Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A note on the stability of an immiscible liquid layer in a porous medium

Author: R. Raghavan
Journal: Quart. Appl. Math. 31 (1974), 481-487
DOI: https://doi.org/10.1090/qam/99692
MathSciNet review: QAM99692
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Abstract | References | Additional Information

Abstract: The Saffman--Taylor instability of a liquid layer is studied by the standard first-order perturbation method. The viscosity and density of the layer and the bounding fluids are assumed to be constant. Interfacial tension is taken into account. An expression for the rate of growth of perturbations at the interface is determined. Results obtained by previous analyses are shown to be particular cases of this solution. The reduction in the rate of growth of the perturbations due to the presence of the liquid layer is demonstrated.

References [Enhancements On Off] (What's this?)

  • [1] R. L. Chuoke, P. van Muers and C. van der Poel, The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media, Trans. AIME 216 (1959), 188
  • [2] H. D. Outmans, Nonlinear theory for frontal stability and viscous fingering in porous media, Soc. Petr. Engr. J. 8 (1962), 165
  • [3] R. Raghavan and S. S. Marsden, The stability of immiscible liquid layers in a porous medium, J. Fluid Mech. 48 (1971) 143
  • [4] 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. London A 245 (1958), 312 MR 0097227

Additional Information

DOI: https://doi.org/10.1090/qam/99692
Article copyright: © Copyright 1974 American Mathematical Society

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