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The Quarterly Journal of Mechanics and Applied Mathematics 1951 4(3):271-282; doi:10.1093/qjmam/4.3.271
© 1951 by Oxford University Press
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THE MOTION OF AN ELASTICO-VISCOUS LIQUID CONTAINED BETWEEN COAXIAL CYLINDERS. I

J. G. OLDROYD

( Courtaulds Limited, Research Laboratory Maidenhead, Berks )

The theory of periodic and steady states of motion of a liquid in a narrow annular gap between long vertical coaxial cylinders is considered, when the viscous and elastic properties of the material at small rates of shear are measured by three constants, a viscosity coefficient and two relaxation times. When the outer cylinder undergoes forced harmonic angular oscillations about its axis, and the inner cylinder is constrained by a torsion wire, the amplitude of uniform oscillation attained by the inner cylinder is calculated. The ratio of the angular amplitudes of the two cylinders has been plotted as a function of the frequency, for different values of the constants of the material and of an available apparatus. From observations of the frequency, amplitude-ratio curves for some actual liquids which are approximately of the type considered, values can be deduced for their elastic and viscous constants. In steady flow between rotating cylinders, elastico-viscous liquids behave like purely viscous liquids whose viscosity is a function of the rate of shear. Additional information about the rheological equations of state of actual liquids can be deduced from steady rotational experiments.


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