Hostname: page-component-89b8bd64d-mmrw7 Total loading time: 0 Render date: 2026-05-09T20:53:34.242Z Has data issue: false hasContentIssue false
  • English
  • Français

The kinetics of ice-lens growth in porous media

Published online by Cambridge University Press:  09 January 2012

Robert W. Style  and
Stephen S. L. Peppin
Robert W. Style*
Affiliation:
Oxford Centre for Collaborative Applied Mathematics, University of Oxford, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK Department of Geology and Geophysics, Yale University, 210 Whitney Avenue, New Haven, CT 06511, USA
Stephen S. L. Peppin
Affiliation:
Oxford Centre for Collaborative Applied Mathematics, University of Oxford, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK
*
† Email address for correspondence: rob.style@yale.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyse the growth rate of segregated ice (ice lenses) in freezing porous media. For typical colloidal materials such as soils we show that the commonly employed Clapeyron equation is not valid macroscopically at the interface between the ice lens and the surrounding porous medium owing to the viscous dynamics of flow in premelted films. The flow in these films gives rise to an ‘interfacial resistance’ to flow towards the growing ice which causes a significant drop in predicted ice-growth (heave) rates. This explains why many previous models predict ice-growth rates that are much larger than those seen in experiments. We derive an explicit formula for the ice-growth rate in a given porous medium, and show that this only depends on temperature and on the external pressures imposed on the freezing system. This growth-rate formula contains a material-specific function which can be calculated (with knowledge of the geometry and material of the porous medium), but which is also readily experimentally measurable. We apply the formula to plate-like particles, and show that the results can be matched with previous experimental data. Finally we show how the interfacial resistance explains the observation that the maximum heave rate in soils occurs in medium-grained particles such as silts, while heave rates are smaller for fine- and coarse-grained particles.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Lubrication theory Phase change: Solidification/melting

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 692 , 10 February 2012 , pp. 482 - 498
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
2.Bell, F. G. 2000 Engineering Properties of Soils and Rocks. Blackwell.Google Scholar
3.Beskow, G. 1935 Soil Freezing and Frost Heaving With Special Attention to Roads and Railroads, The Swedish Geological Society, c, no. 375, year book no. 3. Technological Institute, North-Western University. Reprinted in Historical Perspectives in Frost Heave Research, (ed. P. B. Black and M. J. Hardenberg), pp. 37–157. CRREL Special Report 91-23, 1991.Google Scholar
4.Biermans, M. B. G. M., Dijkema, K. M. & de Vries, D. A. 1978 Water movement in porous media towards an ice front. J. Hydrol. 37, 137–148.CrossRefGoogle Scholar
5.Butt, H. J., Doppenschmidt, A., Huttl, G., Muller, E. & Vinogradova, O. I. 2000 Analysis of plastic deformation in atomic force microscopy: application to ice. J. Chem. Phys. 113, 1194.CrossRefGoogle Scholar
6.Dash, J. G., Rempel, A. W. & Wettlaufer, J. S. 2006 The physics of premelted ice and its geophysical consequences. Rev. Mod. Phys. 78, 695–741.CrossRefGoogle Scholar
7.Deville, S., Saiz, S. & Tomsia, A. P. 2007 Ice-templated porous alumina structures. Acta Mater. 55, 1965–1974.CrossRefGoogle Scholar
8.Engemann, S., Reichert, H., Dosch, H., Bilgram, J., Honkimaki, V. & Snigirev, A. 2004 Interfacial melting of ice in contact with ${\mathrm{SiO} }_{2} $. Phys. Rev. Lett. 92 (20), 205701.CrossRefGoogle Scholar
9.Gao, J., Luedtke, W. D. & Landman, U. 2000 Structures, solvation forces and shear of molecular films in a rough nano-confinement. Tribol. Lett. 9, 3–13.CrossRefGoogle Scholar
10.Goertz, M. P., Houston, J. E. & Zhu, X. Y. 2007 Hydrophilicity and the viscosity of interfacial water. Langmuir 23, 5491–5497.CrossRefGoogle ScholarPubMed
11.Konrad, J. M. 1987 Procedure for determining the segregation potential of freezing soils. Geotech. Testing J. 10, 51–58.CrossRefGoogle Scholar
12.Miller, R. D. 1977 Lens initiation in secondary heaving. In Proceedings of the International Symposium on Frost Action in Soils, vol. 2. Sweden. University of Lulea.Google Scholar
13.Muldrew, K., Acker, J. P., Elliott, J. A. W. & McGann, L. E. 2004 The water to ice transition: implications for living cells. In Life in the Frozen State (ed. Fuller, B. J., Benson, E. E. & Lane, N. ). CRC Press.Google Scholar
14.Ozawa, H. & Kinosita, S. 1989 Segregated ice growth on a microporous filter. J. Colloid Interface Sci. 132, 113–124.CrossRefGoogle Scholar
15.Penner, E. 1968 Particle size as a basis for predicting frost action in soils. Soils Found. 8, 21–29.CrossRefGoogle Scholar
16.Penner, E. 1973 Frost heaving pressures in particulate materials. In OECD Symposium on Frost Action on Roads, vol. 1. pp. 379–385.Google Scholar
17.Penner, E. & Goodrich, L. E. 1981 Location of segregated ice in frost-susceptible soil. Engng Geol. 18, 231–244.CrossRefGoogle Scholar
18.Peppin, S. S. L., Elliott, J. A. W. & Worster, M. G. 2006 Solidification of colloidal suspensions. J. Fluid Mech. 554, 147–166.CrossRefGoogle Scholar
19.Perdigon-Aller, A. C., Aston, M. & Clarke, S. M. 2005 Preferred orientation in filtercakes of kaolinite. J. Colloid Interface Sci. 290, 155–165.CrossRefGoogle ScholarPubMed
20.Pittenger, B., Fain, S. C., Cochran, M. J., Donev, J. M. K., Robertson, B. E., Szuchmacher, A. & Overney, R. M. 2001 Premelting at ice–solid interfaces studied via velocity-dependent indentation with force microscope tips. Phys. Rev. B 63, 134102.CrossRefGoogle Scholar
21.Rempel, A. W. 2007 Formation of ice lenses and frost heave. J. Geophys. Res. 112, F02S21.CrossRefGoogle Scholar
22.Rempel, A. W., Wettlaufer, J. S. & Worster, M. G. 2001 Interfacial premelting and the thermomolecular force: thermodynamic buoyancy. Phys. Rev. Lett. 87 (8), 088501.CrossRefGoogle ScholarPubMed
23.Rempel, A. W., Wettlaufer, J. S. & Worster, M. G. 2004 Premelting dynamics in a continuum model of frost heave. J. Fluid Mech. 498, 227–244.CrossRefGoogle Scholar
24.Roos, Y. H. 1995 Phase Transitions in Foods. Academic.Google Scholar
25.Roseberg, R. 2005 Why is ice slippery? Phys. Today 58, 50–55.CrossRefGoogle Scholar
26.Seto, J. T. C. & Konrad, J.-M. 1994 Pore pressure measurements during freezing of an overconsolidated clayey silt. Cold Reg. Sci. Technol. 22, 319.CrossRefGoogle Scholar
27.Style, R. W., Peppin, S. S. L., Cocks, A. C. F. & Wettlaufer, J. S. 2011 Ice-lens formation and geometrical supercooling in soils and other colloidal materials. Phys. Rev. E 84, 041402.CrossRefGoogle ScholarPubMed
28.Style, R. W. & Worster, M. G. 2005 Surface transport in premelted films with application to grain–boundary grooving. Phys. Rev. Lett. 95, 176102.CrossRefGoogle ScholarPubMed
29.Vlahou, I. & Worster, M. G. 2010 Ice growth in a spherical cavity of a porous medium. J. Glaciol. 56 (196), 271–277.CrossRefGoogle Scholar
30.Watanabe, K. 2002 Relationship between growth rate and supercooling in the formation of ice lenses in a glass powder. J. Cryst. Growth 237–239, 2194–2198.CrossRefGoogle Scholar
31.Watanabe, K. & Mizoguchi, M. 2000 Ice configuration near a growing ice lens in a freezing porous medium consisting of micro glass particles. J. Cryst. Growth 213, 135–140.CrossRefGoogle Scholar
32.Watanabe, K., Mizoguchi, M., Ishizaki, T. & Fukuda, M. 1997 Experimental study on microstructure near freezing front during soil freezing. In Ground Freezing 97: Frost Action in Soils. Proceedings of the International Symposium of Ground Freezing and Frost Action in Soils (ed. S. Knutsen), 15–17 April 1997, Luleå, Sweden. Balkema, Rotterdam.Google Scholar
33.Watanabe, K., Muto, Y. & Mizoguchi, M. 2001 Water and solute distributions near an ice lens in a glass-powder medium saturated with sodium chloride solution under unidirectional freezing. Cryst. Growth Des. 1, 207–211.CrossRefGoogle Scholar
34.Wettlaufer, J. S. 1999 Impurity effects in the premelting of ice. Phys. Rev. Lett 82 (12), 2516–2519.CrossRefGoogle Scholar
35.Wettlaufer, J. S., Worster, M. G., Wilen, L. A. & Dash, J. G. 1996 A theory of premelting dynamics for all power law forces. Phys. Rev. Lett 76 (19), 3602–3605.CrossRefGoogle ScholarPubMed
36.Worster, M. G. & Wettlaufer, J. S. 1999 The fluid mechanics of premelted liquid films. In Fluid Dynamics at Interfaces, pp. 339–351Cambridge University Press.Google Scholar