Fingering versus stability in the limit of zero interfacial tension

Nature Communications

Volumn 5, Issue , 2014, Pages

  Bischofberger, Irmgard ^a   Ramachandran, Radha ^a   Nagel, Sidney R ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISPLACEMENT; TENSION; VISCOSITY; WAVELENGTH;

ARTICLE; DIFFUSION; GROWTH; LIQUID; TENSION; VISCOSITY;

EID: 84923365516     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms6265     Document Type: Article

References (34)

1. Saffman, P. & Taylor, G. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312-329 (1958).
2. Hill, S. Channeling in packed columns. Chem. Eng. Sci. 1, 247-253 (1952).
3. Orr, F. & Taber, J. Use of carbon dioxide in enhanced oil recovery. Science 224, 563-569 (1984).
4. Cinar, Y., Riaz, A. & Tchelepi, H. A. Experimental study of CO2 injection into saline formations. Soc. Petrol. Eng. J. 14, 588-594 (2009).
5. Gorell, S. B. & Homsy, G. A theory of the optimal policy of oil recovery by secondary displacement processes. SIAM J. Appl. Math. 43, 79-98 (1983).
6. Homsy, G. Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271-311 (1987).
7. Pihler-Puzovic, D., Illien, P., Heil, M. & Juel, A. Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes. Phys. Rev. Lett. 108, 074502 (2012).
8. Lindner, A., Bonn, D. & Meunier, J. Viscous fingering in complex fluids. J. Phys. Condens. Matter 12, A477 (2000).
9. Dias, E. O. & Miranda, J. A. Taper-induced control of viscous fingering in variable-gap Hele-Shaw flows. Phys. Rev. E 87, 053015 (2013).
10. Al-Housseiny, T. T., Tsai, P. A. & Stone, H. A. Control of interfacial instabilities using flow geometry. Nat. Phys. 8, 747-750 (2012).
11. Paterson, L. Radial fingering in a Hele Shaw cell. J. Fluid Mech. 113, 513-529 (1981).
12. Bensimon, D., Kadanoff, L., Liang, S., Shraiman, B. & Tang, C. Viscous flows in two dimensions. Rev. Mod. Phys. 58, 977-999 (1986).
13. Chen, J.-D. Growth of radial viscous fingers in a Hele-Shaw cell. J. Fluid Mech. 201, 223-242 (1989).
14. Setu, S. A. et al. Viscous fingering at ultralow interfacial tension. Soft Matter 9, 10599-10605 (2013).
15. Sander, L. M., Ramanlal, P. & Ben-Jacob, E. Diffusion-limited aggregation as a deterministic growth process. Phys. Rev. A 32, 3160-3163 (1985).
16. Witten, T. A. & Sander, L. M. Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400-1403 (1981).
17. Paterson, L. Diffusion-limited aggregation and two-fluid displacements in porous media. Phys. Rev. Lett. 52, 1621-1624 (1984).
18. Bettelheim, E., Agam, O., Zabrodin, A. & Wiegmann, P. Singularities of the Hele-Shaw flow and shock waves in dispersive media. Phys. Rev. Lett. 95, 244504 (2005).
19. Lajeunesse, E., Martin, J., Rakotomalala, N. & Salin, D. 3D instability of miscible displacements in a Hele-Shaw cell. Phys. Rev. Lett. 79, 5254-5257 (1997).
20. Lajeunesse, E., Martin, J., Rakotomalala, N., Salin, D. & Yortsos, Y. Miscible displacement in a Hele-Shaw cell at high rates. J. Fluid Mech. 398, 299-319 (1999).
21. Yang, Z. & Yortsos, Y. Asymptotic solutions of miscible displacements in geometries of large aspect ratio. Phys. Fluids 9, 286-298 (1997).
22. D'Errico, G., Ortona, O., Capuano, F. & Vitagliano, V. Diffusion coefficients for the binary system glycerolwater at 25AC. a velocity correlation study. J. Chem. Eng. Data 49, 1665-1670 (2004).
23. Paterson, L. Fingering with miscible fluids in a Hele Shaw cell. Phys. Fluids 28, 26-30 (1985).
24. Goyal, N. & Meiburg, E. Miscible displacements in Hele-Shaw cells: two dimensional base states and their linear stability. J. Fluid Mech. 558, 329-355 (2006).
25. Nagel, M. & Gallaire, F. A new prediction of wavelength selection in radial viscous fingering involving normal and tangential stresses. Phys. Fluids 25, 124107 (2013).
26. Sadhu, T. & Dhar, D. Modelling proportionate growth. Curr. Sci. 103, 512-517 (2012).
27. Dhar, D. & Sadhu, T. A sandpile model for proportionate growth. J. Stat. Mech. 2013, P11006 (2013).
28. Nittmann, J., Daccord, G. & Stanley, H. Fractal growth of viscous fingers: quantitative characterization of a fluid instability phenomenon. Nature 314, 141-144 (1985).
29. Daccord, G., Nittmann, J. & Stanley, H. Radial viscous fingers and diffusionlimited aggregation: fractal dimension and growth sites. Phys. Rev. Lett. 56, 336-339 (1986).
30. Mathiesen, J., Procaccia, I., Swinney, H. & Thrasher, M. The universality class of diffusion limited aggregation and viscous fingering. Europhys. Lett. 76, 257-263 (2006).
31. Praud, O. & Swinney, H. Fractal dimension and unscreened angles measured for radial viscous fingering. Phys. Rev. E 72, 011406 (2005).
32. Cheng, X., Xu, L., Patterson, A., Jaeger, H. M. & Nagel, S. R. Towards the zerosurface-tension limit in granular fingering instability. Nat. Phys. 4, 234-237 (2008).
33. Lide, D. Handbook of Chemistry and Physics (CRC Press, 1996).
34. Batchelor, G. K. An Introduction to Fluid Dynamics (Cambridge university press, 2000).