Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T12:28:47.984Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillatory motion of an elastico-viscous liquid contained between two coaxial cylinders

Published online by Cambridge University Press:  26 February 2010

J. R. Jones  and
T. S. Walters
J. R. Jones
Affiliation:
Department of Applied Mathematics, University of Wales, Swansea.
T. S. Walters
Affiliation:
Department of Applied Mathematics, University of Wales, Swansea.
Get access

Extract

Some of the elastic properties of liquids in shear can be detected and measured by observing suitable types of oscillatory motion. Oscillating systems have proved to be fairly simple to design and to control in practice, and can lead, in the case of purely viscous liquids, to accurate measurements of the viscosity [see, for example, 1, 2, 3]. One such system, used for the purpose of investigating the rheological properties of dilute polymer solutions, is the coaxial-cylinder elastoviscometer of Oldroyd, Strawbridge and Toms [4]; in this experimental arrangement, the liquid is contained between two cylinders with a common, vertical axis, the inner cylinder being suspended by a vertical torsion wire. The theory of the motion of such an instrument in the case when the outer cylinder is forced to oscillate about its axis, which is fixed, with a known constant frequency, and the resulting motion of the inner cylinder is constrained by the torsion wire, has been considered by Oldroyd [5], who shows that the experimental results available for some typical polymer solutions can be interpreted in terms of an idealised elastico-viscous liquid characterised by three constants (a viscosity and two relaxation times). A new representation of the relaxation spectrum of a liquid has subsequently been used by Walters [6] in order to develop the theory of oscillatory flow of the most general (linear) visco-elastic liquid. Walters has shown that the experimental results for dilute polymer solutions (previously interpreted in terms of a discrete relaxation spectrum by Oldroyd [5]) can, equally, be interpreted in terms of a simple continuous relaxation spectrum characterised by three constants.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 2 , December 1965 , pp. 246 - 256
Copyright
Copyright © University College London 1965

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

1.Kestin, J. and Wang, H. E., J. Appl. Much. 24 (1957), 197.CrossRefGoogle Scholar
2.Kestin, J. and Newell, G. F., Z. angew. Math. Phys. 8 (1957), 433.CrossRefGoogle Scholar
3.Roscoe, R., Proc. Phys. Soc. 72 (1958), 576.CrossRefGoogle Scholar
4.Oldroyd, J. G., Strawbridge, D. J. and Toms, B. A., Proc Phys. Soc. 64B (1951), 44.CrossRefGoogle Scholar
5.Oldroyd, J. G., Strawbridge, D. J. and Toms, B. A., Quart. J. Mech. App. Math. 4 (1951), 271.CrossRefGoogle Scholar
6.Walters, K., Quart. J. Mech. App. Math. 13 (1960), 444.CrossRefGoogle Scholar
7.Oldroyd, J. G., Proc. Roy. Soc. (A), 245 (1958), 278.Google Scholar
8.Oldroyd, J. G., Proc. Roy. Soc. (A), 200 (1950), 523.Google Scholar
9.Watson, G. N., A treatise on the theory of Bessel Functions (Cambridge, 1952).Google Scholar