Abstract
The problem of ice formation in unsaturated soil in the presence of pressure gradient and capillary forces is formulated. The complete system of conditions on the crystallization surface is derived. The one-dimensional problem is investigated in the self-similar formulation. The dependence of the amount of the ice formed on the problem parameters is also investigated. It is found that the ice saturation increases as the pressure on the cooling wall that initiates water inflow to the front decreases and also in the regime of more intense cooling. Increase in the pressure leads to water outflow from the front and decrease in the ice saturation.
Similar content being viewed by others
References
Tsytovich, N.A., The Mechanics of Frozen Ground, Scripta, New York: McGraw-Hill, 1975; Moscow: Vysshaya Shkola, 1983.
Zhestkova, T.N., Formirovanie kriogennogo stroeniya gruntov (Formation of the Cryogenic Texture of Soils), Moscow: Nauka, 1982.
Hoekstra, P., Moisture movement in soils under temperature gradient with the cold-side temperature below freezing, Water Resources Res., 1966, vol. 2, no. 2, pp. 241–250.
Zhang, Y., Carey, S.K., and Quinton, W.L., Evaluation of the algorithms and parametrizations for ground thawing and freezing simulation in permafrost regions, J. Geophys. Research., 2008, vol. 113, p. D17116.
Li, Q., Sun, S., and Dai, Q., The numerical scheme development of a simplified frozen soil model, Adv. Apmosph. Sci., 2009, vol. 26, no. 5, pp. 940–950.
Leverett, M.C., Capillary behavior in porous solids, Trans. AIME, 1941, vol. 142, no. 1, pp. 152–169.
Bear, J., Dynamics of Fluids in Porous Media, New York: Academic Press, 1972.
Udell, K.S., Heat transfer in porous media: considering phase change and capillarity—the heat pipe effect, Int. J. Heat and Mass Transfer, 1985, vol. 28, pp. 485–495.
Li, K. and Horne, R.N., An experimental and analytical study of steam/water capillary pressure, SPE Reservoir Evaluation and Engineering, 2001, vol. 4, pp. 477–482.
Tsypkin, G.G. and Calore, C., Role of capillary forces in vapour extraction from low permeability, water saturated geothermal reservoir, Geothermics, 2003, vol. 32, no. 3, pp. 219–237.
Tsypkin, G.G. and Calore, C., Influence of capillary forces on water injection into hot rock, saturated with superheated vapour, Int. J. Heat and Mass Transfer, 2007, vol. 20, pp. 3195–3202.
Menot, J.M., Equations of frost propagation in unsaturated porous media, Eng. Geology, 1979, vol. 13, nos. 1–4, pp. 101–109.
Tsypkin, G.G., Effect of the capillary forces on the moisture saturation distribution during the thawing of a frozen soil, Fluid Dynamics, 2010, vol. 45, no. 6, pp. 942–951.
Vasil’ev, V.I., Popov, V.V., and Tsypkin, G.G., Nonlinear problem of unsaturated frozen soil thawing in the presence of capillary forces, Fluid Dynamics, 2012, vol. 47, no. 1, pp. 106–113.
Scheidegger, A.E., The Physics of Flow through Porous Media, 3rd ed., Univ. Toronto Press, 1974.
Shargatov, V.A., Instability of a liquid–vapor phase transition front in inhomogeneous wettable porous media, Fluid Dynamics, 2017, vol. 52, no. 1, pp. 146–157.
Tsypkin, G.G., Stability of the evaporation and condensation surfaces in a porous medium, Fluid Dynamics, 2017, vol. 52, no. 6, pp. 777–785.
Funding
The work was carried out on the theme of the State Program (State Registration no. AAAA-A17-117021310375-7).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 5, pp. 93–101.
Rights and permissions
About this article
Cite this article
Tsypkin, G.G. Water—Ice Phase Transition in Unsaturated Soil in the Presence of Capillary Pressure. Fluid Dyn 54, 681–690 (2019). https://doi.org/10.1134/S0015462819050094
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462819050094