Hostname: page-component-5b777bbd6c-kmmxp Total loading time: 0 Render date: 2025-06-21T21:57:13.768Z Has data issue: false hasContentIssue false
  • English
  • Français

The Toms phenomenon: turbulent pipe flow of dilute polymer solutions

Published online by Cambridge University Press:  28 March 2006

P. S. Virk ,
E. W. Merrill ,
H. S. Mickley ,
K. A. Smith  and
E. L. Mollo-Christensen
P. S. Virk
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
E. W. Merrill
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
H. S. Mickley
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
K. A. Smith
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
E. L. Mollo-Christensen
Affiliation:
Department of Meteorology, Massachusetts Institute of Technology, Cambridge, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

Drag reduction caused by dilute, distilled water solutions of five polyethylene oxides, molecular weights from 80,000 to 6,000,000, in turbulent pipe flow was studied experimentally in 0·292 and 3·21 cm ID pipes. It was found that the onset of drag reduction occurs at a well-defined wall shear stress related to the random-coiling effective diameter of the polymer. Laminar to turbulent transition is not, in general, delayed. The extent of drag reduction induced by a homologous series of polymers in a given pipe is a universal function of concentration, flow rate, and molecular weight. The maximum drag reduction possible is limited by an asymptote that is independent of polymer and pipe diameter. Flow structure measurements in a single polymer solution, 1000 ppm of molecular weight 690,000, showed that the mean flow follows an ‘effective slip’ model. In this, the mean velocity profile consists of a ‘Newtonian plug’ convected along at an additional, ‘effective slip’ velocity. The turbulent flow structure follows the ‘effective slip’ model towards the pipe wall, but is significantly different from Newtonian towards the pipe axis; in particular, the inertial subrange observed in isotropic Newtonian turbulence was absent in an energy spectrum taken on the pipe axis in the polymer solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 2 , 9 November 1967 , pp. 305 - 328
Copyright
© 1967 Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Astarita, G. & Nicodemo, L. 1966 Velocity distributions and normal stresses in viscoelastic turbulent pipe flow. A.I.Ch.E. J. 12, 478.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer, in Advances in Applied Mechanics, H. L. Dryden and Th. von Kármán, Ed., vol. IV, p. 1. New York: Academic Press.
Fabula, A. G. 1963 The Toms Phenomenon in the turbulent flow of very dilute polymer solutions. 4th Int. Congress on Rheology, Brown U., Providence, Rhode Island.
Flory, P. J. 1953 Principles of Polymer Chemistry. Ithaca, New York: Cornell University Press.
Hershey, H. C. & Zakin, J. L. 1965 A study of turbulent drag reduction of solutions of high polymers in organic solvents. Preprint 21B, Symposium on Mechanics of Viscoelastic Fluids, Part II, 58th Meeting, A.I.Ch.E., Philadelphia, Pa.
Hinze, J. O. 1959 Turbulence. New York: McGraw-Hill.
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA Rept. no. 1174.
Metzner, A. B. & Park, M. G. 1964 Turbulent flow characteristics of visco-elastic fluids. J. Fluid Mech. 20, 291.Google Scholar
Oldroyd, J. G. 1948 A suggested method of detecting wall effects in turbulent flow through pipes. Proc. 1st Int. Congress on Rheology, vol. II, pp. 130–4. North Holland Publ. Co.
Peterlin, A. 1960 Gradient dependence of intrinsic viscosity of freely flexible linear macromolecules. J. Chem. Phys. 33, 1799.Google Scholar
Savins, J. G. 1964 Drag reduction characteristics of solutions of macromolecules in turbulent pipe flow. Soc. Petrol. Eng. J. 4, 203.Google Scholar
Shin, H. 1965 Reduction of Drag in Turbulence by Dilute Polymer Solutions. Sc.D. Thesis, M.I.T., Cambridge, Mass.
Smith, K. A., Merrill, E. W., Mickley, H. S. & Virk, P. S. 1967 Anomalous Pitot tube and hot film measurements in dilute polymer solutions. Chem. Engng Sci. 22, 619.Google Scholar
Tanford, D. 1961 The Physical Chemistry of Macromolecules. New York: John Wiley.
Toms, B. A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. 1st Int. Congress on Rheology, vol. II, pp. 135–41. North Holland Publ. Co.
Virk, P. S., Merrill, E. W., Mickley, H. S. & Smith, K. A. 1965 The Critical wall shear stress for reduction of turbulent drag in pipe flow, in Modern Developments in the Mechanics of Continua, S. Eskanazi, Ed. New York: Academic Press.
Virk, P. S. 1966 The Toms Phenomenon—Turbulent Pipe Flow of Dilute Polymer Solutions. Sc.D. Thesis, M.I.T., Cambridge, Mass.
Zimm, B. H. 1956 Dynamics of polymer molecules in dilute solutions: viscoelasticity, flow birefringence and dielectric loss. J. Chem. Phys. 24, 269.Google Scholar