Miscible displacements in Hele-Shaw cells: Two-dimensional base states and their linear stability

Journal of Fluid Mechanics

Volumn 558, Issue , 2006, Pages 329-355

  Goyal, N ^a   Meiburg, E ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY FLOW; COMPUTER SIMULATION; CONCENTRATION (PROCESS); EIGENVALUES AND EIGENFUNCTIONS; VISCOSITY; VISCOUS FLOW;

HELE-SHAW CELLS; LINEAR STABILITY; MISCIBLE DISPLACEMENTS; MISCIBLE FINGERING;

SOLUBILITY;

CAPILLARY FLOW; COMPUTER SIMULATION; CONCENTRATION (PROCESS); EIGENVALUES AND EIGENFUNCTIONS; SOLUBILITY; VISCOSITY; VISCOUS FLOW;

COMPUTER SIMULATION; STOKES FORMULA; VISCOSITY;

EID: 33745698876     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006009992     Document Type: Article

References (43)

1. Chen, C. & Meiburg, E. 1996 Miscible displacements in capillary tubes. Part 2. Numerical simulations. J. Fluid Mech. 326, 57-90.
2. Chen, C. & Meiburg, E. 1998 Miscible porous media displacements in the quarter five-spot configuration. Part 1. The homogeneous case. J. Fluid Mech. 371, 233-268.
3. Chouke, R., Meurs, P. & Poel, C. V. 1959 The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media. Trans. AIME 216, 188-194.
4. Cox, B. 1962 On driving a viscous fluid out of a tube. J. Fluid Mech. 14, 81-96.
5. Davis, T. 2003a Algorithm 8xx: umfpack v4.1, an unsymmetric-pattern multifrontal method with a column pre-ordering strategy. Tech. Rep. Department of Computer and Information Science and Engineering, University of Florida.
6. Davis, T. 2003b UMFPACK Version 4.1 User Guide. Department of Computer and Information Science and Engineering, University of Florida.
7. Davis, T. & Duff, I. 1997 An unsymmetric-pattern multifrontal method for sparse lu factorization. SIAM J. Matrix Anal. Applics. 18, 140-158.
8. Fernandez, J., Kurowski, P., Limat, L. & Petitjeans, P. 2001 Wavelength selection of fingering instability inside Hele-Shaw cells. Phys. Fluids 13, 3120-3125.
9. Fernandez, J., Kurowski, P., Petitjeans, P. & Meiburg, E. 2002 Density-driven, unstable flows of miscible fluids in a Hele-Shaw cell. J. Fluid Mech. 451, 239-260.
10. Fletcher, C. 1990 Computational Techniques for Fluid Dynamics, vol. 2. Springer.
11. Goyal, N. & Meiburg, E. 2004 Unstable density stratification of miscible fluids in a vertical Hele-Shaw cell: Influence of variable viscosity on the linear stability. J. Fluid Mech. 516, 211-238.
12. Graf, F. & Meiburg, E. 2002 Density-driven instabilities of miscible fluids in a Hele-Shaw cell: Linear stability analysis of the three-dimensional Stokes equations. J. Fluid Mech. 451, 261-282.
13. Hickernell, F. & Yortsos, Y. 1986 Linear stability of miscible displacement processes in porous media in the absence of dispersion. Stud. Appl. Maths 74, 93-115.
14. Hill, S. 1952 Channeling in packed columns. Chem. Engng. Sci. 1, 247.
15. Homsy, G. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271.
16. Lajeunesse, E., Martin, J., Rakotomalala, N. & Salin, D. 1997 3D instability of miscible displacement in a Hele-Shaw cell. Phys. Rev. Lett. 79, 5254-5257.
17. Lajeunesse, E., Martin, J., Rakotomalala, N., Salin, D. & Yortsos, Y. 1999 Miscible displacement in a Hele-Shaw cell at high rates. J. Fluid Mech. 398, 299-319.
18. Lehoucq, R., Sorenson, D. & Yang, C. 1998 ARPACK USERS GUIDE: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM Philadelphia.
19. Lele, S. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16-42.
20. Manickam, O. & Homsy, G. 1995 Fingering instabilities in vertical miscisble displacement flows in porous media. J. Fluid Mech. 288, 75-102.
21. Maxworthy, T. 1989 Experimental study of interface instability in a Hele-Shaw cell. Phys. Rev. A 39, 5863-5867.
22. Panton, R. L. 1984 Incompressible Flow, vol. 2. John Wiley.
23. Park, C., Gorell, S. & Homsy, G. 1984 Two-phase displacements in Hele-Shaw cells: Experiments on viscously driven instabilities. J. Fluid Mech. 141, 275-287.
24. Park, C. & Homsy, G. 1984 Two-phase displacements in Hele-Shaw cells: theory. J. Fluid Mech. 139, 291-308.
25. Paterson, L. 1985 Fingering with miscible fluids in a Hele-Shaw cell. Phys. Fluids 28, 26-30.
26. Petitjeans, P., Chen, C., Meiburg, E. & Maxworthy, T. 1999 Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion. Phys. Fluids 11, 1705-1716.
27. Petitjeans, P. & Maxworthy, T. 1996 Miscible displacements in capillary tubes. Part 1. Experiments. J. Fluid Mech. 326, 37-56.
28. Rakotomalala, N., Salin, D. & Watzky, P. 1997 Miscible displacement between two parallel plates: BGK lattice gas simulations. J. Fluid Mech. 338, 277-297.
29. Reinelt, D. & Saffman, P. 1985 The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Stat. Comput. 6, 542-561.
30. Ruith, M. & Meiburg, E. 2000 Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium. J. Fluid Mech. 420, 225-257.
31. Saffman, P. & Taylor, G. 1958 The penetration of a fluid into a porous medium or a Hele-Shaw cell containing a more viscous fluid. Proc. R. Soc. Lond. A 245, 312-329.
32. Schwartz, L. 1986 Stability of Hele-Shaw flows: The wetting layer effect. Phys. Fluids 29, 3086-3088.
33. Snyder, D. & Tait, S. 1998 A flow-front instability in viscous gravity currents. J. Fluid Mech. 369, 1-21.
34. Tan, C. & Homsy, G. 1986 Stability of miscible displacements in porous media: Rectilinear flow. Phys. Fluids 29, 3549-3556.
35. Tan, C. & Homsy, G. 1987 Stability of miscible displacements: Radial source flow. J. Fluid Mech. 30, 1239-1245.
36. Taylor, G. 1953 Dispersion of soluble matter in a solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186.
37. Taylor, G. 1961 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10, 161-165.
38. Vanaparthy, S., Meiburg, E. & Wilhelm, D. 2003 Density-driven instabilities of miscible fluids in a capillary tube: Linear stability analysis. J. Fluid Mech. 497, 99-121.
39. Wooding, R. 1969 Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell. J. Fluid Mech. 39, 477-495.
40. Wray, A. 1991 Minimal storage time advancement schemes for spectral methods. Preprint.
41. Yang, Z. & Yortsos, Y. 1997 Asymptotic solutions of miscible displacements in geometries of large aspect ratio. Phys. Fluids 9, 286-298.
42. Yortsos, Y. 1987 Stability of displacement processes in porous media in radial flow geometries. Phys. Fluids 30, 2928-2935.
43. Yortsos, Y. & Zeybek, M. 1988 Dispersion driven instability in miscible displacement in porous media. Phys. Fluids 31, 3511-3518.