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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
Affiliation:
Welsh College of Advanced Technology, Cardiff
K. Walters
Affiliation:
University College of Wales, Aberystwyth

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
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.