Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-23T19:34:22.592Z Has data issue: false hasContentIssue false

Radial fingering in a Hele Shaw cell

Published online by Cambridge University Press:  20 April 2006

Lincoln Paterson
Affiliation:
Department of Engineering Physics, Research School of Physical Sciences, The Australian National University, Canberra, 2600, Australia

Abstract

The results of experiments involving instability, known as fingering, in a circular Hele Shaw cell with inward and outward flow are presented. The width of fingers in this situation is examined, and an approximate equation for the growth of fingers is proposed. The equation rα = cos (nθ) is shown to fit the shape of long fingers.

Type
Research Article
Copyright
© 1981 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

Bataille, J. 1968 Revue Inst. Pétrole, 23, 13491364.
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.
Carden, P. O. & Paterson, L. 1979 Int. J. Hydrogen Energy, 4, 559569.
Chuoke, R. L., van Meurs, P. & van der Poel, C. 1959 Trans. A.I.M.E. 216, 188194.
Gupta, S. P., Varnon, J. E. & Greenkorn, R. A. 1973 Water Resour. Res. 9, 10391046.
Habermann, B. 1960 Trans. A.I.M.E. 219, 264272.
Peterson, L. 1980 The implications of fingering in underground hydrogen storage. In Proc. 3rd World Hydrogen Energy Conference, Tokyo, June 23–26. Pergamon Press.
Pitts, E. 1980 J. Fluid Mech. 97, 5364.
Pollard, D. D., Muller, O. H. & Dockstad, D. R. 1975 Geol. Soc. Am. Bull. 86, 351363.
Richardson, J. G. 1961 In Handbook of Fluid Dynamics (ed. V. L. Streeter). McGraw-Hill.
Roark, R. J. 1965 Formulas for Stress and Strain, 4th edn. McGraw Hill.
Saffman, P. G. & Taylor, G. I. 1958 Proc. Roy. Soc. A 245, 312329.
Saffman, P. G. 1959 Quart. J. Mech. Appl. Math. 12, 146150.
Scheideggar, A. E. 1960a Phys. Fluids, 3, 94104.
Scheideggar, A. E. 1960b Can. J. Phys. 38, 153162.
Settari, A., Price, H. S. & Dupont, T. 1977 Soc. Pet. Eng. J. June, 228–246.
Taylor, G. I. & Saffman, P. G. 1959 Quart. J. Mech. Appl. Math. 12, 265279.
Van Meurs, P. 1957 Trans. A.I.M.E. 210, 295301.
White, I., Colombera, P. M. & Philip, J. R. 1976 Soil Sci. Soc. Am. J. 40, 824829.
Wilson, S. D. R. 1975 J. Colloid Interface Sci. 51, 532534.
Wooding, R. A. 1969 J. Fluid Mech. 39, 477495.
Wooding, R. A. & Morel-Seytoux, H. 1976 Ann. Rev. Fluid Mech. 8, 233274.