Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T00:32:57.213Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids

Published online by Cambridge University Press:  28 March 2006

D. W. Beard ,
M. H. Davies  and
K. Walters
D. W. Beard
Affiliation:
Department of Applied Mathematics, University College of Wales, Aberystwyth
M. H. Davies
Affiliation:
Department of Applied Mathematics, University College of Wales, Aberystwyth
K. Walters
Affiliation:
Department of Applied Mathematics, University College of Wales, Aberystwyth
Get access Rights & Permissions [Opens in a new window]

Abstract

Consideration is given to the possibility of overstability in the Couette flow of viscous and elastico-viscous liquids. The relevant linear perturbation equations are solved numerically using an initial-value technique. It is shown that over-stability is not possible in the case of Newtonian liquids for the cases considered. In contrast, overstability is to be expected in the case of moderately-elastic Maxwell liquids. The Taylor number associated with the overstable mode decreases steadily as the amount of elasticity in the liquid increases, and it is concluded that highly elastic Maxwell liquids can be very unstable indeed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 2 , February 1966 , pp. 321 - 334
Copyright
© 1966 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

Chandrasekhar, S. 1954 Mathematika, 1, 5.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Oldroyd, J. G. 1950 Proc. Roy. Soc. A, 200, 523.
Shield, R. T. & Green, A. E. 1963 Arch. Rat. Mech. Anal. 12, 35.
Taylor, G. I. 1923 Phil. Trans., A 223, 289.
Thomas, R. H. & Walters, K. 1964a J. Fluid Mech. 18, 3.
Thomas, R. H. & Walters, K. 1964b J. Fluid Mech. 19, 55.
Walters, K. 1960 Quart. J. Mech. Appl. Math. 13, 44.
Walters, K. 1964 Second-Order Effects in Elasticity, Plasticity and Fluid Dynamics, p. 507. London: Pergamon Press.