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The laminar flow of dilute polymer solutions around circular cylinders

Published online by Cambridge University Press:  29 March 2006

David F. James  and
Allan J. Acosta
David F. James
Affiliation:
University of Toronto, Toronto, Ontario, Canada
Allan J. Acosta
Affiliation:
California Institute of Technology, Pasadena, California
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Abstract

This paper describes the measurements of heat transfer and drag for the flow of dilute polymer solutions around very small cylinders. The thermal experiments were carried out at Reynolds numbers less than 50, and the results establish the dependence of the heat transfer on fluid velocity, cylinder diameter, solution concentration, and polymer molecular weight. The drag measurements were conducted with the same type of solutions and in the same Reynolds-number range. To complement the heat-transfer and drag measurements, the flows around a cylinder and through an orifice were examined visually. These flow-visualization studies showed that the streamline pattern with dilute polymer solutions can be significantly different from that with Newtonian fluids because of viscoelastic effects.

An analysis of Rouse's theory of macromolecules shows that for low accelerations a dilute polymer solution behaves mechanically like a Maxwell model. The analysis thereby produces a relaxation time, a single parameter representing the elasticity of the fluid, which can be related to the properties of the solute and solvent. This relaxation time is contained in a new dimensionless group which governs dynamic similarity when induced elastic stresses dominate viscous stresses in the flow around a circular cylinder. The dimensionless group is shown to correlate the thermal data when the heat transfer does not depend on the free stream velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 2 , 22 June 1970 , pp. 269 - 288
Copyright
© 1970 Cambridge University Press

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References

Coleman, B. D., Markovitz, H. & Noll, W. 1966 Viscometric Flows of Non-Newtonian Fluids, New York: Springer.
Davis, A. H. 1924 Phil. Mag. 47, 105.
Elata, C., Lehrer, J. & Kohanovitz, A. 1966 Israel J. Tech. 4, 8.
Fabula, A. G. 1966 Ph.D. thesis, the Pennsylvania State University.
Hoyt, J. W. & Fabula, A. G. 1964 U.S. Naval Ordnance Test Station. China Lake, California, NAVWEPS Report 8636.
James, D. F. 1967 Ph.D. thesis, California Institute of Technology.
Lodge, A. S. 1964 Elastic Liquids. New York: Academic.
Mcadams, W. H. 1954 Heat Transmission (3rd. edn.). New York: McGraw-Hill.
Metzner, A. B., White, J. L. & Denn, M. M. 1966 A.I.Ch.E. J. 12, 86.
Metzner, A. B. & Astarita, G. 1967 A.I.Ch.E. J. 13, 55.
Piret, E. L., James, W. & Stacey, W. 1947 Ind. Engin. Chem. 39, 109.
Poreh, M. & Paz, U. 1968 Int. J. Heat Mass Transfer, 11, 805.
Rouse, P. E. 1953 J. Chem. Phys. 21, 127.
Shin, H. 1965 Sc.D. thesis, M.I.T.
Smith, K. A., Merrill, E. W., Mickley, H. S. & Virk, P. S. 1967 Chem. Eng. Sci. 22, 61.
Tanford, D. 1961 Physical Chemistry of Macromolecules. New York: Wiley.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.
Walsh, M. A. 1967 Ph.D. thesis, California Institute of Technology.
Wieselsberger, C. 1923 Ergebn. aerodyn. VersAnstalt zu Göttingen, II Lieferung, 24.