Experimental constraints on the kinetics of ice lens initiation and growth

Abstract

Ice lenses are formed by the migration and solidification of unfrozen water during soil freezing, which can lead to the upwards displacement of the ground surface known as frost heave. The complicated interplay between heat and mass transport that causes ice lens formation has been addressed by several theoretical models, but uncertainties remain that require further experimental constraints. In particular, the initiation of ice lenses has long posed theoretical difficulties. We performed a series of stepwise freezing experiments in fine granular materials to observe the initiation and growth of ice lenses. Our experiments demonstrate clear and systematic relationships between the behavior of ice lenses, and the particle size and cooling temperature. Ice lenses are thicker when formed in sediments with smaller particle sizes and the initial formation position is further from the cooled boundary when it is set to lower temperatures. Our temperature measurements and photographic documentation demonstrate that ice lenses are formed below the nominal melting temperature, at a location that is sufficiently distant for the freezing velocity to have slowed below a threshold. We compared our experimental results to numerical predictions of ice lens formation that were applied to our experimental conditions. Our experimental trends are consistent with predictions of our simple, initial model. However, important quantitative differences motivate a refined treatment that emphasizes the kinetics of liquid supply from the pore space through the thin films that separate ice lenses from particle surfaces. We obtained good quantitative agreement between our experimental measurements and the refined model predictions, emphasizing the importance of kinetic effects as a control in ice lens initiation and growth.

Indirect measurement of interfacial melting from macroscopic ice observations

“…One of the signature natural consequences of premelting is the migration of liquid towards the solidification front in soils to supply the growth of segregated ice lenses that cause frost heave at the ground surface [8][9][10][11][12][13]. Building upon the results of past studies that emphasized the importance of premelted water to ice-lens formation [10,11,13,14], Saruya et al [15] showed that the macroscopic (mm-scale) characteristics of lenses that develop in step-freezing experiments agree with predictions of a simple numerical model in which the nanometer-scale film thickness is the sole unknown parameter. In this Rapid Communication, we report the results of an extended suite of experiments in which we vary the host particle size and use observed ice-lens positions to infer the thicknesses of premelted films against soda-lime glass.…”

“…Initially, when the rate of heat flow is rapid, the T f isotherm migrates much more quickly into the overlying sediments than water can be transported to supply ice-lens growth. Saruya et al [15] found that the position of the single macroscopic lens corresponds with the location of the T f isotherm when its rate of motion can be matched by the rate of lens growth. This growth rate V l is predicted by balancing the difference between the thermomolecular and overburden forces with the net hydrodynamic force associated with permeable flow from the water reservoir and the lubrication flow through the premelted films.…”

“…This growth rate V l is predicted by balancing the difference between the thermomolecular and overburden forces with the net hydrodynamic force associated with permeable flow from the water reservoir and the lubrication flow through the premelted films. These considerations predict that [15] …”

“…We used a simple one-dimensional model [15] that tracks the temperature evolution and allows us to determine the location L = z l at which the rate of motion of the T f isotherm matches V l from Eq. (1), with T = T f from the Gibbs-Thomson relation above and R p = αR, where α ≈ 0.7.…”

Wall friction and Janssen effect in the solidification of suspensions

“…The solidification of a suspension (i.e. of a two phase mixture involving solid particles dispersed in a fluid) arises in a number of situations either natural as the freezing of soils [1][2][3][4][5][6][7][8] or man-made as in the food industry 9 , the casting of particle rich alloys [10][11][12] or the making of bio-inspired composite materials 13 . Its physics involves phenomena referring either to solidification, to suspension, or to the interaction between a solidification front and the suspension particles.…”