Reconstructing the hydraulic conductivity model of freezing soils based on lubrication theory
Abstract
Accurate characterization of hydraulic conductivity is essential for understanding coupled heat and water transport during soil freezing and thawing. However, conventional models can produce a nonphysical conductivity cutoff under strong supercooling because they oversimplify film-driven transport. Here, an existing combined capillary-film framework is extended by deriving a physically based expression for film flow conductivity. Using established film-thickness relationships to define the geometry, classical lubrication theory is applied to quantify flow velocity and hydraulic conductivity within thin adsorbed water films. Integrating this lubrication-based expression with the capillary flow equation yields a continuous hydraulic conductivity model without an artificial dry-end cutoff. Validation against diverse unfrozen and frozen soil datasets shows that the model performs consistently across the full moisture range and avoids the dry-end failure of the Campbell and van Genuchten models. Parameter sensitivity analyses further clarify how film flow responds to particle radius and porosity. Smaller particles provide greater specific surface area to sustain film flow at low-water contents, whereas lower porosity delays the transition from capillary-dominated to film-dominated transport. The model therefore provides a physically interpretable basis for representing continuous unfrozen-water migration in frozen soils.
Document Type: Original article
Cited as: Yu, C., Wang, F., Hui, C., Li, L., Zhang, S., Li, S. Reconstructing the hydraulic conductivity model of freezing soils based on lubrication theory. Capillarity, 2026, 19(3): 75-85. https://doi.org/10.46690/capi.2026.06.02
DOI:
https://doi.org/10.46690/capi.2026.06.02Keywords:
Frozen soil, hydraulic conductivity, lubrication theory, film flowReferences
Azmatch, T. F., Sego, D. C., Arenson, L. U., et al. Using soil freezing characteristic curve to estimate the hydraulic conductivity function of partially frozen soils. Cold Regions Science and Technology, 2012, 83-84: 103-109.
Becher, H. H. A method for measuring unsaturated hydraulic conductivity. Journal of Plant Nutrition and Soil Science, 1971, 128(1): 1-12. (in German)
Campbell, G. S. A simple method for determining unsaturated conductivity from moisture retention data. Soil Science, 1974, 117(6): 311-314.
Chen, H., Gao, X., Wang, Q. Research progress and prospect of frozen soil engineering disasters. Cold Regions Science and Technology, 2023, 212: 103901.
Chen, L., Ming, F., Zhang, X., et al. Comparison of the hydraulic conductivity between saturated frozen and unsaturated unfrozen soils. International Journal of Heat and Mass Transfer, 2021, 165: 120718.
Dall’Amico, M., Endrizzi, S., Gruber, S., et al. A robust and energy-conserving model of freezing variably-saturated soil. The Cryosphere, 2011, 5: 469-484.
Dash, J. G., Rempel, A. W., Wettlaufer, J. S. The physics of premelted ice and its geophysical consequences. Reviews of Modern Physics, 2006, 78(3): 695-741.
Fujimaki, H., Inoue, M. A transient multistep outflow method to determine unsaturated hydraulic properties of a soil column. Vadose Zone Journal, 2003, 2(2): 154-163.
Golparvar, A., Zhou, Y., Wu, K., et al. A comprehensive review of pore-scale modeling methodologies for multiphase flow in porous media. Advances in Geo-Energy Research, 2018, 2(4): 418-440.
Hansen-Goos, H., Wettlaufer, J. S. Theory of ice premelting in porous media. Physical Review E, 2010, 81(3): 031604.
Hansson, K., Šim˚unek, J., Mizoguchi, M., et al. Water flow and heat transport in frozen soil: Numerical solution and freeze-thaw applications. Vadose Zone Journal, 2004, 3(2): 693-704.
Hussain, S. T., Regenauer-Lieb, K., Zhuravljov, A., et al. Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media. Advances in Geo-Energy Research, 2023, 9(1): 38-53.
Ireson, A. M., van der Kamp, G., Ferguson, G., et al. Hydrogeological processes in seasonally frozen northern latitudes: Understanding, gaps and challenges. Hydrogeology Journal, 2013, 21(1): 53-66.
Jin, T., Cai, X., Chen, Y., et al. A fractal-based model for soil water characteristic curve over entire range of water content. Capillarity, 2019, 2(4): 66-75.
Kurylyk, B. L., MacQuarrie, K. T. B., McKenzie, J. M. Climate change impacts on groundwater and soil temperatures in cold and temperate regions: Implications, mathematical theory, and emerging simulation tools. Earth-Science Reviews, 2014, 138: 313-334.
Lamontagne-Hallé, P., McKenzie, J. M., Kurylyk, B. L., et al. Changing permafrost conditions influence terrestrial water storage and river discharge across the northern hemisphere. The Cryosphere, 2018, 12(11): 3501-3521.
Lamontagne-Hallé, P., McKenzie, J. M., Kurylyk, B. L., et al. Guidelines for cold-regions groundwater numerical modeling. WIREs Water, 2020, 7(6): e1467.
Lan, T., Hu, R., Zhao, B. Impact of pore-scale corner and film flows on macroscopic transport in porous media. Capillarity, 2025, 16(1): 1-4.
Lebeau, M., Konrad, J. M. A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 2010, 46(12): W12554.
Li, X. K., Li, X., Chen, X. S., et al. Modeling hydraulic conductivity function of frozen soil. Journal of Hydrology, 2024, 634: 131049.
Mehta, B. K., Shani, U., Guymon, G. L. Comparison of unsaturated hydraulic conductivity functions. Agricultural Water Management, 1994, 25(2): 203-213.
Ming, F., Chen, L., Li, D., et al. Estimation of hydraulic conductivity of saturated frozen soil from the soil freezing characteristic curve. Science of the Total Environment, 2020, 698: 134132.
Ming, F., Pei, W. S., Zhang, M. Y., et al. A hydraulic conductivity model of frozen soils with the consideration of water films. European Journal of Soil Science, 2022, 73(1): e13210.
Nemes, A., Schaap, M. G., Leij, F. J., et al. Description of the unsaturated soil hydraulic database UNSODA 2.0. Journal of Hydrology, 2001, 251(3-4): 151-162.
Niu, G. Y., Yang, Z. L. Effects of frozen soil on snowmelt runoff and soil water storage at a continental scale. Journal of Hydrology, 2006, 327(3-4): 448-467.
Pachepsky, Y. A., Shcherbakov, R. A., Varallyay, G. Prediction of the soil water retention curve from the soil particle size distribution and bulk density data. Agrochemistry and Soil Science, 1984, 33: 323-347.
Painter, S. L., Moulton, J. D., Wilson, C. J. Modeling challenges for predicting hydrologic response to degrading permafrost. Hydrogeology Journal, 2013, 21(1): 221-224.
Rempel, A. W., Wettlaufer, J. S., Worster, M. G. Premelting dynamics in porous media. Journal of Fluid Mechanics, 2004, 498: 227-244.
Saruya, T., Rempel, A. W., Kurita, K. Hydrodynamic transitions with changing particle size that control ice lens growth. The Journal of Physical Chemistry B, 2014, 118(47): 13420-13426.
Taber, S. The mechanics of frost heaving. The Journal of Geology, 1930, 38(4): 303-317.
Tang, R., Zhou, G., Jiao, W., et al. Theoretical model of hydraulic conductivity for frozen saline/non-saline soil based on freezing characteristic curve. Cold Regions Science and Technology, 2019, 165: 102794.
Tokunaga, T. K. Hydraulic properties of adsorbed water films in unsaturated porous media. Water Resources Research, 2009, 45(6): W06415.
van Genuchten, M. T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 1980, 44(5): 892-898.
Vereecken, H., Weihermüller, L., Assouline, S., et al. Infiltration from the pedon to global grid scales: An overview and outlook for terrestrial system modeling. Vadose Zone Journal, 2019, 18(1): 180191.
Vitel, M., Maugis, P., Gouttevin, I., et al. Modeling heat and water transfer of frozen soils: Comparison of two simulation approaches of the liquid water content. Geoscientific Model Development, 2016, 9(5): 1867-1874.
Walvoord, M. A., Kurylyk, B. L. Hydrologic impacts of thawing permafrost: A review. Vadose Zone Journal, 2016, 15(6): 1-20.
Wan, J., Tokunaga, T. K. Film straining of colloids in unsaturated porous media: Conceptual model and experimental testing. Environmental Science & Technology, 1997, 31(8): 2413-2420.
Wang, H., Vanapalli, S. K. Model for predicting the hydraulic conductivity of frozen soils using the soil freezing characteristic curve. Water Resources Research, 2025, 61: e2024WR039453.
Wang, Y., Ma, J., Guan, H. A mathematically continuous model for describing the hydraulic properties of unsaturated porous media over the entire range of matric suctions. Journal of Hydrology, 2016, 541: 873-888.
Watanabe, K., Flury, M. Capillary bundle model of hydraulic conductivity for frozen soil. Water Resources Research, 2008, 44(12): W12402.
Wettlaufer, J. S. Ice surfaces: Macroscopic properties and thermodynamic influences. Physical Review Letters, 1999, 82(12): 2516-2519.
Zhang, X., Li, D., Chen, L., et al. A new integral model for predicting the hydraulic conductivity of saturated frozen soil. Journal of Hydrology, 2021, 603: 126838.
Zhang, Y., Chen, W., Riseborough, D. W. Unfrozen water contents of different soils and their implications for geoengineering in cold regions. Cold Regions Science and Technology, 2016, 123: 114-124.
Zhao, J., Liu, Y., Qin, F., et al. Pore-scale fluid flow simulation coupling lattice Boltzmann method and pore network model. Capillarity, 2023, 7(3): 41-46.
Zheng, F., Zhang, L., Ma, J., et al. Improving the numerical stability of water flow simulations in frozen soils. Journal of Hydrology, 2021, 598: 126260.
Zhou, Y., Guan, W., Zhao, C., et al. Spontaneous imbibition behavior in porous media with various hydraulic fracture propagations: A pore-scale perspective. Advances in Geo-Energy Research, 2023, 9(3): 185-197.
Downloads
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Ceting Yu, Fugang Wang, Hui Cheng, Longxuan Li, Yinteng Li, Zhaohui Peng
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.