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

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