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Wetting front dynamics in an isotropic porous medium

Published online by Cambridge University Press:  02 February 2012

Yulii D. Shikhmurzaev*
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
James E. Sprittles
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
*
Email address for correspondence: yulii@for.mat.bham.ac.uk

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.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

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References

1. Adler, P. M. & Brenner, H. 1988 Multiphase flow in porous media. Annu. Rev. Fluid Mech. 20, 3559.CrossRefGoogle Scholar
2. Aker, E. & Måløy, K. J. 2000 Dynamics of stable viscous displacement in porous media. Phys. Rev. E 61, 29362946.CrossRefGoogle Scholar
3. Alava, M., Dubé, M. & Rost, M. 2004 Imbibition in disordered media. Adv. Phys. 53, 83175.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
5. Blake, T. D. & Shikhmurzaev, Y. D. 2002 Dynamic wetting by liquids of different viscosity. J. Colloid Interface Sci. 253, 196202.CrossRefGoogle ScholarPubMed
6. Clarke, A. & Stattersfield, E. 2006 Direct evidence supporting nonlocal hydrodynamic influence on the dynamic contact angle. Phys. Fluids 18, 048109.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
11. Hassanizadeh, S. M. & Gray, W. G. 1993 Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29, 33893405.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
14. Lago, M. & Araujo, M. 2001 Capillary rise in porous media. J. Colloid Interface Sci. 234, 3543.CrossRefGoogle ScholarPubMed
15. Lenormand, R., Touboul, E. & Zarcone, C. 1988 Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165187.CrossRefGoogle Scholar
16. Leverett, M. C. 1941 Capillary behaviour in porous solids. Trans. AIME 142, 152169.CrossRefGoogle Scholar
17. Mitkov, I., Tartakovsky, D. M. & Winter, C. L. 1998 Dynamics of wetting fronts in porous media. Phys. Rev. E 58, R5245R5248.CrossRefGoogle Scholar
18. Olbricht, W. L. 1996 Pore-scale prototypes of multiphase flow in porous media. Annu. Rev. Fluid Mech. 28, 187213.CrossRefGoogle Scholar
19. Richards, L. A. 1931 Capillary conductivity of liquids through porous mediums. Physics 1, 318333.CrossRefGoogle Scholar
20. Shikhmurzaev, Y. D. 2007 Capillary Flows with Forming Interfaces. Chapman & Hall/CRC.CrossRefGoogle Scholar
21. Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273283.CrossRefGoogle Scholar
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