, R. Seemann, Annu. Rev. Fluid Mech. 51, 429 (2019)
A. Anbari, H.T. Chien, S.S. Datta, W. Deng, D.A. Weitz, J. Fan, Small 14, 1703575 (2018)
I. Zacharoudiou, E.S. Boek, J. Crawshaw, Sci. Rep. 8, 1 (2018)
B. Zhao, C.W. MacMinn, R. Juanes, Proc. Natl. Acad. Sci. 113, 10251 (2016)
B.K. Primkulov, A.A. Pahlavan, X. Fu, B. Zhao, C.W. MacMinn, R. Juanes, J. Fluid Mech. 875, R4 (2019)
M. Cieplak, M.O. Robbins, Phys. Rev. Lett. 60, 2042 (1988)
M. Cieplak, M.O. Robbins, Phys. Rev. B 41, 11508 (1990)
R. Holtzman, E. Segre, Phys. Rev. Lett. 115, 164501 (2015)
M. Jung, M. Brinkmann, R. Seemann, T. Hiller, M. Sanchez de La Lama, S. Herminghaus, Phys. Rev. Fluids 1, 074202 (2016)
B. Zhao, C.W. MacMinn, B.K. Primkulov, Y. Chen, A.J. Valocchi, J. Zhao, Q. Kang, K. Bruning, J.E. McClure, C.T. Miller et al., Proc. Natl. Acad. Sci. 116, 13799 (2019)
F. Basirat, Z. Yang, A. Niemi, Adv. Water Resour. 109, 181 (2017)
H. Liu, A.J. Valocchi, C. Werth, Q. Kang, M. Oostrom, Adv. Water Resour. 73, 144 (2014)
M. Bussmann, J. Mostaghimi, S. Chandra, Phys. Fluids 11, 1406 (1999)
S. Afkhami, S. Zaleski, M. Bussmann, J. Comput. Phys. 228, 5370 (2009)
Y. Sui, H. Ding, P.D.M. Spelt, Annu. Rev. Fluid Mech. 46, 97 (2014)
C.S. Peskin, J. Comput. Phys. 10, 252 (1972)
R. Mittal, G. Iaccarino, Annu. Rev. Fluid Mech. 37, 239 (2005)
A. O’Brien, M. Bussmann, J. Comput. Phys. 402, 109089 (2020)
A. O’Brien, M. Bussmann, Comput. Fluids 165, 43 (2018)
R. Hilfer, P.E. Øren, Transport Porous Med. 22, 53 (1996)
J.O. Helland, S.M. Skjæveland, Water Resour. Res. 43, W12S10 (2007)
W.B. Haines, J. Agric. Sci. 20, 97 (1930)
O. Ubbink, R. Issa, J. Comput. Phys. 153, 26 (1999)
J.U. Brackbill, D.B. Kothe, C. Zemach, J. Comput. Phys. 100, 335 (1992)
A.J. Chorin, Bull. Am. Math. Soc. 73, 928 (1967)
M.M. Francois, S.J. Cummins, E.D. Dendy, D.B. Kothe, J.M. Sicilian, M.W. Williams, J. Comput. Phys. 213, 141 (2006)
S. Afkhami, J. Buongiorno, A. Guion, S. Popinet, Y. Saade, R. Scardovelli, S. Zaleski, J. Comput. Phys. 374, 1061 (2018)
K. Singh, H. Scholl, M. Brinkmann, M.D. Michiel, M. Scheel, S. Herminghaus, R. Seemann, Sci. Rep. 7, 1 (2017)
R.T. Armstrong, N. Evseev, D. Koroteev, S. Berg, Adv. Water Resour. 77, 57 (2015)
C. Zhang, M. Oostrom, T.W. Wietsma, J.W. Grate, M.G. Warner, Energy Fuels 25, 3493 (2011)
A. Ferrari, I. Lunati, Adv. Water Resour. 57, 19 (2013)
S. Mei, J.L. Bryan, A. Kantzas, inSPE Heavy Oil Conference Canada, 2012, pp. 1–11
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
O’Brien, A., Afkhami, S. & Bussmann, M. Pore-scale direct numerical simulation of Haines jumps in a porous media model. Eur. Phys. J. Spec. Top. 229, 1785–1798 (2020). https://doi.org/10.1140/epjst/e2020-000008-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2020-000008-0