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Geophysical Aspects of Non-Newtonian Fluid Mechanics

  • N. J. Balmforth
  • R. V. Craster
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 582)

Abstract

Non-Newtonian fluid mechanics is a vast subject that has several journals partly, or primarily, dedicated to its investigation (Journal of Non-Newtonian Fluid Mechanics, Rheologica Acta, Journal of Fluid Mechanics, Journal of Rheology, amongst others). It is an area of active research, both for industrial fluid problems and for applications elsewhere, notably geophysically motivated issues such as the flow of lava and ice, mud slides, snow avalanches and debris flows. The main motivation for this research activity is that, apart from some annoyingly common fluids such as air and water, virtually no fluid is actually Newtonian (that is, havinga simple linear relation between stress and strain-rate characterized by a constant viscosity). Several textbooks are useful sources of information; for example, [1],[2],[3] are standard texts giving mathematical and engineering perspectives upon the subject. In these lecture notes, Ancey’s chapter on rheology (Chap. 3) gives further introduction.

Keywords

Debris Flow Maxwell Model Emulsion Droplet Snow Avalanche Carreau Model 
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.

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References

  1. 1.
    R.B. Bird, R.C. Armstrong, O. Hassager: Dynamics of polymeric liquids, Vol. 1: Fluid dynamics (Wiley, New York 1977)Google Scholar
  2. 2.
    A.S. Lodge: Elastic Liquids (Academic Press, New York 1964)Google Scholar
  3. 3.
    R.I. Tanner: Engineering Rheology (Clarendon Press, Oxford 1985)zbMATHGoogle Scholar
  4. 4.
    D.H. Everett: Basic principles of colloid science (Royal Society of Chemistry, London 1988)Google Scholar
  5. 5.
    K. Weissenberg: Nature 159, 310 (1947)ADSCrossRefGoogle Scholar
  6. 6.
    K. Walters: Rheometry (Chapman Hall, London 1975)Google Scholar
  7. 7.
    D.D. Joseph, J.E. Matta, K.P. Chen: J. Non-Newtonian Fluid Mech. 24, 31 (1987)CrossRefGoogle Scholar
  8. 8.
    M.V. Keentok, A.G. Georgescu, A.A. Sherwood, R.I. Tanner: J. Non-Newt. Fluid Mech. 6, 303 (1980)CrossRefGoogle Scholar
  9. 9.
    O. Hassager: Nature 279, 402 (1979)CrossRefADSGoogle Scholar
  10. 10.
    G.K. Batchelor: An introduction to Fluid Mechanics (Cambridge University Press, Cambridge 1967)Google Scholar
  11. 11.
    J.G. Oldroyd: Proc. Roy. Soc. Lond. A 232, 567 (1955)ADSCrossRefGoogle Scholar
  12. 12.
    M. Doi, S.F. Edwards: The theory of polymer dynamics (Oxford University Press, Oxford 1986)Google Scholar
  13. 13.
    W.H. Herschel, R. Bulkley: Am. Soc. Testing Mater. 26, 621 (1923)Google Scholar
  14. 14.
    Q.D. N’Guyen, D.V. Boger: Ann. Rev. Fluid Mech. 24, 47 (1992)CrossRefADSGoogle Scholar
  15. 15.
    H.A. Barnes: J. Non-Newtonian Fluid Mech. 81, 133 (1999)zbMATHCrossRefGoogle Scholar
  16. 16.
    J.P. Dent, T.E. Lang: Ann. Glaciology 4, 42 (1983)ADSGoogle Scholar
  17. 17.
    I.C. Walton, S.H. Bittleston: J. Fluid Mech. 222, 39 (1991)zbMATHCrossRefADSGoogle Scholar
  18. 18.
    A.N. Beris, J.A. Tsamopoulos, R.C. Armstrong, R.A. Brown: J. Fluid Mech. 158, 219 (1985)zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    P. Coussot: Mudflow rheology and dynamics (IAHR Monograph Series, Balkema 1997)Google Scholar
  20. 20.
    K.F. Liu, C.C. Mei: J. Fluid Mech. 207, 505 (1989)zbMATHCrossRefADSGoogle Scholar
  21. 21.
    R.M. Iverson: Reviews of Geophysics 35, 245(1997)CrossRefADSGoogle Scholar
  22. 22.
    M. Manga, J. Castro, K.V. Cashman, M. Loewenberg: J. Volcan. Geotherm. Res. 87, 15(1998)CrossRefADSGoogle Scholar
  23. 23.
    H. Pinkerton, G. Norton: J. Volcan. Geotherm. Res. 68, 307 (1995)CrossRefADSGoogle Scholar
  24. 24.
    H.R. Shaw: J. Petrology 10, 510 (1969)Google Scholar
  25. 25.
    A.R. McBirney, T. Murase: Ann. Rev. Earth Planet. Sci. 12, 337 (1984)CrossRefADSGoogle Scholar
  26. 26.
    D.K. Chester, A.M. Duncan, J.E. Guest, C.R.J. Kilburn: Mount Etna: The anatomy of a volcano (Chapman Hall, London 1985)Google Scholar
  27. 27.
    F.J. Spera, A. Borgia, J. Strimple: J. Geophys. Res. 93, 10273 (1988)ADSCrossRefGoogle Scholar
  28. 28.
    J.H. Fink, R.W. Griffiths: J. Fluid Mech. 221, 485(1990)CrossRefADSGoogle Scholar
  29. 29.
    M.V. Stasiuk, C. Jaupart, R.S.J. Sparks: Geology 21, 335(1993)CrossRefADSGoogle Scholar
  30. 30.
    M.R. Annis: J. Petrol. Technol. 19, 1074 (1967)Google Scholar
  31. 31.
    H.J. Alderman, A. Gavignet, D. Guillot, G.C. Maitland: SPE (1988), paper 18035Google Scholar
  32. 32.
    B.J. Briscoe, P.F. Luckham, S.R. Ren: Phil. Trans. R. Soc. Lond. A 348, 179 (1994)CrossRefADSGoogle Scholar
  33. 33.
    K. Hutter: Theoretical Glaciology (D. Reidel, Dordrecht 1983)Google Scholar
  34. 34.
    W.S.B. Paterson: The physics of glaciers (Pergamon, Oxford 1969)Google Scholar
  35. 35.
    J.W. Glen: Proc. Roy. Soc. Lond. A 228, 519 (1955)ADSCrossRefGoogle Scholar
  36. 36.
    R.L. Hooke: Rev. Geophys. Space Phys. 19, 664 (1981)ADSCrossRefGoogle Scholar
  37. 37.
    I.M. Kreiger: Adv. Colloid Interface Sci. 3, 111 (1972)CrossRefGoogle Scholar
  38. 38.
    P.M. Adler, A. Nadim, H. Brenner: Adv. Chem. Eng. 15, 1 (1990)CrossRefGoogle Scholar
  39. 39.
    H. Pinkerton, R.J. Stevenson: J. Volcan. Geotherm. Res. 53, 47 (1992)CrossRefADSGoogle Scholar
  40. 40.
    K. Hutter, H. Blatter, M. Funk: J. Geophys. Res. 93, 12205(1988)ADSCrossRefGoogle Scholar
  41. 41.
    D. Leighton, A. Acrivos: J. Fluid Mech. 181, 415(1987)CrossRefADSGoogle Scholar
  42. 42.
    R.J. Phillips, R.C. Armstrong, R.A. Brown, A.L. Graham, J.R. Abbott: Phys. Fluids A 4, 29 (1992)CrossRefADSGoogle Scholar
  43. 43.
    P. Coussot, under review (unpublished)Google Scholar
  44. 44.
    J.M. Rallison: Ann. Rev. Fluid Mech. 16, 45(1984)CrossRefADSGoogle Scholar
  45. 45.
    J.M. Rallison, E.J. Hinch: J. Non-Newt. Fluid Mech. 29, 37 (1988)CrossRefGoogle Scholar
  46. 46.
    D.V. Boger: J. Non-Newt. Fluid Mech. 3, 87 (1977)CrossRefGoogle Scholar
  47. 47.
    C.W. Butler, M.B. Bush: Rheol. Acta 28, 294 (1989)CrossRefGoogle Scholar
  48. 48.
    K.P. Jackson, K. Walters, R.W. Williams: J. Non-Newt. Fluid Mech. 14, 173 (1984)CrossRefGoogle Scholar
  49. 49.
    S. Webb: Rev. Geophys. 35, 191 (1997)CrossRefADSGoogle Scholar
  50. 50.
    P. Coussot: J. Hydr. Res. 32, 535 (1994)CrossRefGoogle Scholar
  51. 51.
    X. Huang, M.H. Garcia: J. Fluid Mech. 374, 305(1998)zbMATHCrossRefADSGoogle Scholar
  52. 52.
    R.M. Iverson, M.E. Reid, R.G. LaHusen: Ann. Rev. Earth Planet Sci. 25, 85 (1997)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • N. J. Balmforth
    • 1
  • R. V. Craster
    • 2
  1. 1.Department of Applied Mathematics and Statistics, School of EngineeringUniversity of CaliforniaSanta CruzUSA
  2. 2.Department of MathematicsImperial College of Science, Technology and MedicineLondonUK

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