Abstract
In this paper we undertake a numerical investigation of the dynamics of the interface in the problem of immiscible radial viscous fingering in a Hele-Shaw cell when the areal flow rate is maintained constant. Comparison is made with experimental results to check if there is a need to introduce velocity-dependent boundary conditions and to incorporate the effect of thickness of the film left behind by the moving interface. Some new scaling results are suggested by the numerical data. These data, along with those available from laboratory experiments, provide support for a mean field theory for radial immiscible viscous fingering published recently [Phys. Rev. Lett. 65, 2680 (1990)].
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References
J S Langer,Rev. Mod. Phys. 52, 1 (1980)
P Pelcé:Dynamics of curved fronts (Perspectives in Physics series), edited by H Araki, A Libchaber and G Parisi (Academic Press, New York, 1988)
D Bensimon, L P Kadanoff, S Liang, B I Shraiman, and C Tang,Rev. Mod. Phys. 58, 977 (1986)
D A Kessler, J Koplik and H Levine,Adv. Phys. 37, 255 (1988)
J Bataille,Rev. Inst. Pétrole 23, 1349 (1968)
L Paterson,J. Fluid Mech. 113, 513 (1981)
S N Rauseo, P D Barnes, and J V Maher,Phys. Rev. A35, 1245 (1987)
S E May and J V Maher,Phys. Rev. A40, 1723 (1989)
C W Park and G M Homsy,J. Fluid Mech. 139, 291 (1984)
S C Huang and M E Glicksman,Acta Metall. 29, 701, 717 (1981)
K Somboonsuk, J T Mason and R Trivedi,Metall. Trans. A15, 967 (1984)
R Trivedi,Metall. Trans. A15, 977 (1984)
S de Cheveigné, C Guthmann, and M M Lebrun,J. Phys. (Paris) 47, 2095 (1986)
P G Saffman and G I Taylor,Proc. R. Soc. London, Ser. A245, 312 (1958)
P Tabeling and A Libchaber,Phys. Rev. A33, 794 (1986)
P Tabeling, G Zocchi, and A Libchaber,J. Fluid Mech. 177, 67 (1987)
S K Sarkar and D Jasnow,Phys. Rev. A35, 4900 (1987) and references therein.
H Thomé, M Rabaud, V Hakim and Y Couder,Phys. Fluids A1, 224 (1989)
M Ben-Amar,Phys. Rev. A43, 5724 (1991)
S K SarkarPhys. Rev. Lett. 65, 2680 (1990)
T A Witten and L M Sander,Phys. Rev. Lett. 47, 1400 (1981)
L Paterson,Phys. Fluids 28, 26 (1985)
G Daccord, J Nittmann and H E Stanley,Phys. Rev. Lett. 56, 336 (1986)
D Jasnow and C Yeung,Phys. Rev. E47 1087 (1993)
S K Sarkar,Superlattices and microstructures 3, 589 (1987)
S K Sarkar and D Jasnow,Phys. Rev. A39, 5299 (1989)
L M Sander, P Ramanlal and E Ben-Jacob,Phys. Rev. A32, 3160 (1985)
K J Måløy, F Boger, J Feder and T Jøssang, inTime dependent effects in disordered materials, edited by R Pynn and T Riste (Plenum, New York, 1987)
T H Tong and J A O’Brien,Phys. Rev. A41, 4430 (1990)
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Sarkar, S.K., Jasnow, D. Dynamics of immiscible radial viscous fingering: A numerical study. Pramana - J. Phys. 41, 389–399 (1993). https://doi.org/10.1007/BF02847402
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DOI: https://doi.org/10.1007/BF02847402