Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension

Applied Mathematics Letters

Volumn 11, Issue 6, 1998, Pages 57-62

  Aldushin, A P ^a   Matkowsky, B J ^b  

^a INSTITUTE OF STRUCTURAL MACROKINETICS AND MATERIALS SCIENCE   (Russian Federation)

^b NORTHWESTERN UNIVERSITY   (United States)

Author keywords

Bubble interface; Finger; Front; Saffman Taylor

Indexed keywords

EID: 0038513212     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(98)00103-7     Document Type: Article

References (12)

1. P.G. Saffman and G.I. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. Roy. Soc. A 245, 312-329, (1958).
2. J.W. MacLean and P.G. Saffman, The effect of surface tension on the shape of fingers in a Hele-Shaw cell, J. Fluid. Mech. 102, 455-469, (1981).
3. J.M. Vandenbroeck, Fingers in a Hele-Shaw cell with surface tension, Phys. Fluids 26, 2033-2044, (1983).
4. A.J. DeGregoria and L.W. Schwartz, A boundary integral method for two-phase displacement in Hele-Shaw cells, J. Fluid Mech. 164, 383-400, (1986).
5. A.P. Aldushin and B.J. Matkowsky, Instabilities, fingering and the Saffman-Taylor problem in filtration combustion, (submitted).
6. B.I. Shraiman, Velocity selection and the Saffman-Taylor problem, Phys. Rev. Lett. 56, 2028-2031, (1986).
7. D.C. Hong and J.S. Langer, Analytic theory of the selection mechanism in the Saffman-Taylor problem, Phys. Rev. Lett. 56, 2032-2035, (1986).
8. R. Combescot, T. Dombre, V. Hakim and Y. Pomeau, Shape selection of Saffman-Taylor fingers, Phys. Rev. Lett. 56, 2036-2039, (1986).
9. S. Tanveer, Analytic theory for the selection of a symmetric Saffman-Taylor finger in a Hele-Shaw cell, Phys. Fluids 30, 1589-1605, (1987).
10. A.N. Kolmogorov, I.G. Petrovsky and N.S. Piskunov, Study of the diffusion equation with growth of quantity of matter and its application to a biology problem, Bull. de l'Universite d'Etat Moscou, Ser. Int'l., Sect A 1, 1-25, (1937).
11. G.I. Taylor and P.G. Saffman, A note on the motion of bubbles in a Hele-Shaw cell and porous medium, Quart. J. Mech. Appl. Math. 12, 265-279, (1959).
12. M. Mineev-Weinstein, Selection of the Saffman Taylor finger width in the absence of surface tension: An exact result, (preprint).