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Some remarks on Hele-Shaw flow and viscous tails

Published online by Cambridge University Press:  29 March 2006

J. Buckmaster
J. Buckmaster
Affiliation:
New York University, University Heights, N.Y.
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Abstract

A simple model is suggested to describe flow in a Hele-Shaw cell when the Hele-Shaw parameter Λ is not necessarily small. The averaged flow is potential with a conservative body force proportional to the local velocity. The elementary ramifications of this are deduced and comparisons made with experiment. In particular no separation is predicted if Λ is less than O(1), in agreement with experiment. Furthermore, the separation cavities occurring for large Λ are completely stagnant. The theory predicts attached viscous shear layers in the wake of a lifting body, reminiscent of certain MHD problems. These tails were not observed experimentally.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 3 , 29 April 1970 , pp. 523 - 530
Copyright
© 1970 Cambridge University Press

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References

Hele-Shaw, H. S. 1897 Trans. Roy. Inst. Nav. Arch. 41, 21.
Hele-Shaw, H. S. 1898a Trans. Roy. Inst. Nav. Arch. 42, 49.
Hele-Shaw, H. S. 1898b Rept. 68th Mtg. Br. Ass. p. 136.
Ludford, G. S. S. & Fan, D. N. 1969 I.I.T. J. Math. Phys. Sci.
Riegels, F. 1938 Zeit. Ang. Math. Mech. 18, 95.
Salathe, P. & Sirovich, L. 1967 Phys. Fluids, 10, 1477.
Stokes, G. G. 1898 Appendix to Hele-Shaw (1898 b).
Thompson, B. W. 1968 J. Fluid. Mech. 31, 379.