Phenomenological Coefficients of Water

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


This chapter is based on the work done by Hutter and Trösch [35] and extensions of it. We shall list the phenomenological coefficients which describe water as a heat-conducting viscous fluid.


Pure Water Dynamic Viscosity Salt Water Newtonian Fluid Bulk Viscosity 
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  1. 1.
    ASME-Steam-Tables.: Thermodynamic and Transport Properties of Steam. ASME, New York, NY (1967)Google Scholar
  2. 2.
    Assur, A.: Composition of Sea Ice and Its Tensile Strength. National Academy of Sciences, National Research Council, Washington, DC vol. 598 (1958)Google Scholar
  3. 3.
    Barrett, T. and Nettleton, H.R.: Thermal conductivity of liquids and solids. In: Vol. V of International Critical Tables of Numerical Data, Physics, Chemistry and Technology, (Ed. E.W. Washburn), McGraw-Hill Book Co. Inc., New York, pp. 218–233 (1929)Google Scholar
  4. 4.
    Batchelor, G.K.: Slender body theory for particles of arbitrary cross section in Stokes-flow. J. Fluid Mech. 44, 419 (1970)CrossRefGoogle Scholar
  5. 5.
    Batchelor, G.K.: The stress system in a suspension of forced particles. J. Fluid Mech. 41, 545 (1970)CrossRefGoogle Scholar
  6. 6.
    Batchelor, G.K.: Sedimentation in a dilute suspension of spheres. J. Fluid Mech. 52, 245 (1972)CrossRefGoogle Scholar
  7. 7.
    Batchelor, G.K.: Transport properties of two-phase materials with random structure. Annu. Rev. Fluid Mech. 6, 227 (1974)CrossRefGoogle Scholar
  8. 8.
    Batchelor, G.K. and Green, J.T.: The hydrodynamic interaction of two small freely moving spheres in a linear flow field. J. Fluid Mech. 56, 375 (1972)CrossRefGoogle Scholar
  9. 9.
    Batchelor, G.K. and Green, J.T.: The determination of the bulk stress in a suspension of spheres to order c 2. J. Fluid Mech. 56, 401 (1972)CrossRefGoogle Scholar
  10. 10.
    Bingham, E.C. and Jackson, R.F. Standard Substances for the calibration of viscometers. Bull. US Bur. Stand. 14(298), 59 (1917)Google Scholar
  11. 11.
    Bowman, H.A. and Schoonover, R.M.: Procedure for high precision density determinations by hydrostatic weighing. J. Res. Natl. Bur. Stand. 71c(3), 179 (1967)Google Scholar
  12. 12.
    Bradshaw A. and Schleicher K.E.: Direct measurement of thermal expansion of sea water under pressure. Deep Sea Res. 17(4), 691–706 (1970)Google Scholar
  13. 13.
    Bromley, L.A., Desaussure, V.A., Clipp, J.C. and Wright, J.S.: Heat capacities of sea water solutions. J. Chem. Eng. Data 12(2), 202–206 (1967)CrossRefGoogle Scholar
  14. 14.
    Bromley L.A., Diamond A.E., Salami E. and Wilkins D.C.: Heat capacities and enthalpies of sea salt solutions to 200 \(^{\circ}\)C. J. Chem. Eng. Data 15(2), 246–253 (1970)CrossRefGoogle Scholar
  15. 15.
    Bührer, H. and Ambühl, H.: Die Einleitung von gereinigtem Abwasser in Seen. Interner Bericht der Eidg. Anstalt für Wasserversorgung, Abwasserreinigung und Gewässerschutz. Dübendorf, Switzerland (1975)Google Scholar
  16. 16.
    Camp, T.R.: Water and its Impurities. Reinhold, New York, NY (1963)Google Scholar
  17. 17.
    Castelli, V.J., Stanley, E.M. and Fischer, E.C.: The thermal conductivity of seawater as a function of pressure and temperature. Deep Sea Res. 21(4), 311–319 (1974)Google Scholar
  18. 18.
    Chapman, S. and Cowling, T.G.: Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge (1939)Google Scholar
  19. 19.
    Chen, C.T. and Millero, F.J.: Precise thermodynamic properties for natural waters covering only the limnological range. Limnol. Oceanogr. 31, 657–662 (1986)CrossRefGoogle Scholar
  20. 20.
    Cox, R.A. and Smith, N.D.: The specific heat of sea water. Proc. R. Soc. Lond. 252A, 51–62 (1959)Google Scholar
  21. 21.
    Defant, A.: Physical Oceanography. Vol. I, Pergamon, New York, NY (1961)Google Scholar
  22. 22.
    Dorsey, N.E.: Properties of Ordinary Water Substance. Reinhold, New York, NY (1940)Google Scholar
  23. 23.
    Einstein, A.: Eine neue Bestimmung der Moleküldimensionen. Ann. d. Phys. 29, 298 (1906)Google Scholar
  24. 24.
    Einstein, A.: Berichtigung zu meiner Arbeit Eine neue Bestimmung der Moleküldimensionen. Ann. d. Phys. 34, 591 (1911)CrossRefGoogle Scholar
  25. 25.
    Ekman, V.W.: Die Zusammendrückbarkeit des Meerwassers. Publ. Circonst. Cons. Perm. Inst. Explor. Mer. 43, 1 (1908)Google Scholar
  26. 26.
    Ekman, V.W.: Der adiabatische Temperaturgradient im Meere. Ann. d. Hydrogr. u. Mar. Meteor. 42(1), 340–44 (1914)Google Scholar
  27. 27.
    Emerson, W.H. and Jamieson, D.T.: Some physical properties of sea water in various concentrations. Desalination 3(2), 213–224 (1967)CrossRefGoogle Scholar
  28. 28.
    Fabuss, B.M.: Thermophysical Properties of Saline Water System Research and Development Progress. U.S. Department of the Interior, Office of Saline Water, Report No 189, May (1966)Google Scholar
  29. 29.
    Fabuss, B.M. and Corosi, A.: Office Saline Water Research, Development Progress Report No 384 (1968)Google Scholar
  30. 30.
    Fabuss, B.M. and Corosi, A.: Viscosities of aqueous solutions of several electrolytes present in sea water. J. Chem. Eng. Data 14, 192 (1969)CrossRefGoogle Scholar
  31. 31.
    Fofonoff, N.P.: Physical properties of sea water. In: The Sea, Physical Oceanography. Vol. 1 (ed. Hill, M. N., London: Interscience, pp. 3–30 (1962)Google Scholar
  32. 32.
    Hall, L.: The origin of excess ultrasonic absorption in water. Phys. Rev. 73, 775 (1948)CrossRefGoogle Scholar
  33. 33.
    Handbook of Chemistry and Physics (44th Edition) ed. by C.D. Hodgman, Chemical Rubber Publishing Company, Cleveland, OH (1962)Google Scholar
  34. 34.
    Henderson-Sellers, B.: Engineering Limnology. Pitman, Boston, MA, 1–265, 356 p. (1984)Google Scholar
  35. 35.
    Hutter, K. and Trösch, J.: Über die hydrodynamischen und thermodynamischen Grundlagen der Seezirkulation. Mitteilung Nr 20 der Versuchsanstalt für Wasserbau, Hydroligie und Glaziologie an der ETHZ (ed. Vischer, D.), Zürich, 164 p. (1975)Google Scholar
  36. 36.
    Imboden, D.M. and Wüest, A.: Mixing mechanisms in lakes. In: Physics and Chemistry of Lakes. (eds. Lerman, A., Imboden, D.M. and Gat, J.R.), Springer, Berlin, 83–138 (1995)Google Scholar
  37. 37.
    Isdale, J.D. and Morris, R.: Physical properties of sea water solutions. Desalination 10, 329–338 (1972)CrossRefGoogle Scholar
  38. 38.
    Isdale, J.D., Spence, C.M. and Thudhope, J.S.: Physical properties of sea water solutions. Desalination 10, 319–328 (1972)CrossRefGoogle Scholar
  39. 39.
    Jäger, W. and Steinwehr, H.: Thermal Capacity of Water between 5° and 50°. Sitzungsber. Preuss. Akad. Wiss. Berlin, 424–432 (1915)Google Scholar
  40. 40.
    Jeffrey, D.J.: Group expansions for the bulk properties of a statistically homogeneous random suspension. Proc. R. Soc. Lond. 338A, 503 (1974)Google Scholar
  41. 41.
    Jeffrey, G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond., 102A, 161 (1922)Google Scholar
  42. 42.
    Kearsley, E.A.: An analysis of an absolute torsional pendulum viscometer. Trans. Soc. Rheol. 3, 69 (1959)CrossRefGoogle Scholar
  43. 43.
    Knudsen, M.: Hydrographical Tables. Gad. Copenhagen and Williams Margate, London, 1–63 (1901)Google Scholar
  44. 44.
    Krümmel, O.: Handbuch der Ozeanographie. Bd. 1, Engelhorn, Stuttgart (1907)Google Scholar
  45. 45.
    Kuwahara, S.: The velocity of sound in sea water and calculation of the velocity for use in sonic sounding. Jpn. J. Astron. Geophys., 16(1), 1 (1938)Google Scholar
  46. 46.
    Lin, C.H., Perry, J.H. and Schowalter, W.R.: Simple shear flow round a rigid sphere: Inertial effects and suspension rheology. J. Fluid Mech. 44, 1 (1970)CrossRefGoogle Scholar
  47. 47.
    Marvin, R.S.: The accuracy of measurements of viscosity of liquids. J. Res. Natl. Bur. Stand. 75A(6), 535 (1971)CrossRefGoogle Scholar
  48. 48.
    Maxwell, J.C.: Electricity and Magnetism. (1st Edition), Clarendon Press, Oxford, 365 p. (1873)Google Scholar
  49. 49.
    Millero F.J. and Kubinski T.: Speed of sound in seawater as a function of of temperature and salinity at 1 atm. J. Acoust. Soc. Am. 57(2), 312–319 (1961)CrossRefGoogle Scholar
  50. 50.
    Millero, F.J., Perron, G. and Desnoyers, J.E.: Heat capacity of seawater solutions. J. Geophys. Res. 78(21), 4499–4507 (1973)CrossRefGoogle Scholar
  51. 51.
    Miyake, Y. and Koizumi, M.: The measurement of the viscosity coefficient of sea water. J. Mar. Res. 7(2), 63 (1948)Google Scholar
  52. 52.
    Montgomery, R.B.: Oceanographic Data. American Institute of Physics Handbook. Sec. 2, Mechanics. McGraw Hill, New York, NY, 115–124 (1957)Google Scholar
  53. 53.
    Newton, M. and Kennedy, G.: An experimental study of the P-V-T-S relatioins in sea water. J. Mar. Res. 23, 88 (1965)Google Scholar
  54. 54.
    Penn, R.W. and Kearsley, E.A.: An absolute determination of viscosity using channel flow. J. Res. Natl. Bur. Stand. 75(6), 553 (1971)Google Scholar
  55. 55.
    Poiseuille, J.: Recherches experimentales sur le movement des liquids dans les tubes de très petits diamters. Compt. Rend. 11, 961 (1840), 12, 1041 (1841)Google Scholar
  56. 56.
    Ponizovsky, A.M., Meleshko, E.P. and Globina, N.I.: Viscosity and specific heat capacity of sea water and natural solutions. Proc. Crimea Branch Rus. Acad. Sci. 4(1), 75–80 (1953) (in Russian)Google Scholar
  57. 57.
    Popov, N.I., Fedorov, K.N. and Orlov, V.M.: Marine Water. Nauka, Moscow, 328 p. (1979)Google Scholar
  58. 58.
    Riedel, L.: Die Wärmeleitfähigkeit von wässrigen Lösungen starker Elektrolyte. Chem. Ing. Technik 23(3), 59–64 (1951)CrossRefGoogle Scholar
  59. 59.
    Shimaraev M.N., Verbolov V.I., Granin N.G. and Sherstyankin P.P.: Physical Limnology of Lake Baikal: A Review. (Eds. Shimaraev, M.N., Okuda, S.) Baikal International Center for Ecological Research Irkutsk-Okayama. 89 p. (1994)Google Scholar
  60. 60.
    Stein, W.A.: Gleichungen für die dynamische Viskosität und Wärmeleitfähigkeit von reinem fluidem Wasser. Wärme- und Stoffübertragung 2, 210 (1969)CrossRefGoogle Scholar
  61. 61.
    Stein, W.A.: Das erweiterte Korresponndenzprinzip für die dynamische Idealviskosität und die Idealwärmeleitfähigkeit reiner Stoffe. Wärme- und Stoffübertragung 4, 127 (1971)CrossRefGoogle Scholar
  62. 62.
    Stokes, R.H. and Mills, R.: Viscosity of electrolytes and related properties. Int. Encycl. phys. chem. chem. phys., 3, 16, Pergamon, London (1965)Google Scholar
  63. 63.
    Taylor, G.I.: The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. 138A, 41 (1932)Google Scholar
  64. 64.
    Thoulet, J. and Chevallier, A.: Sur la chaleur specifique de l’eau de mer a divers degres de dilution et de concentration. C. R. Acad. Sci. Paris 108(15), 794–796 (1889)Google Scholar
  65. 65.
    Tilton, L.W. and Taylor, J.K.: Accurate representation of the refractivity and density of distilled water as a function of temperature. J. Res. Natl. Bur. Stand. 18, 205 (1937)CrossRefGoogle Scholar
  66. 66.
    Truesdell, C.A. and Muncaster, R.G.: Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas. Academic, New York, NY, XXVIII+593 p. (1980)Google Scholar
  67. 67.
    Tufeu, R.: Etude expérimental en fonction de la température et de la conductivité thermique de l’ensemble des gaz rares et de mélanges hélium-argon. Ph.D. thesis, Université de Paris VI, 120 p., 47 figures, XIV tables (1971)Google Scholar
  68. 68.
    Wang D.P. and Millero F.J.: Precise representation of the P-V-T properties of water and sea water determined from sound speeds. J. Geophys. Res. 78(30), 7122–7128 (1973)CrossRefGoogle Scholar
  69. 69.
    Wilson, W. and Bradley, D.: An absolute determination of viscosity using a torsional pendulum. Deep Sea Res. 15, 355 (1968)Google Scholar
  70. 70.
    White, H.S. and Kersley, E.A.: An absolute determination of viscosity using a torsional pendulum. J. Res. Natl. Bur. Stand. 75A(6), 541 (1971)CrossRefGoogle Scholar
  71. 71.
    Zubov, N.N.: Oceanological Tables. Hydrometeoizdat, Leningrad, 126 p. (1957) (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.ETH Zürich, c/o Versuchsanstalt für Wasserbau Hydrologie und GlaziologieZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  3. 3.Russian Academy of Sciences, P.P. Shirshov Institute of OceanologyKaliningradRussia

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