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Rheometrical flow systems Part 3. Flow between rotating eccentric cylinders

Published online by Cambridge University Press:  29 March 2006

T. N. G. Abbott  and
K. Walters
T. N. G. Abbott
Affiliation:
Department of Applied Mathematics, University College of Wales, Aberystwyth
K. Walters
Affiliation:
Department of Applied Mathematics, University College of Wales, Aberystwyth
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Abstract

We give further consideration to flow situations which are steady in the sense that ∂/∂t ≡ 0 but for which individual fluid elements are subjected to a small sinusoidal deformation. The particular situation studied involves the flow between eccentric circular cylinders which rotate about their axes with the same angular velocity Ω. The eccentricity is assumed to be small. It is shown that measurements of the force on the inner cylinder can be used to determine the complex dynamic viscosity of an elastico-viscous liquid.

The theory provides the necessary mathematical background for the operation of a new commercial rheometer. Consideration is given to the possibility of ‘on-line’ use of such an instrument for control purposes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 2 , 28 August 1970 , pp. 257 - 267
Copyright
© 1970 Cambridge University Press

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References

Abbott, T. N. G. & Walters, K. 1970 J. Fluid Mech. 40, 20.
Coleman, B. D. & Noll, W. 1961 Rev. Mod. Phys. 33, 23.
Jones, J. R. 1964 J. Mécanique 3, 7.
Kamal, M. M. 1966 J. Basic Engng. 88, 71.
Maxwell, B. & Chartoff, R. P. 1965 Trans. Soc. Rheol. 9, 4.
Oldroyd, J. G. 1950 Proc. Roy. Soc. A 200, 523.
Pipkin, A. C. 1964 Rev. Mod. Phys. 36, 103.
Walters, K. 1968 Basic concepts and Formulae for the Rheogoniometer. Sangamo Controls Ltd.
Walters, K. 1970 J. Fluid Mech. 40, 19.
Watson, G. N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.
Wood, W. W. 1957 J. Fluid Mech. 3, 15.