Skip to main content Accessibility help
×
Home

Wetting front dynamics in an isotropic porous medium

  • Yulii D. Shikhmurzaev (a1) and James E. Sprittles (a1)

Abstract

A new approach to the modelling of wetting fronts in porous media on the Darcy scale is developed, based on considering the types (modes) of motion the menisci go through on the pore scale. This approach is illustrated using a simple model case of imbibition of a viscous incompressible liquid into an isotropic porous matrix with two modes of motion for the menisci, the wetting mode and the threshold mode. The latter makes it necessary to introduce an essentially new technique of conjugate problems that allows one to link threshold phenomena on the pore scale with the motion on the Darcy scale. The developed approach (a) makes room for incorporating the actual physics of wetting on the pore scale, (b) brings in the physics associated with pore-scale thresholds, which determine when sections of the wetting front will be brought to a halt (pinned), and, importantly, (c) provides a regular framework for constructing models of increasing complexity.

Copyright

Corresponding author

Email address for correspondence: yulii@for.mat.bham.ac.uk

References

Hide All
1. Adler, P. M. & Brenner, H. 1988 Multiphase flow in porous media. Annu. Rev. Fluid Mech. 20, 3559.
2. Aker, E. & Måløy, K. J. 2000 Dynamics of stable viscous displacement in porous media. Phys. Rev. E 61, 29362946.
3. Alava, M., Dubé, M. & Rost, M. 2004 Imbibition in disordered media. Adv. Phys. 53, 83175.
4. Blake, T. D., Bracke, M. & Shikhmurzaev, Y. D. 1999 Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle. Phys. Fluids 11, 19952007.
5. Blake, T. D. & Shikhmurzaev, Y. D. 2002 Dynamic wetting by liquids of different viscosity. J. Colloid Interface Sci. 253, 196202.
6. Clarke, A. & Stattersfield, E. 2006 Direct evidence supporting nonlocal hydrodynamic influence on the dynamic contact angle. Phys. Fluids 18, 048109.
7. Deinert, M. R., Dathe, A., Parlange, J.-Y. & Cady, K. B. 2008 Capillary pressure in a porous medium with distinct pore surface and pore volume fractal dimensions. Phys. Rev. E 77, 021203.
8. Delker, T., Pengra, D. B. & Wong, P.-z. 1996 Interface pinning and the dynamics of capillary rise in porous media. Phys. Rev. Lett. 76, 29022905.
9. DussanE. B., V E. B., V 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371.
10. DussanE. B., V E. B., V & Davis, S. H. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 71.
11. Hassanizadeh, S. M. & Gray, W. G. 1993 Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29, 33893405.
12. Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85101.
13. Joekar-Niasar, V., Hassanizadeh, S. M. & Dahle, H. K. 2010 Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling. J. Fluid Mech. 655, 3871.
14. Lago, M. & Araujo, M. 2001 Capillary rise in porous media. J. Colloid Interface Sci. 234, 3543.
15. Lenormand, R., Touboul, E. & Zarcone, C. 1988 Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165187.
16. Leverett, M. C. 1941 Capillary behaviour in porous solids. Trans. AIME 142, 152169.
17. Mitkov, I., Tartakovsky, D. M. & Winter, C. L. 1998 Dynamics of wetting fronts in porous media. Phys. Rev. E 58, R5245R5248.
18. Olbricht, W. L. 1996 Pore-scale prototypes of multiphase flow in porous media. Annu. Rev. Fluid Mech. 28, 187213.
19. Richards, L. A. 1931 Capillary conductivity of liquids through porous mediums. Physics 1, 318333.
20. Shikhmurzaev, Y. D. 2007 Capillary Flows with Forming Interfaces. Chapman & Hall/CRC.
21. Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273283.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Wetting front dynamics in an isotropic porous medium

  • Yulii D. Shikhmurzaev (a1) and James E. Sprittles (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed