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The rotating rod viscometer

Published online by Cambridge University Press:  29 March 2006

G. S. Beavers  and
D. D. Joseph
G. S. Beavers
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis
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Abstract

This paper reports the development of practical methods of viscometry to characterize non-Newtonian fluids in slow flow. It is shown that measurements of the free surface near rods rotating in STP and polyacrylamide are accurate, reproducible, and in excellent agreement with a theory of rod climbing. Results are presented that establish the theory and experiment as a viscometer for determining the values of certain (Rivlin-Ericksen) constants that arise in the theory of slow flow. The variation of these constants with temperature in our sample of STP has been explicitly and accurately determined. The experiments in STP show that there is a range of rotational speeds for which STP may be well described by the fluids of grade four. Depth-averaged equations are derived from the equations governing steady axisymmetric flow of any incompressible simple fluid. From the depth-averaged equations, we prove a theorem about the variation of the torque required to turn the rod.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 3 , 10 June 1975 , pp. 475 - 511
Copyright
© 1975 Cambridge University Press

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References

Coleman, B. D., Markovitz, H. & Noll, W. 1966 Viscometric Flows of Non-Newtonian Fluids. Springer Tracts in Natural Philosophy, vol. 5. Springer.
Coleman, B. D. & Noll, W. 1960 An approximation theorem for functions with applications in continuum mechanics Arch. Rat. Mech. Anal. 6, 355.Google Scholar
Coleman, B. D. & Noll, W. 1961 Foundations of linear visco-elasticity Rev. Modern Phys. 33, 239.Google Scholar
Giesekus, VON H. 1961 Einige Bemerkungen zum Fließverhalten elasto-viskoser Flüssigkeiten in stationären Schichtströmungen Rheologica Acta, 1, 404.Google Scholar
Joseph, D. D. 1973 Domain perturbations: the higher order theory of infinitesimal water waves. Arch. Rat. Mech. Anal. 51, 295.Google Scholar
Joseph, D. D., Beavers, G. S. & Fosdick, R. L. 1973 The free surface on a liquid between cylinders rotating at different speeds. Part 2 Arch. Rat. Mech. Anal. 49, 381.Google Scholar
Joseph, D. D. & Fosdick, R. L. 1973 The free surface on a liquid between cylinders rotating at different speeds. Part 1 Arch. Rat. Mech. Anal. 49, 321.Google Scholar
Joseph, D. D. & Sturges, L. 1975 The free surface on a liquid in a trench heated from its side J. Fluid Mech. 69, 565.Google Scholar
Langlois, W. E. & Rivlin, R. S. 1963 Slow steady-state flow of visco-elastic fluids through non-circular tubes Rendiconti di Matematica, 22, 169.Google Scholar
Markovitz, H. & Coleman, B. D. 1964 Incompressible second-order fluids. Advances in Applied Mechanics, vol. 8. Academic.
Noll, W. 1958 A mathematical theory of the mechanical behaviour of continuous media Arch. Rat. Mech. Anal. 2, 197.Google Scholar
Pipkin, A. C. & Tanner, R. I. 1973 A survey of theory and experiment in viscometric flows of viscoelastic liquids. Mechanics Today, vol. 1. Pergamon.
Pritchard, W. G. 1971 Measurements of the viscometric functions for a fluid in steady shear flow. Phil. Trans. A 270, 507.Google Scholar
Serrin, J. 1959 Poiseuille and Couette flow of non-Newtonian fluids Z. angew. Math. Mech. 39, 295.Google Scholar
Tanner, R. I. 1970 Some methods for estimating the normal stress functions in viscometric flows Trans. Soc. Rheol. 14, 483.Google Scholar
Truesdell, C. 1974 The meaning of viscometry in fluid dynamics. Annual Reviews of Fluid Mechanics, vol. 6. Annual Reviews Inc.
Truesdell, C. & Noll, W. 1965 The nonlinear field theories of mechanics. Handbuch der Physik, vol. III/3. Springer.
Wineman, A. S. & Pipkin, A. C. 1966 Slow viscoelastic flow in tilted troughs Acta Mechanica, 2, 104.Google Scholar