The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell

European Journal of Mechanics, B/Fluids

Volumn 28, Issue 4, 2009, Pages 564-577

  Pritchard, David ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Instability; Viscous fingering

Indexed keywords

A THERMALS; HELE-SHAW CELLS; INSTABILITY; LINEAR STABILITIES; MISCIBLE DISPLACEMENTS; PARAMETER SPACES; POROUS MEDIUMS; TWO REGIMES; VISCOSITY CONTRASTS; VISCOUS FINGERING; VISCOUS INSTABILITIES; WAVE-NUMBERS;

CHANNEL FLOW; DISSOLUTION; FLOW PATTERNS; POROUS MATERIALS;

STABILITY;

EID: 67349151772     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2009.01.004     Document Type: Article

References (23)

1. Homsy G.M. Viscous fingering in porous media. Annual Review of Fluid Mechanics 19 (1987) 271-311
2. Saffman P.G., and Taylor G.I. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proceedings of the Royal Society A 245 1242 (1958) 312-329
3. Dake L.P. Fundamentals of Reservoir Engineering. Developments in Petroleum Science vol. 8 (1978), Elsevier
4. Needham R.B., and Doe P.H. Polymer flooding review. Journal of Petroleum Technology (1987) 1503-1507 SPE paper 17140
5. CRC Handbook of Chemistry and Physics. 82nd ed. (2001), CRC Press
6. Stefánsson V. Geothermal reinjection experience. Geothermics 26 (1997) 99-139
7. Turner J.S. Multicomponent convection. Annual Review of Fluid Mechanics 17 (1985) 11-44
8. De Wit A. Fingering of chemical fronts in porous media. Physical Review Letters 87 5 (2001) 054502
9. D'Hernoncourt J., Merkin J.H., and De Wit A. Front fingering and complex dynamics driven by the interaction of buoyancy and diffusive instabilities. Physical Review E 76 (2007) 035301R
10. Pritchard D. The instability of thermal and fluid fronts during radial injection in a porous medium. Journal of Fluid Mechanics 508 (2004) 133-163
11. Phillips O.M. Flow and Reactions in Permeable Rocks (1991), Cambridge University Press
12. Lajeunesse E., Martin J., Rakotomalala N., Salin D., and Yortsos Y.C. Miscible displacement in a Hele-Shaw cell at high rates. Journal of Fluid Mechanics 398 (1999) 299-319
13. Schafroth D., Goyal N., and Meiburg E. Miscible displacements in Hele-Shaw cells: nonmonotonic viscosity profiles. European Journal of Mechanics B 26 (2007) 444-453
14. Tan C.T., and Homsy G.M. Stability of miscible displacements in porous media: radial source flow. Physics of Fluids 30 5 (1987) 1239-1245
15. Tan C.T., and Homsy G.M. Stability of miscible displacements in porous media: rectilinear flow. Physics of Fluids 29 11 (1986) 3549-3556
16. Ben Y., Demekhin E.A., and Chang H.-C. A spectral theory for small-amplitude miscible fingering. Physics of Fluids 14 3 (2002) 999-1010
17. Hickernell F.J., and Yortsos Y.C. Linear stability of miscible displacement processes in porous media in the absence of dispersion. Studies in Applied Mathematics 74 (1986) 93-115
18. Manickam O., and Homsy G.M. Stability of miscible displacements in porous media with nonmonotonic viscosity profiles. Physics of Fluids A 5 6 (1993) 1356-1367
19. Barenblatt G., and Scaling. Self-Similarity and Intermediate Asymptotics (1996), Cambridge University Press
20. Tan K.K., and Thorpe R.B. The onset of convection driven by buoyancy effects caused by various modes of transient heat conduction: Part I. Transient Rayleigh numbers. Chemical Engineering Science 54 (1999) 225-238
21. Riaz A., Hesse M., Tchelepi H.A., and Orr F.M. Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. Journal of Fluid Mechanics 548 (2006) 87-111
22. Loggia D., Salin D., and Yortsos Y.C. The effect of dispersion on the stability of non-monotonic mobility profiles in porous media. Physics of Fluids 10 3 (1998) 747-749
23. Cardoso S.S.S., and Woods A.W. The formation of drops through viscous instability. Journal of Fluid Mechanics 289 (1995) 351-378