Motion of a finger with bubbles in a Hele-Shaw cell: An exact solution

Physics of Fluids

Volumn 11, Issue 6, 1999, Pages 1281-1283

  Vasconcelos, Giovani L ^a  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003007023     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869992     Document Type: Article

References (13)

1. A comprehensive bibliography on Hele-Shaw flow is available at http:// www.maths.ox.ac.uk/∼howison/Hele-Shaw.
2. P. G. Saffman and G. I. Taylor, "The penetration of a fluid into a porous medium or Hele-Shaw cell containing a mora viscous liquid," Proc. R. Soc. London, Ser. A 245, 312 (1958).
3. For reviews, see, e.g., D. Kessler, J. Koplik, and H. Levine, "Pattern selection in fingered growth phenomena," Adv. Phys. 37, 255 (1988); P. Pelcé, Dynamics of Curved Fronts (Academic, New York, 1988); S. Tanveer, in Arymptotics beyond All Orders, edited by H. Segur, S. Tanveer, and H. Levine (Plenum, New York, 1991), pp. 131-153.
4. For reviews, see, e.g., D. Kessler, J. Koplik, and H. Levine, "Pattern selection in fingered growth phenomena," Adv. Phys. 37, 255 (1988); P. Pelcé, Dynamics of Curved Fronts (Academic, New York, 1988); S. Tanveer, in Arymptotics beyond All Orders, edited by H. Segur, S. Tanveer, and H. Levine (Plenum, New York, 1991), pp. 131-153.
5. For reviews, see, e.g., D. Kessler, J. Koplik, and H. Levine, "Pattern selection in fingered growth phenomena," Adv. Phys. 37, 255 (1988); P. Pelcé, Dynamics of Curved Fronts (Academic, New York, 1988); S. Tanveer, in Arymptotics beyond All Orders, edited by H. Segur, S. Tanveer, and H. Levine (Plenum, New York, 1991), pp. 131-153.
6. M. B. Mineev-Weinstein, "Selection of the Saffman-Taylor finger width in the absence of surface tension: an exact result," Phys. Rev. Lett. 80, 2113 (1998).
7. F. X. Magdaleno and J. Casademunt, "Surface tension and dynamics of fingering patterns," Phys. Rev. E 57, R3707 (1998).
8. Y. Couder, N. Gérard, and M. Rabaud, "Narrow fingers in the Saffman-Taylor instability," Phys. Rev. A 34, 5175 (1986); M. Rabaud, Y. Couder, and N. Gérard, "Dynamics and stability of anomalous Saffman-Taylor fingers," ibid. 37, 935 (1988).
9. Y. Couder, N. Gérard, and M. Rabaud, "Narrow fingers in the Saffman-Taylor instability," Phys. Rev. A 34, 5175 (1986); M. Rabaud, Y. Couder, and N. Gérard, "Dynamics and stability of anomalous Saffman-Taylor fingers," ibid. 37, 935 (1988).
10. D. C. Hong and J. S. Langer, "Pattern selection and tip perturbations in the Saffman-Taylor problem," Phys. Rev. A 36, 2325 (1987).
11. F. R. Tian and G. L. Vasconcelos, "Rotation invariance for steady Hele-Shaw flows," Phys. Fliuds A 5, 1863 (1993).
12. G. L. Vasconcelos, "Multiple bubbles in a Hele-Shaw cell," Phys. Rev. E 50, R3306 (1994).
13. G. F. Carrier, M. Krook, and C. Pearson, Functions of a Complex Variable (Hod Books, Ithaca, 1983).