Radial fingering in a Hele-Shaw cell: A weakly nonlinear analysis

Physica D: Nonlinear Phenomena

Volumn 120, Issue 3-4, 1998, Pages 315-328

  Miranda, José A ^a,b   Widom, Michael ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

Hydrodynamic instability; Interfacial dynamics; Pattern formation; Weakly nonlinear analysis

Indexed keywords

FLOW PATTERNS; FLUID DYNAMICS; HARMONIC ANALYSIS; HYDRODYNAMICS; INTERFACIAL ENERGY; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; PHASE DIAGRAMS;

HELE-SHAW CELL; INTERFACIAL DYNAMICS; LINEAR STABILITY THEORY; PATTERN FORMATION; RADIAL FINGERING; SAFFMAN-TAYLOR VISCOUS FINGERING INSTABILITY; SUB HARMONIC PERTURBATIONS;

VISCOUS FLOW;

EID: 0032163003     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00097-9     Document Type: Article

References (40)

1. D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, C. Tang, Rev. Mod. Phys. 58 (1986) 977;
2. S. Tanveer, in: H. Segur, S. Tanveer, H. Levine (Eds.), Asymptotics Beyond All Orders, NATO ASI series B, vol. 284 Plenum, New York, 1991, pp. 131;
3. K.V. McCloud, J.V. Maher, Phys. Rep. 260 (1995) 139.
4. E. Ben-Jacob, Nature 343 (1990) 523.
5. P.G. Saffman, G.I. Taylor, Proc. Roy. Soc. London Ser. A 245 (1958) 312.
6. L. Paterson, J. Fluid Mech. 113 (1981) 513.
7. M. Siegel, S. Tanveer, W.-S. Dai, J. Fluid Mech. 323 (1996) 201;
8. S. Tanveer, Phil. Trans. Roy. Soc. Lond. Ser. A 343 (1993) 155.
9. T.Y. Hou, J.S. Lowengrub, M.J. Shelley, J. Comp. Phys. 114 (1994) 312;
10. W.-S. Dai, M.J. Shelley, Phys. Fluids A 5 (1993) 2131.
11. L.N. Brush, R.F. Sekerka, J. Crystal Growth 96 (1989) 419.
12. L.N. Brush, R.F. Sekerka, G.B. McFadden, J. Crystal Growth 100 (1990) 89.
13. P.P. Debroy, R.F. Sekerka, Phys. Rev. E 53 (1996) 6244.
14. J.A. Miranda, M. Widom, Int. J. Mod. Phys. B 12 (1998) 931.
15. J.-D. Chen, J. Fluid Mech. 201 (1989) 223;
16. J.-D. Chen, Exp. Fluids 5 (1987) 363.
17. H. Thomé, M. Rabaud, V. Hakim, Y. Couder, Phys. Fluids A 1 (1989) 224.
18. J. Bataille, Revue Inst. Pétrole 23 (1968) 1349.
19. G. Homsy, Ann. Rev. Fluid Mech. 19 (1987) 271.
20. S.D.R. Wilson, J. Colloid Interface Sci. 51 (1975) 532.
21. J.E. Sader, D.Y.C. Chan, B.D. Hughes, Phys. Rev. E 49 (1994) 420.
22. Ll. Carrillo, F.X. Magdaleno, J. Casademunt, J. Ortín, Phys. Rev. E 54 (1996) 6260.
23. S.S.S. Cardoso, A.W. Woods, J. Fluid Mech. 289 (1995) 351.
24. B.A. Dubrovin, A.T. Fomenko, S.P. Novikov, Modern Geometry-Methods and Applications, Part 1, Springer, Berlin, 1984.
25. J.W. McLean, P.G. Saffman, J. Fluid Mech. 102 (1981) 455;
26. P.G. Saffman, in: R. Burridge, S. Childress, G. Papanicolaou (Eds.), Macroscopic Properties of Disordered Media, Lecture Notes in Physics, vol. 154 Springer, Berlin, 1982, pp. 208.
27. For a discussion on the influence of wall wetting effects on the curvature in the direction perpendicular to the plates, see C.-W. Park, G.M. Homsy, J. Fluid Mech. 139 (1984) 291;
28. D.A. Reinelt, J. Fluid Mech. 183 (1987) 219.
29. R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985.
30. M.J.P. Gingras, Z. Rácz, Phys. Rev. A 40 (1989) 5960.
31. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1994.
32. L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory (Pergamon Press, New York, 1977).
33. S. Tanveer, Phys. Fluids 30 (1987) 1589.
34. R. Combescot, T. Dombre, Phys. Rev. A 38 (1988) 2573.
35. E. Brener, H. Müller-Krumbhaar, Y. Saito, D. Temkin, Phys. Rev. E 47 (1993) 1151;
36. T. Ihle, H. Müller-Krumbhaa, Phys. Rev. E 49 (1994) 2972.
37. R. Kupferman, D.A. Kessler, E. Ben-Jacob, Physica A 213 (1995) 451.
38. M.B. Amar, E. Brener, Physica D 98 (1996) 128.
39. D.P. Jackson, R.E. Goldstein, A.O. Cebers, Phys. Rev. E 50 (1994) 298 and references therein.
40. H.A. Stone, H.M. McConnell, Proc. R. Soc. London Ser. A 448 (1995) 97 and references therein.