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Geophysical Aspects of Non-Newtonian Fluid Mechanics

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Geomorphological Fluid Mechanics

Part of the book series: Lecture Notes in Physics ((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.

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References

  1. R.B. Bird, R.C. Armstrong, O. Hassager: Dynamics of polymeric liquids, Vol. 1: Fluid dynamics (Wiley, New York 1977)

    Google Scholar 

  2. A.S. Lodge: Elastic Liquids (Academic Press, New York 1964)

    Google Scholar 

  3. R.I. Tanner: Engineering Rheology (Clarendon Press, Oxford 1985)

    MATH  Google Scholar 

  4. D.H. Everett: Basic principles of colloid science (Royal Society of Chemistry, London 1988)

    Google Scholar 

  5. K. Weissenberg: Nature 159, 310 (1947)

    Article  ADS  Google Scholar 

  6. K. Walters: Rheometry (Chapman Hall, London 1975)

    Google Scholar 

  7. D.D. Joseph, J.E. Matta, K.P. Chen: J. Non-Newtonian Fluid Mech. 24, 31 (1987)

    Article  Google Scholar 

  8. M.V. Keentok, A.G. Georgescu, A.A. Sherwood, R.I. Tanner: J. Non-Newt. Fluid Mech. 6, 303 (1980)

    Article  Google Scholar 

  9. O. Hassager: Nature 279, 402 (1979)

    Article  ADS  Google Scholar 

  10. G.K. Batchelor: An introduction to Fluid Mechanics (Cambridge University Press, Cambridge 1967)

    Google Scholar 

  11. J.G. Oldroyd: Proc. Roy. Soc. Lond. A 232, 567 (1955)

    Article  ADS  Google Scholar 

  12. M. Doi, S.F. Edwards: The theory of polymer dynamics (Oxford University Press, Oxford 1986)

    Google Scholar 

  13. W.H. Herschel, R. Bulkley: Am. Soc. Testing Mater. 26, 621 (1923)

    Google Scholar 

  14. Q.D. N’Guyen, D.V. Boger: Ann. Rev. Fluid Mech. 24, 47 (1992)

    Article  ADS  Google Scholar 

  15. H.A. Barnes: J. Non-Newtonian Fluid Mech. 81, 133 (1999)

    Article  MATH  Google Scholar 

  16. J.P. Dent, T.E. Lang: Ann. Glaciology 4, 42 (1983)

    ADS  Google Scholar 

  17. I.C. Walton, S.H. Bittleston: J. Fluid Mech. 222, 39 (1991)

    Article  MATH  ADS  Google Scholar 

  18. A.N. Beris, J.A. Tsamopoulos, R.C. Armstrong, R.A. Brown: J. Fluid Mech. 158, 219 (1985)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. P. Coussot: Mudflow rheology and dynamics (IAHR Monograph Series, Balkema 1997)

    Google Scholar 

  20. K.F. Liu, C.C. Mei: J. Fluid Mech. 207, 505 (1989)

    Article  MATH  ADS  Google Scholar 

  21. R.M. Iverson: Reviews of Geophysics 35, 245(1997)

    Article  ADS  Google Scholar 

  22. M. Manga, J. Castro, K.V. Cashman, M. Loewenberg: J. Volcan. Geotherm. Res. 87, 15(1998)

    Article  ADS  Google Scholar 

  23. H. Pinkerton, G. Norton: J. Volcan. Geotherm. Res. 68, 307 (1995)

    Article  ADS  Google Scholar 

  24. H.R. Shaw: J. Petrology 10, 510 (1969)

    Google Scholar 

  25. A.R. McBirney, T. Murase: Ann. Rev. Earth Planet. Sci. 12, 337 (1984)

    Article  ADS  Google Scholar 

  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. F.J. Spera, A. Borgia, J. Strimple: J. Geophys. Res. 93, 10273 (1988)

    Article  ADS  Google Scholar 

  28. J.H. Fink, R.W. Griffiths: J. Fluid Mech. 221, 485(1990)

    Article  ADS  Google Scholar 

  29. M.V. Stasiuk, C. Jaupart, R.S.J. Sparks: Geology 21, 335(1993)

    Article  ADS  Google Scholar 

  30. M.R. Annis: J. Petrol. Technol. 19, 1074 (1967)

    Google Scholar 

  31. H.J. Alderman, A. Gavignet, D. Guillot, G.C. Maitland: SPE (1988), paper 18035

    Google Scholar 

  32. B.J. Briscoe, P.F. Luckham, S.R. Ren: Phil. Trans. R. Soc. Lond. A 348, 179 (1994)

    Article  ADS  Google Scholar 

  33. K. Hutter: Theoretical Glaciology (D. Reidel, Dordrecht 1983)

    Google Scholar 

  34. W.S.B. Paterson: The physics of glaciers (Pergamon, Oxford 1969)

    Google Scholar 

  35. J.W. Glen: Proc. Roy. Soc. Lond. A 228, 519 (1955)

    Article  ADS  Google Scholar 

  36. R.L. Hooke: Rev. Geophys. Space Phys. 19, 664 (1981)

    Article  ADS  Google Scholar 

  37. I.M. Kreiger: Adv. Colloid Interface Sci. 3, 111 (1972)

    Article  Google Scholar 

  38. P.M. Adler, A. Nadim, H. Brenner: Adv. Chem. Eng. 15, 1 (1990)

    Article  Google Scholar 

  39. H. Pinkerton, R.J. Stevenson: J. Volcan. Geotherm. Res. 53, 47 (1992)

    Article  ADS  Google Scholar 

  40. K. Hutter, H. Blatter, M. Funk: J. Geophys. Res. 93, 12205(1988)

    Article  ADS  Google Scholar 

  41. D. Leighton, A. Acrivos: J. Fluid Mech. 181, 415(1987)

    Article  ADS  Google Scholar 

  42. R.J. Phillips, R.C. Armstrong, R.A. Brown, A.L. Graham, J.R. Abbott: Phys. Fluids A 4, 29 (1992)

    Article  ADS  Google Scholar 

  43. P. Coussot, under review (unpublished)

    Google Scholar 

  44. J.M. Rallison: Ann. Rev. Fluid Mech. 16, 45(1984)

    Article  ADS  Google Scholar 

  45. J.M. Rallison, E.J. Hinch: J. Non-Newt. Fluid Mech. 29, 37 (1988)

    Article  Google Scholar 

  46. D.V. Boger: J. Non-Newt. Fluid Mech. 3, 87 (1977)

    Article  Google Scholar 

  47. C.W. Butler, M.B. Bush: Rheol. Acta 28, 294 (1989)

    Article  Google Scholar 

  48. K.P. Jackson, K. Walters, R.W. Williams: J. Non-Newt. Fluid Mech. 14, 173 (1984)

    Article  Google Scholar 

  49. S. Webb: Rev. Geophys. 35, 191 (1997)

    Article  ADS  Google Scholar 

  50. P. Coussot: J. Hydr. Res. 32, 535 (1994)

    Article  Google Scholar 

  51. X. Huang, M.H. Garcia: J. Fluid Mech. 374, 305(1998)

    Article  MATH  ADS  Google Scholar 

  52. R.M. Iverson, M.E. Reid, R.G. LaHusen: Ann. Rev. Earth Planet Sci. 25, 85 (1997)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, School of Engineering, University of California, 95064, Santa Cruz, CA, USA

    N. J. Balmforth

  2. Department of Mathematics, Imperial College of Science, Technology and Medicine, SW7 2BZ, London, UK

    R. V. Craster

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  1. N. J. Balmforth
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  2. R. V. Craster
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Editors and Affiliations

  1. School of Engineering, University of California at Santa Cruz, 1156 High St., 95064, Santa Cruz, CA, USA

    N. J. Balmforth

  2. Istituto di Scienze dell’Atmosfera e del Clima, CNR, Corso Fiume 4, 10133, Torino, Italy

    A. Provenzale

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Balmforth, N.J., Craster, R.V. (2001). Geophysical Aspects of Non-Newtonian Fluid Mechanics. In: Balmforth, N.J., Provenzale, A. (eds) Geomorphological Fluid Mechanics. Lecture Notes in Physics, vol 582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45670-8_2

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  • DOI: https://doi.org/10.1007/3-540-45670-8_2

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  • Print ISBN: 978-3-540-42968-5

  • Online ISBN: 978-3-540-45670-4

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