Non-Newtonian Fluid and Flow

  • H. Yamaguchi
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 85)


Shear Rate Viscoelastic Fluid Normal Stress Difference Material Function Elongational Viscosity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


The most fundamental treatment of non-Newtonian fluids, in particular to polymeric liquids, is found in rather authoritative texts, with which every student of non-Newtonian fluid mechanics should be acquainted:

  1. R.B. Bird, R.C. Armstrong and O. Hassager, Dynamics of polymeric liquids, 1. Wiley, New York, 1977.Google Scholar
  2. R.B. Bird, C.F. Curtiss, R.C. Armstrong and O. Hassanger, Dynamics of Polymeric Liquids, Vol.1 Fluid Mechanics and Vol. 2 Kinetic Theory (2nd edition), A Wiley-Interscience Publication, New York, NY, 1987.Google Scholar
  3. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena (2nd edition), John Wiley & Sons, Inc., Hoboken, NJ, 2002.Google Scholar

A lucid mathematical treatment on flows of non-Newtonian fluids, in which conceptual and logical thinking is developed, is given with

  1. J. Harris, Rheology and Non-Newtonian Flow, Longman Inc., New York, 1977.zbMATHGoogle Scholar
  2. R.R. Huilgol and N. Phan-Thien, Fluid Mechanics of Viscoelasticity, Elsevier Science Publishers B.V., Amsterdam, 1997.Google Scholar
  3. N.W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior, Springer-Verlag, New York, 1989.zbMATHGoogle Scholar

Some of flow problems, the boundary layer behavior, are derived from the reference 3. Some selective topics of flow problems in viscoelastic liquids with a good deal of literature citation is found in

  1. D.D. Joseph, Fluid Dynamics of Viscoelastic Liquids, Springer-Verlag New York Inc., New York, 1990.zbMATHGoogle Scholar

The current approach in flow problems of non-Newtonian fluids is largely dependent upon numerical analysis with ultrahigh performance computer. A basic computational viscoelastic fluid dynamic is found in the reference 4, and

  1. R.G. Owens and T.N. Phillips, Computational Rheology, Imperial College Press, London, 2002.zbMATHGoogle Scholar
  2. M.J. Crochet, A.R. Davies and K. Walters, Numerical Simulation of Non-Newtonian Flow (3rd edition), Elsevier Science Publishers B.V., Amsterdam, 1991.Google Scholar

Rheological treatment of non-Newtonian fluids and the derivation of the expression for the constitutive equations are well presented in

  1. F.A. Morrison, Understanding Rheology, Oxford University Press, Inc., Oxford, 2001.zbMATHGoogle Scholar
  2. R.I. Tanner, Engineering Rheology, Oxford University, Inc., Oxford, (Reprinted) 1992.Google Scholar
  3. P.J. Carreau, D.C.R. De Kee, and R.P. Chhabra, Rheology of Polymeric Systems, Hanser/Gardner Publications, Inc., Cincinnati, OH, 1997.Google Scholar
  4. R.G. Larson, Constitutive Equations for Polymer Melts and Solutions, Butterworths Series in Chemical Engineering, AT&T Bell Laboratories, Inc., Murray Hill, NJ, 1988Google Scholar

The transport phenomena in simple flows, including the boundary layer flows in power law fluids, are well presented in the reference 11. A few texts of standard measurement methods and the contribution of the melt rheology contain some useful materials on industrial applications. Three examples are those by

  1. A.A. Collyer and D.W. Clegg, Rheological Measurement, Elsevier Applied Science Publishers LTD, Amsterdam, 1988.Google Scholar
  2. J.M. Dealy and K.F. Wissbrun, Melt Rheology and Its Role in Plastics Processing, Kluwer Academic Publishers, Boston, MA (Reprinted) 1999.Google Scholar
  3. J.R.A. Pearson, Mechanics of Polymer Processing, Elsevier Applied Science Publishers, LTD, Amsterdam, (Reprinted) 1986.Google Scholar

In particular, although not being quoted in the present text, but as one of current topics in engineering fluid mechanics, the drag reduction of turbulent flows in view of dilute polymeric substance adding is found in

  1. A. Gyr and H.W. Bewersdorff, Drag Reduction of Turbulent Flows by Additives, Kluwer Academic Publishers, Boston, MA, 1995.zbMATHGoogle Scholar

Flow Phenomena, specific date, correlations and approximations that are referred to in this text are presented in

  1. W. Ostwald, Quantitative Filtrationsanalyse als dispersoidanalytische Methode, Kolloid Z., 36, 1925.Google Scholar
  2. K. Yasuda, Ph.D thesis, Massachusetts Institute of Technology, Cambridge, MA, 1979. also K.Yasuda, R.C. Arm strong and R.E.Cohen, Shear flow properties of concentrated solutions of linear and star branched polyst, Rheol. Acta, 20. pp. 163–178, 1981Google Scholar
  3. T. Ree and H. Eyring, Theory of Non-Newtonian Flow. I. Solid Plastic System, Appl. Phys., 26(7), 1955.Google Scholar
  4. J.G. Oldroyd, The interpretation of observed pressure gradients in laminar flow of non-Newtonian liquids through tubes, J. Call. Sci., 4, 1949.Google Scholar
  5. J.G. Oldroyd, On the formulation of rheological equations of state, Proc. Roy. Soc., A200, 1950.Google Scholar
  6. J.G. Oldroyd, Finite strains in an anisotropic elastic continuum, Proc. Roy. Soc., A202, 1950.Google Scholar
  7. J.G. Oldroyd, Non-Newtonian effects in steady motion of some indealized elastico-viscous liquids, Proc. Roy. Soc., A245, 1958.Google Scholar
  8. E.C. Bingham, Fluidity and Plasticity, McGraw-Hill, New York, NY, 1922.Google Scholar
  9. H. Yamaguchi, Behavior of laminar boundary layer with shear thickening-thinning characteristics of non-Newtonian flows, Soc. Rheol. Japan, 22(2), 1994.Google Scholar
  10. H. Yamaguchi, J. Fujiyoshi and H. Matsui, Spherical Couette flow of a viscoelastic fluid, J. Non-Newtonian Fluid Mech., Part I and Part II, 69, 1997.Google Scholar
  11. F.T. Trouton, The pressure in equilibrium with substances holding varying amounts of moisture, Proc. Roy. Soc., A77, 1906.Google Scholar
  12. M. Sentmanat, B.N. Wang and G.H. McKinley, Measuring the transient extensional rheology of polyethylene melts using the SER universal testing platform, J. Rheol., 49, 2005.Google Scholar
  13. V. Tirtaatmadja and T. Snidhar, A filament stretching device for measurement of extensional viscosity, J. Rheol., 37(6), 1993.Google Scholar
  14. W.P. Cox and E.H. Mertz, Correlation of dynamic and steady flow viscosities, J. Polym. Sci., 28, 1958.Google Scholar
  15. H.M. Laun, Prediction of elastic strains of polymer melts in shear and elongation, J. Rheol., 30, 1986.Google Scholar
  16. J. Sampers and P.J.R. Leblans, An experimental and theoretical study of the effect of the elongational history on the dynamics of isothermal melt spinning, J. Non-Newtonian Fluid Mech., 30, 1988.Google Scholar
  17. T. Hsu, P. Shirodkar, R.L. Laurence and H.H. Winter, The wall effect in orthogonal stagnation flow, Proc. 8th Int. Congr. Rheol., 2, 1980.Google Scholar
  18. F.N. Cogswell, Converging flow and stretching flow : a compilation, J. Non-Newtonian Fluid Mech., 4, 1978.Google Scholar
  19. B.Z. Rabinowitsch, Physik chemie, A145, 1929.Google Scholar
  20. H. Giesekus, A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility, J. Non-Newtonian Fluid Mech., 11, 1982.Google Scholar
  21. A.I. Leonov, Nonequilibrium thermodynamics and rheology of viscoelastic polymer media, Rheol. Acta, 15(2), 1976.Google Scholar
  22. N. Phan-Thien and R.I. Tanner, A new constitutive equation derived from network theory , J. Non-Newtonian Fluid Mech., 2, 1977.Google Scholar
  23. A.S. Lodge, Elastic Liquids, Academic Press, New York, NY, 1964.Google Scholar
  24. A. Kaye, A study of stress relaxation with finite strain, College of Aeronautics Cranfield, UK Note 134, 1962.Google Scholar
  25. B. Bernstein, E.A. Kearsley and L.J. Zapas, Irans. Soc. Rheol., 7, 1963.Google Scholar
  26. C.F. Curtiss and R.B. Bird, A kinetic theory for polymer melts, J. Chem. Phys., 74(3), 1981.Google Scholar
  27. I. Etter and W.R. Schowalter, Unsteady flow of an Oldroyd fluid in a circular tube, Trans. Soc. Rheol., 9(2), 1965.Google Scholar
  28. J.D. Goddard and C. Miller, An inverse for the Jaumann derivative and some applications to the rheology of viscoelastic fluids, Rheol. Acta, 5, 1966Google Scholar
  29. B.A. Toms, Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers, North Holland, Amsterdam, Proc. 1st Intern. Congr. on Rheol. 2, 135–141.Google Scholar
  30. J.L. White and A.B. Metzner, Development of constitutive equations for polymeric melts and solutions, J. Appl. Polym. Sci., 1867–1889. 1963.Google Scholar
  31. K. Nakamura, Non-Newtonian Fluid Mechanics, Corona Pub. Co., LTD., Tokyo, 1997 (in Japanese).Google Scholar
  32. H. Giesekus, Die Elastizitat von Flussigkeiten, Rheol Acta 5, 29–35, 1966.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • H. Yamaguchi
    • 1
  1. 1.Doshisha UniversityKyo-TanabeshiJapan

Personalised recommendations