An extension of the capillary and thin film flow model for predicting the hydraulic conductivity of air-free frozen porous media

Water Resources Research

Volumn 48, Issue 7, 2012, Pages

  Lebeau, Marc ^a   Konrad, Jean Marie ^a  

^a UNIVERSITÉ LAVAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FREEZING POINT; HYDRODYNAMIC MODEL; MODEL PARAMETERS; MODEL RESULTS; MODERN SCIENCE; PREDICTIVE MODELS; PURE WATER; SOLID PARTICLES; THERMAL EQUILIBRIUMS; THIN FILM FLOW; THIN INTERLAYERS; THIN LIQUIDS; WATER FREEZING; WATER RETENTION; WATER TRANSPORT;

FREEZING; HYDRAULIC CONDUCTIVITY; ICE; THIN FILMS; VAN DER WAALS FORCES;

POROUS MATERIALS;

CAPILLARITY; FILM; FLOW MODELING; FREEZING; HYDRAULIC CONDUCTIVITY; HYDRODYNAMICS; HYDROGEOLOGY; ICE FREE CORRIDOR; LOW TEMPERATURE; NUMERICAL MODEL; POROUS MEDIUM;

EID: 84864556536     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2012WR011916     Document Type: Article

References (78)

1. Aguirre-Puente, J., and J. Gruson (1983), Measurement of permeabilities of frozen soils, in Fourth International Conference on Permafrost, pp. 5-9, National Acad. of Sci., Fairbanks, Alaska.
2. Andersland, O. B., D. C. Wiggert, and S. H. Davies (1996), Hydraulic conductivity of frozen granular soils, J. Environ. Eng., 122(3), 212-216, doi:10.1061/(ASCE)0733-9372(1996)122:3(212). (Pubitemid 28077207)
3. Anderson, D. M. (1967), The interface between ice and silicate surfaces, J. Colloid Interface Sci., 25(2), 174-191, doi:10.1016/0021-9797(67) 90021-5.
4. Anderson, D. M., and P. Hoekstra (1965), Crystallization of clay-Adsorbed water, Science, 149(3681), 318-319.
5. Anderson, D. M., and N. R. Morgenstern (1973), Physics, chemistry, and mechanics of frozen ground: A review, in Second International Conference on Permafrost, North American Contribution, pp. 257-288, National Acad. of Sci., Yakutsk, USSR.
6. Bird, R. B., W. E. Stewart, and E. N. Lightfoot (1960), Transport Phenomena, 780 pp., John Wiley, N. Y.
7. Bittelli, M., M. Flury, and G. S. Campbell (2003), A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media, Water Resour. Res., 39(2), 1041, doi:10.1029/2001WR000930.
8. Black, P. B. (1995), Applications of the Clapeyron equation to water and ice in porous media, CRREL Report 95-6, 7 pp., U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H.
9. Black, P. B., and R. D. Miller (1990), Hydraulic conductivity and unfrozen water content of air-free frozen silt, Water Resour. Res., 26(2), 323-329, doi:10.1029/93WR02676.
10. Bouyoucos, G. J. (1915), Effects of temperature on some of the most important physical processes in soils, Tech. Bull. 22, Michigan Coll. of Agriculture, Exp. Station., East Lansing, Michigan, 63 pp.
11. Bouyoucos, G. J. (1917), Measurement of the inactive, or unfree, moisture in the soil by means of the dilatometer method, J. Agric. Res., 8(6), 195-217.
12. Brooks, R. H., and A. T. Corey (1964), Hydraulic properties of porous media, in Hydrology Paper 3, pp. 1-27, Colorado State Univ., Fort Collins, Colo.
13. Brutsaert, W. (1967), Some methods of calculating unsaturated permeability, Trans. ASAE, 10(3), 400-404.
14. Burt, T. P., and P. J. Williams (1976), Hydraulic conductivity in frozen soils, Earth Surf. Processes, 1(4), 349-360, doi :10.1002/esp.3290010404.
15. Campbell, G. S., and S. Shiozawa (1992), Prediction of hydraulic properties of soils using particle-size distribution and bulk density data, in Proceedings of the International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, edited by M. T. van Genuchten, F. J. Leij, and L. J. Lund, pp. 317-328, Univ. of California, Riverside, Calif.
16. Churaev, N. V. (2004), Mass transfer in frozen porous bodies, Colloid J., 66(6), 751-755, doi:10.1007/s10595-005-0018-3. (Pubitemid 40329277)
17. Churaev, N. V., S. A. Bardasov, and V. D. Sobolev (1993), On the nonfreezing water interlayers between ice and a silica surface, Colloids Surf., A, 79(1), 11-24, doi:10.1016/0927-7757(93)80155-8.
18. Côp, A., and N. Kallay (2004), Surface potential of ice in aqueous electrolyte solutions, in Trends in Colloid and Interface Science XVII, edited by V. Cabuil, P. Leviz, and C. Treiner, pp. 83-85, Springer, Berlin, Germany.
19. Dash, J. G., A. W. Rempel, and J. S. Wettlaufer (2006), The physics of premelted ice and its geophysical consequences, Rev. Mod. Phys., 78(3), 695-741, doi:10.1103/RevModPhys.78.695. (Pubitemid 44464360)
20. Derjaguin, B. V., and L. Landau (1941), Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes, Prog. Surf. Sci., 43(1-4), 30-59, doi :10.1016/ 0079-6816(93)90013-l.
21. Derjaguin, B. V., N. V. Churaev, and V. M. Muller (1987), Surface Forces, 440 pp., Consultants Bureau, N. Y.
22. Fayer, M. J., and C. S. Simmons (1995), Modified soil water retention functions for all matric suctions, Water Resour. Res., 31(5), 1233-1238, doi:10.1029/95WR00173. (Pubitemid 26437818)
23. Fisher, E. A. (1924), The freezing of water in capillary systems: A critical discussion, J. Phys. Chem., 28(4), 360-367, doi:10.1021/j150238a006.
24. Fukusako, S. (1990), Thermophysical properties of ice, snow, and sea ice, Int. J. Thermophys., 11(2), 353-372, doi:10.1007/bf01133567.
25. Gregory, J. (1975), Interaction of unequal double layers at constant charge, J. Colloid Interface Sci., 51(1), 44-51, doi:10.1016/0021-9797(75)90081- 8.
26. Hamaker, H. C. (1937), The London-van der Waals attraction between spherical particles, Physica, 4(10), 1058-1072, doi:10.1016/s0031- 8914(37)80203-7.
27. Hansen-Goos, H., and J. S. Wettlaufer (2010), Theory of ice premelting in porous media, Phys. Rev. E, 81(3), 031604, doi:10.1103/PhysRevE.81. 031604.
28. Hare, D. E., and C. M. Sorensen (1987), The density of supercooled water. II. Bulk samples cooled to the homogeneous nucleation limit, J. Chem. Phys., 87(8), 4840-4845, doi:10.1063/1.453710.
29. Harlan, R. L. (1973), Analysis of coupled heat-fluid transport in partially frozen soil, Water Resour. Res., 9(5), 1314-1323.
30. Hodge, I. M., and C. A. Angell (1978), The relative permittivity of supercooled water, J. Chem. Phys., 68(4), 1363-1368, doi:10.1063/1.435955.
31. Hoekstra, P., and E. Chamberlain (1964), Electro-osmosis in frozen soil, Nature, 203(4952), 1406-1407, doi:10.1038/2031406b0.
32. Hoekstra, P., and R. D. Miller (1967), On the mobility of water molecules in the transition layer between ice and a solid surface, J. Colloid Interface Sci., 25(2), 166-173, doi:10.1016/0021-9797(67)90020-3.
33. Hogg, R., T. W. Healy, and D. W. Fuerstenau (1966), Mutual coagulation of colloidal dispersions, Trans. Faraday Soc., 62, 1638-1651, doi:10.1039/ TF9666201638.
34. Horiguchi, K., and R. D. Miller (1980), Experimental studies with frozen soil in an "ice sandwich" permeameter, Cold Reg. Sci. Technol., 3(2-3), 177-183, doi:10.1016/0165-232x(80)90023-3. (Pubitemid 11421828)
35. Horiguchi, K., and R. D. Miller (1983), Hydraulic conductivity functions of frozen materials, in Fourth International Conference on Permafrost, pp. 504-508, National Acad. of Sci., Fairbanks, Alaska. (Pubitemid 14579373)
36. Jumikis, A. R. (1958), Some concepts pertaining to the freezing soil systems, Spec. Rep.-Natl. Res. Counc. Highw. Res. Board, 40, 178-190.
37. Khlosi, M., W. M. Cornelis, D. Gabriels, and G. Sin (2006), Simple modification to describe the soil water retention curve between saturation and oven dryness, Water Resour. Res., 42, W11501, doi:10.1029/ 2005WR004699.
38. Khlosi, M., W. M. Cornelis, A. Douaik, M. T. van Genuchten, and D. Gabriels (2008), Performance evaluation of models that describe the soil water retention curve between saturation and oven dryness, Vadose Zone J., 7(1), 87-96, doi:10.2136/vzj2007.0099. (Pubitemid 351362691)
39. Konrad, J.-M. (1999), Frost susceptibility related to soil index properties, Can. Geotech. J., 36(3), 403-417, doi:10.1139/t99-008. (Pubitemid 30149873)
40. Koopmans, R. W. R., and R. D. Miller (1966), Soil freezing and soil water characteristic curves, Soil Sci. Soc. Am. J., 30(6), 680-685, doi:10.2136/ sssaj1966.03615995003000060011x.
41. Kosugi, K. (1996), Lognormal distribution model for unsaturated soil hydraulic properties, Water Resour. Res., 32(9), 2697-2703, doi:10.1029/ 96WR01776.
42. Kudryavtsev, V. A., E. D. Yershov, and V. G. Cheverev (1978), Migration of moisture in fine-grained soil of different composition, structure, and properties, in Second International Conference on Permafrost, USSR Contribution, edited by F. J. Sanger, pp. 292-298, National Acad. of Sci., Yakutsk, USSR.
43. Langmuir, I. (1938), Repulsive forces between charged surfaces in water, and the cause of the Jones-Ray effect, Science, 88(2288), 430-432, doi:10.1126/science.88.2288.430.
44. Lebeau, M., and J.-M. Konrad (2010), A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 46(12),W12554, doi:10.1029/2010WR009092.
45. Liu, L., and I. Neretnieks (2008), Homo-interaction between parallel plates at constant charge, Colloids Surf., A, 317(1-3), 636-642, doi:10.1016/ j.colsurfa.2007.11.055.
46. Luo, G., H. Wang, and J. Jin (2001), Strong interaction of colloidal particles : An extension of Langmuir's method, Langmuir, 17(7), 2167-2171, doi:10.1021/la0013796. (Pubitemid 35330156)
47. Masliyah, J. H., and S. Bhattacharjee (2006), Electrokinetic and Colloid Transport Phenomena, 707 pp., John Wiley
48. Hoboken, N. J. McCauley, C. A., D. M. White, M. R. Lilly, and D. M. Nyman (2002), A comparison of hydraulic conductivities, permeabilities and infiltration rates in frozen and unfrozen soils, Cold Reg. Sci. Technol., 34(2), 117-125, doi:10.1016/s0165-232x(01)00064-7. (Pubitemid 34466089)
49. Miller, R. D. (1966), Phase equilibria and soil freezing, in First International Conference on Permafrost, pp. 193-197, National Acad. of Sci., Lafayette, IN.
50. Miller, R. D. (1980), Freezing phenomena in soil, in Application of Soil Physics, edited by D. Hillel, pp. 255-299, Academic, New York.
51. Miller, R. D., J. P. G. Loch, and E. Bresler (1975), Transport of water and heat in a frozen permeameter, Soil Sci. Soc. Am. J., 39(6), 1029-1036, doi:10.2136/sssaj1975.03615995003900060011x.
52. Morrison, I. D., and S. Ross (2002), Colloidal Dispersions: Suspensions, Emulsions and Foams, 616 pp., John Wiley, New York.
53. Mualem, Y. (1976), A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12(3), 513-522, doi:10.1029/WR012i003p00513.
54. Mualem, Y. (1986), Hydraulic conductivity of unsaturated soils : Prediction and formulas, in Methods of Soil Analysis: Part 1. Physical and Mineralogical Methods, edited by A. Klute, pp. 799-823, Am. Soc. of Agronomy and Soil Sci. Soc. of America, Madison, Wis.
55. Ohshima, H., T.W. Healy, and L. R.White (1982), Improvement on the Hogg- Healy-Fuerstenau formulas for the interaction of dissimilar double layers: I. Second and third approximations for moderate potentials, J. Colloid Interface Sci., 89(2), 484-493, doi:10.1016/0021-9797(82)90199-0.
56. Patterson, D. E., and M. W. Smith (1980), The use of time domain reflectometry for the measurement of unfrozen water content in frozen soils, Cold Reg. Sci. Technol., 3(2-3), 205-210, doi:10.1016/0165-232x(80) 90026-9.
57. Pennell, K. D. (2002), Specific surface area, in Methods of Soil Analysis: Part 4. Physical Methods, edited by J. Dane, H. Topp, and G. Clarke, pp. 295-315, Soil Sci. Soc. of America, Madison, Wis.
58. Perfect, E., and P. J. Williams (1980), Thermally induced water migration in frozen soils, Cold Reg. Sci. Technol., 3(2-3), 101-109, doi:10.1016/ 0165-232x(80)90015-4.
59. Peters, A., W. Durner, and G. Wessolek (2011), Consistent parameter constraints for soil hydraulic functions, Adv. Water Resour., 34(10), 1352-1365, doi:10.1016/j.advwatres.2011.07.006.
60. Resurreccion, A. C., P. Moldrup, M. Tuller, T. P. A. Ferré, K. Kawamoto, T. Komatsu, and L. W. de Jonge (2011), Relationship between specific surface area and the dry end of the water retention curve for soils with varying clay and organic carbon contents, Water Resour. Res., 47(6), W06522, doi:10.1029/2010WR010229.
61. Schofield, R. K. (1935), The pF of the water in soil, in Transactions of the 3rd International Congress of Soil Science, pp. 38-48, T. Murby, Oxford, U. K.
62. Schofield, R. K., and J. V. Botelho da Costa (1938), The measurement of pF in soil by freezing-point, J. Agric. Sci., 28(04), 644-653, doi:10.1017/ S0021859600051042.
63. Spaans, E. J. A., and J. M. Baker (1996), The soil freezing characteristic: Its measurement and similarity to the soil moisture characteristic, Soil Sci. Soc. Am. J., 60(1), 13-19, doi:10.2136/sssaj1996. 03615995006000010005x.
64. Tokunaga, T. K. (2009), Hydraulic properties of adsorbed water films in unsaturated porous media, Water Resour. Res., 45(6),W06415, doi :10.1029/ 2009WR007734.
65. Tokunaga, T. K. (2011), Physicochemical controls on adsorbed water film thickness in unsaturated geological media, Water Resour. Res., 47(8), W08514, doi:10.1029/2011WR010676.
66. Tuller, M., and D. Or (2005), Water films and scaling of soil characteristic curves at low water contents, Water Resour. Res., 41(9), W09403, doi:10.1029/2005WR004142. (Pubitemid 41552189)
67. van Genuchten, M. T. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44(5), 892-898, doi:10.2136/sssaj1980.03615995004400050002x.
68. Verwey, E. J. W., and J. T. G. Overbeek (1948), Theory of the Stability of Lyophobic Colloids, 205 pp., Elsevier, N. Y.
69. Watanabe, K., and M. Flury (2008), Capillary bundle model of hydraulic conductivity for frozen soil, Water Resour. Res., 44(12),W12402, doi:10.1029/ 2008WR007012.
70. Watanabe, K., and M. Mizoguchi (2002), Amount of unfrozen water in frozen porous media saturated with solution, Cold Reg. Sci. Technol., 34(2), 103-110, doi:10.1016/s0165-232x(01)00063-5. (Pubitemid 34466087)
71. Watanabe, K., and T. Wake (2008), Hydraulic conductivity in frozen unsaturated soil, in Ninth International Conference on permafrost, edited by D. L. Kane and K. M. Hinkel, pp. 1927-1932, Institute of Northern Engineering, Univ. of Alaska Fairbanks, Alaska.
72. Wettlaufer, J. S., and M. G. Worster (2006), Premelting dynamics, Annu. Rev. Fluid Mech., 38(1), 427-452, doi:10.1146/annurev.fluid.37.061903. 175758. (Pubitemid 43240183)
73. Wettlaufer, J. S., M. G. Worster, L. A. Wilen, and J. G. Dash (1996), A theory of premelting dynamics for all power law forces, Phys. Rev. Lett., 76(19), 3602, doi:10.1103/PhysRevLett.76.3602.
74. Wilen, L. A., and J. G. Dash (1995), Frost heave dynamics at a single crystal interface, Phys. Rev. Lett., 74(25), 5076-5079, doi:10.1103/ PhysRevLett.74.5076.
75. Wilen, L. A., J. S. Wettlaufer, M. Elbaum, and M. Schick (1995), Dispersion- force effects in interfacial premelting of ice, Phys. Rev. B, 52(16), 12426-12433, doi:10.1103/PhysRevB.52.12426.
76. Williams, P. J. (1966), Suction and its effects in unfrozen water of frozen soils, in First International Conference on Permafrost, pp. 225-229, National Acad. of Sci., Lafayette, IN.
77. Williams, P. J., and T. P. Burt (1974), Measurement of hydraulic conductivity of frozen soils, Can. Geotech. J., 11(4), 647-650, doi:10.1139/ t74-066.
78. Zhang, Y., J. Jin, G. Luo, and H. Wang (2003), The extended Langmuir's method and its application to double-layer interaction, Colloid Polym. Sci., 281(5), 401-406, doi:10.1007/s00396-002-0781-1. (Pubitemid 36626218)