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The stability of elastico-viscous flow between rotating cylinders. Part 2

Published online by Cambridge University Press:  28 March 2006

R. H. Thomas  and
K. Walters
R. H. Thomas
Affiliation:
Welsh College of Advanced Technology, Cardiff
K. Walters
Affiliation:
University College of Wales, Aberystwyth
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Abstract

Further consideration is given to the stability of the flow of an idealized elasticoviscous liquid contained in the narrow channel between two rotating coaxial cylinders. The work of Part 1 (Thomas & Walters 1964) is extended to include highly elastic liquids. To facilitate this, use is made of the orthogonal functions used by Reid (1958) in his discussion of the associated Dean-type stability problem. It is shown that the critical Taylor number Tc decreases steadily as the amount of elasticity in the liquid increases, until a transition is reached after which the roots of the determinantal equation which determines the Taylor number T as a function of the wave-number ε become complex. It is concluded that the principle of exchange of stabilities may not hold for highly elastic liquids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 4 , August 1964 , pp. 557 - 560
Copyright
© 1964 Cambridge University Press

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References

Chandrasekhar, S. 1954 Mathematika, 1, 5.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, p. 304. Oxford University Press.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312.
Reid, W. H. 1958 Proc. Roy. Soc. A, 244, 186.
Thomas, R. H. & Walters, K. 1963 Proc. Roy. Soc. A, 274, 371.
Thomas, R. H. & Walters, K. 1964 J. Fluid Mech. 18, 33.
Walters, K. 1960 Quart. J. Mech. Appl. Math. 13, 444.
Walters, K. 1964 Second-Order Effects in Elasticity, Plasticity and Fluid Dynamics, p. 507. London: Pergamon Press.