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Flow in porous media

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Theoretical and Applied Mechanics

Part of the book series: IUTAM Symposia ((IUTAM))

Abstract

The problems of flow and transport in porous media present many fascinating challenges to students of mechanics: and it is surprising that, over the years, these questions have received relatively little attention at the Congresses and Symposia of IUTAM and of its predecessors. The 1964 Grenoble Symposium (Kravtchenko and Sirieys 1966) touched on certain special aspects and the 1966 Vienna Symposia (Parkus and Sedov 1968) had some relevance; but the first specific involvement of the Union with flow in porous media was a useful but limited meeting, sponsored jointly by IUTAM and IUGG, at Calgary in 1971.

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References

  • Benjamin, T. B., Mahony, J. J.: J. Fluid Mech. 49 (1971) 385–390.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Blasius, H.: Z. Math. u. Phys. 56 (1908) 1–37.

    Google Scholar 

  • Bolt, G. H.: Geotechnique 6 (1956) 86–93.

    Article  Google Scholar 

  • Boltzmann, L.: Ann. Phys. (Leipzig) 53 (1894) 959–964.

    Google Scholar 

  • Braester, C., Dagan, G., Neuman, S., Zaslavsky, D.: A survey of the equations and solutions of unsaturated flow in porous media. Rep. Hydrodynamics Hydr. Eng. Lab., Technion, Israel (1971).

    Google Scholar 

  • Buckingham, E.: U.S. Dept. Agr. Bur. Soils Bull. 38 (1907).

    Google Scholar 

  • —: Phys. Rev. Ser. 2, 4 (1914) 345–376.

    Article  ADS  Google Scholar 

  • Burgers, J. M.: Adv. Appl. Mech. 1 (1948) 171–199.

    Article  MathSciNet  Google Scholar 

  • Childs, E. C.: Soil Sci. 97 (1964) 173–178.

    Article  Google Scholar 

  • —, George, N. C.: Disc. Faraday Soc. 3 (1948) 78–85.

    Article  Google Scholar 

  • —, Collis-George, N.: Advan. Agron. 2 (1950) 233–272.

    Article  Google Scholar 

  • —: Proc. Roy. Soc. A 201 (1951) 392–405.

    ADS  Google Scholar 

  • Cole, J. D.: Proc. 6th U.S. Nat. Congr. Appl. Mechs. (1970). 3–10

    Google Scholar 

  • Coleman, J. D., Croney, D.: Road Res. Lab. Note RN/1709/JDC.DC (unpublished) (1952).

    Google Scholar 

  • Collis-George, N.: Soil Sci. 91 (1961) 306–311.

    Article  Google Scholar 

  • Cowan, I. R.: J. Appl. Ecol. 2 (1965) 221–239.

    Article  Google Scholar 

  • Croney, D., Coleman, J. D., Bridge, P. M.: Road Res. Tech. Paper 24 (1952).

    Google Scholar 

  • Day, P. R., Luthin, J. N.: Soil Sci. Soc. Amer. Proc. 20 (1956) 443–447.

    Google Scholar 

  • Drake, R. L. Ellingson, N. B.: J. Comp. Phys. 6 (1970) 200–218.

    Article  ADS  MATH  Google Scholar 

  • Edlefsen, N. E., Anderson, A. B. C.: Hilgardia 16 (1943) 31–299.

    Google Scholar 

  • Fried, J. J., Combarnous, M. A.: Adv. Hydroscience 7 (1971) 169–182.

    Google Scholar 

  • Gardner, W. R.: Soil Sci. 89 (1960) 63–73.

    Article  Google Scholar 

  • Gersevanov, N.M.: The foundations of dynamics of soils. Stroiizdat: Moscow-Lsningrad, 3rd Ed. (1937).

    Google Scholar 

  • Green, W. H., Ampt, G. A.: J. Agr. Sci. 4 (1911) 1–24.

    Article  Google Scholar 

  • Groenevelt, P. H., Bolt, G. H.: Soil Sci. 113 (1972) 238–245.

    Article  Google Scholar 

  • Hartley, G. S., Crank, J.: Trans. Faraday Soc. 45 (1949) 801–818.

    Article  Google Scholar 

  • Hill, D.E., Parlange, J.-Y.: Soil Sci. Soc. Amer. Proc. 36 (1972) 697–702.

    Google Scholar 

  • Holmes, J. W., Taylor, S. A., Richards, S. J.: pp. 275 — 303 of Irrigation of Agricultural Lands (eds. Hagen, R. M., Haise, H. R., Edminster, T. W.): Amer. Soc. Agronomy, Madison (1967).

    Google Scholar 

  • Howarth, L.: Proc. Roy. Soc. A 164 (1938) 547–579.

    Article  ADS  MATH  Google Scholar 

  • Keen, N. A.: The physical properties of the soil. London: Longmans (1931).

    Google Scholar 

  • Kirchhoff, G.: Vorlesungen über die Theorie der Wärme. Leipzig: Barth (1894).

    Google Scholar 

  • Klute, A.: Soil Sci. 73 (1951) 105–116.

    Article  Google Scholar 

  • Knight, J. H., Philip, J. R.: On solving the unsaturated flow equation: 2. Critique of Parlange’s method. Soil. Sci. (in press) (2974).

    Google Scholar 

  • Kravtchenko, J., Sirieys, P. M.: (eds).IUTAM Symposium Grenoble Berlin: Springer (1966).

    Google Scholar 

  • Lane, W. R., Green, H. L.: pp. 162 — 215 of Surveys in Mechanics (eds.: Batchelor, G. K., Davies, R. M.). Cambridge: University Press (1956).

    Google Scholar 

  • Lighthill, M. J.: pp. 250–251 of Surveys in Mechanics (eds. Batchelor, G. K., Davies, R. M.). University Press: Cambridge (1956).

    Google Scholar 

  • Macey, R. I.: Bull. Math. Biophys. 21 (1959) 19–32.

    Article  MathSciNet  Google Scholar 

  • McNabb, A.: Q. Appl. Math. 17 (1960) 337–347.

    MathSciNet  MATH  Google Scholar 

  • Mahony, J. J.: Bull. Australian Math. Soc. 7 (1972) 77–89.

    Article  MATH  Google Scholar 

  • Marshall, T. J.: Relations between water and soil. Commonwealth Agricult. Bureau: Farnham Royal (1959).

    Google Scholar 

  • Miller, E. E., Klute, A: pp. 209–244 of Irrigation of Agricultural Lands (eds.: Hagen, R., M. Haise, H. R., Edminster, T. W). Amer. Soc. Agronomy: Madison (1967).

    Google Scholar 

  • Miller, E. E., Miller, R. D.: J. Appi. Phys. 27 (1956) 324–332.

    Article  ADS  Google Scholar 

  • Molière (Poquelin, J. B.): Le Bourgeois gentilhomme. Paris: Le Monnier 1671.

    Google Scholar 

  • Moore, R. E.: Hilgardia 12 (1939) 383–426.

    Google Scholar 

  • Parkus, H., Sedov, L. I.: (eds.) IUTAM Symposium Vienna. Wien: Springer (1968).

    Google Scholar 

  • Parlange, J.-Y.: Soil Sci. Ill (1971a) 134–137

    Article  Google Scholar 

  • —: Soil Sci. Ill (1971b) 170–174.

    Article  Google Scholar 

  • —: Soil Sci. 112 (1971c) 313–317.

    Article  Google Scholar 

  • Philip, J. R.: J. Inst. Engrs. Australia 26 (1954) 255–259.

    Google Scholar 

  • —: Proc. Natn. Acad. Sci. India (Allahabad) 24A (1955a) 93–104.

    Google Scholar 

  • —: Trans. Faraday Soc. 51 (1955b) 885–892.

    Article  MathSciNet  Google Scholar 

  • —: Proc. 3rd. Int. Congr. Irrig. Drainage, San Francisco 8.125–8.154 (1957a).

    Google Scholar 

  • —: Australian J. Phys. 10 (1957b) 43–53.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • —: Soil Sci. 83 (1957c) 345–357.

    Article  Google Scholar 

  • —: Soil Sci. 83 (1957d) 435–448.

    Article  Google Scholar 

  • —: Soil Sci. 84 (1957e) 163–178.

    Article  Google Scholar 

  • —: Soil Sci. 84 (1957f) 257–264.

    Article  Google Scholar 

  • —: Soil Sci. 84 (1957g) 329–339.

    Article  Google Scholar 

  • —: J. Meteorology 14 (1957h) 354–366.

    Article  Google Scholar 

  • —: Proc. 2nd Australian Conf. Soil Sci. 1 (1957i) 63.1–63.9.

    Google Scholar 

  • —: Trans. Amer. Geophys. Un. 38 (1957j) 782–784.

    Google Scholar 

  • —: Soil Sci. 85 (1958a) 278–286.

    Article  Google Scholar 

  • —: Soil Sci. 85 (1958b) 333–337.

    Article  Google Scholar 

  • —. spec. Rep. Highway. Res. Board, Washington 40 (1958c) 147–163.

    Google Scholar 

  • —: Australian J. Phys. 13 (1960) 1–12.

    MathSciNet  ADS  MATH  Google Scholar 

  • —: Symposium Wageningen, UNESCO 1 (1966a) 503–525.

    Google Scholar 

  • —: Symposium Wageningen, UNESCO 2 (1966b) 559–564.

    Google Scholar 

  • —: Symposium Wageningen, UNESCO 1 (1966c) 471–478.

    Google Scholar 

  • —: Review No. 1457. Appi. Mech. Rev. 21 (1968a) 205.

    Google Scholar 

  • —: Australian J. Soil Res. 6 (1968b) 1–19.

    Article  Google Scholar 

  • —: Australian J. Soil Res. 6 (1968c) 21–30.

    Article  Google Scholar 

  • —: Australian J. Soil Res. 6 (1968d) 249–267.

    Article  Google Scholar 

  • —: Water Resources Res. 4 (1968e) 1039–1047.

    Article  ADS  Google Scholar 

  • —: Adv. Hydroscience 5 (1969a) 214–296.

    Google Scholar 

  • —: Australian J. Soil Res 7 (1969b) 99 — 120.

    Google Scholar 

  • —: Australian J. Soil Res. 7 (1969c) 121–141.

    Article  Google Scholar 

  • —: Water Resources Res. 5 (1969d) 1070–1077.

    Article  ADS  Google Scholar 

  • —: pp. 25–48 of Circulatory and Respiratory Mass Transport. Symposium Ciba Fdn. (eds. Wolstenholme, G.E.W., Knight, J.) London: Churchill (1969e).

    Google Scholar 

  • —: Australian J. Soil Res. 7 (1969f) 213–221.

    Article  Google Scholar 

  • —: Soil Sci. 109 (1970a) 294–298.

    Article  Google Scholar 

  • —: Ann. Rev. Fluid Mech. 2 (1970b) 177–204.

    Article  ADS  Google Scholar 

  • —: Water Resources Res. 6 (1970c) 1248–1251.

    Article  ADS  Google Scholar 

  • —: pp. 95 —107 of Salinity and Water Use (eds. Talsma, T, Philip, J. R.). London: Macmillan (1971a).

    Google Scholar 

  • —: Soil Sci. Soc. Amer. Proc. 35 (1971b) 867–871.

    Google Scholar 

  • —: Soil Sci. 113 (1972a) 294–300.

    Article  Google Scholar 

  • —: ZAMP 23 (1972b) 353–372.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • —: ZAMP 23 (1972c) 960–968.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • —: Soil Sci. Soc. Amer. Proc. 36 (1972d) 268–273.

    Google Scholar 

  • —: Proc. 8th Int. Congr. Irrig. Drainage, Varna. C.13-C.28 (1972e).

    Google Scholar 

  • —: On solving the unsaturated flow equation: 1. The flux-concentration relation. Soil Sci. (in press) (1973).

    Google Scholar 

  • —, Knight, J. H.: On solving the unsaturated flow equation: 3. New quasi-analytical technique. Soil Sci. (in press) (1974).

    Google Scholar 

  • —, de Vries, D. A.: Trans. Amer. Geophys. Un. 38 (1957) 222–232.

    Google Scholar 

  • —, Smiles, D. E.: Australian J. Soil Res. 7 (1969) 1–19.

    Article  Google Scholar 

  • Pohlhausen, K.: ZAMM 1 (1921) 252–268.

    Article  ADS  Google Scholar 

  • Polubarinova-Kochina, P. Ya.: Theory of Ground Water Movement. Gosizdat. Tekhn.-teor. Liter.: Moscow 1952.

    Google Scholar 

  • Prager, S.: J. Chem. Phys. 21 (1953) 1344–1347.

    Article  ADS  Google Scholar 

  • Raats, P. A. C.: Development of equations describing transport of mass and momentum in porous media, with special reference to soils. Doctoral thesis, Univ. of Illinois 1965.

    Google Scholar 

  • —: Soil Sci. Soc. Amer. Proc. 34 (1970) 709–714.

    Google Scholar 

  • —: Soil Sci. Soc. Amer. Proc. 35 (1971) 689–694.

    Google Scholar 

  • —: Soil Sci. Soc. Amer. Proc. 36 (1972) 399–401.

    Google Scholar 

  • Richards, L. A.: Physics 1 (1931) 318–333.

    Article  ADS  MATH  Google Scholar 

  • —: Soil Sci. 68 (1949) 95–112.

    Article  Google Scholar 

  • —: Desert Research. Res. Council Israel Spec. Rep. 2 (1965) 523–546.

    Google Scholar 

  • Rose, C. W.: Agricultural Physics. London: Pergamon Press 1966.

    Google Scholar 

  • — Stern, W. R., Drummond, J. E.: Australian J. Soil Res. 3 (1965) 1–9.

    Article  Google Scholar 

  • Schofield, R. K.: Trans. 3rd Congr. Soil Sci. 1 (1935a) 30–33.

    Google Scholar 

  • —: Trans. 3rd Int. Congr. Soil Sci. 2 (1935 b) 37–48.

    Google Scholar 

  • Scotter, D. R., Raats, P. A. C.: Soil Sci. 109 (1970) 170–178.

    Article  Google Scholar 

  • Sedov, L. I.: A Course in Continuum Mechanics, Vol. 1. Groningen: Wolters-Noordhof (1971).

    MATH  Google Scholar 

  • Smiles, D. E., Rosenthal, M. J.: Australian J. Soil Res. 6 (1968) 237–248.

    Article  Google Scholar 

  • Staple, W. J., Lehane J. J.: Canadian J. Agr. Sci. 34 (1954) 329–342.

    Google Scholar 

  • Taylor, G. I.: Proc. Roy. Soc. A 84 (1910) 371–377.

    Article  ADS  MATH  Google Scholar 

  • Terzaghi, K.: Sitzb. Akad. Wiss. Wien. Abt 2 a, 132 (1923) 125–138.

    Google Scholar 

  • Truesdell, C., Noll, W.: The non-linear field theories of mechanics. Handbuch der Physik III/3. Berlin: Springer (1965).

    Google Scholar 

  • Van Dyke, M.: Perturbation Methods in Fluid Mechanics. New York: Academic Piess (1964).

    MATH  Google Scholar 

  • Vries, D. A. de: Trans. Amer. Geophys. Un. 39 (1958) 909–916.

    Google Scholar 

  • Philip, J. R.: J. Geophys. Res. 64 (1959) 386–388.

    Article  ADS  Google Scholar 

  • Whisler, F. D., Watson, K. K.: J. Hydrol. 6 (1968) 277–296.

    Article  ADS  Google Scholar 

  • Wooding, R. A.: Water Resources Res. 4 (1968) 1259–1273.

    Article  ADS  Google Scholar 

  • Yuster, S. T.: Proc. 3rd World Petroleum Congr. The Hague II (1951) 437–445.

    Google Scholar 

  • Zaslavsky, D.: Soil Sci. 106 (1968) 358–362.

    Article  Google Scholar 

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Philip, J.R. (1973). Flow in porous media. In: Becker, E., Mikhailov, G.K. (eds) Theoretical and Applied Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65590-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-65590-6_18

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