Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T19:17:47.336Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of immiscible liquid layers in a porous medium

Published online by Cambridge University Press:  29 March 2006

R. Raghavan  and
S. S. Marsden
R. Raghavan
Affiliation:
Stanford University, Stanford, California
S. S. Marsden
Affiliation:
Stanford University, Stanford, California
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of liquid layers in a porous medium under the action of viscous and surface forces is described. An extension of previous studies on the stability of a single interface in a porous medium is presented as the basis for solutions to many problems of practical interest where flow in porous media are involved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 1 , 13 July 1971 , pp. 143 - 159
Copyright
© 1971 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chang, C. T. 1959 Dynamic instability of accelerated fluids Phys. Fluids, 2, 656.Google Scholar
Chuoke, R. L., van Muers, P. & van der Poel, C. 1959 The instability of slow, immiscible, viscous liquid—liquid displacements in permeable media Trans. AIME 216, 188.Google Scholar
Davies, J. T. & Haydon, D. A. 1957 Spontaneous emulsification, gas—liquid and liquid—liquid interface. In Proceedings of the 2nd International Congress of Surface Activity, vol. I, p. 417. Butterworth.
Dietz, D. W. 1953 A theoretical approach to the problem of encroachment and by-passing edge water. Proc. K. Ned. Akad. Wet. B 56, 83.Google Scholar
Jeffreys, H. 1926 The stability of a layer of fluid heated below. Lond. Edinb. Dubl. Phil. Mag. II, Ser. 7, 833.Google Scholar
Keller, J. B. & Kolodner, I. 1954 Instability of liquid surfaces and formation of drops J. Appl. Phys. 25, 913.Google Scholar
Kidder, R. E. 1956 Motion of the interface between two immiscible liquids of unequal density in a porous solid J. Appl. Phys. 27, 867.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, vol. 6: Course on Theoretical Physics. Pergamon.
Lewis, D. J. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II. Proc. Roy. Soc. A 202, 192.Google Scholar
Miller, F. G. 1962 Theory of unsteady state influx in linear reservoirs J. Inst. Petrol. 48, 365.Google Scholar
Outmans, H. D. 1962 Nonlinear theory for frontal stability and viscous fingering in porous media Soc. Petr. Engrs J. 8, 165.Google Scholar
Raghavan, R. 1970 The instability of liquid-liquid interfaces and model systems for emulsion formation in porous media. Ph.D. Dissertation, Stanford University.
Raghavan, R. & Marsden, S. S. 1971 Theoretical aspects of emulsification in porous media. To be published in Soc. Petr. Engrs J. 11.Google Scholar
Rayleigh, LORD. 1899 On stability and instability of certain fluid motions. Scientific Papers, vol. 1. Cambridge University Press.
Saffman, P. G. & Taylor, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. Roy. Soc. A 245, 312.Google Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. Roy. Soc. A 201, 192.Google Scholar