Water and Solute Distributions near an Ice Lens in a
Glass-Powder Medium Saturated with Sodium Chloride
Solution under Unidirectional Freezing
Kunio Watanabe,* Yoshiko Muto, and Masaru Mizoguchi†

CRYSTALGROWTH& DESIGN
2001
VOL. 1, NO. 3
207-211

Nougyo-Doboku, Faculty of Bioresources, Mie University, Tsu 514-8507, Japan
Received November 30, 2000

ABSTRACT: Water and solute distributions near ice lenses, which were formed in uniformly sized glass powder
saturated with sodium chloride solution at various concentrations under unidirectional freezing, were measured.
At higher initial solute concentrations, ice lenses were thinner and developed at lower temperatures. In the warmer
adjacent region, extending about 30 mm from the growing ice lens into the unfrozen area, the water content andsolute concentration of pore water decreased from their initial values, while in other unfrozen areas the initialvalues were maintained. The water content and solute concentration in the warmer adjacent region increased withincreasing initial solute concentration.
Introduction
Freezing sometimes causes the water in unfrozen soil
to flow toward the freezing front, where regions of ice
form that are almost devoid of soil particles; these arecalled ice lenses. Ice lenses raise the ground surface andcause severe frost heave. A feature of ice lensing is theformation of intermittent ice layers, which result fromthe repeated generation, growth, and spacing of ice
lenses near the freezing front. The formation of ice
lenses has been observed in various porous media; thephenomenon is not limited to soil.1,2
When a porous medium containing solution is frozen
unidirectionally, water and solute are transported invarying degrees toward the freezing front.3-5 This
redistribution of soil water has profound effects on thedrainage, erosion, and trafficability of surface soils andon the stability of earthen dams, hillsides, building
foundations, highways, and airport runways. The redistribution of solute toward the soil surface by thewater flow also affects plant growth and agriculturalwork.6 Changes in soil-water salinity can drasticallyalter the mechanical properties of frozen soils and areof major concern when working with frozen soils.7,8 The
formation of ice lenses plays an important role inredistributing water and solute. It has been reported
that when ice lenses appear, a low water content region
is formed near the freezing front.9 Chamberlain10 identified unbonded brine-rich soil zones between ice lenses
as layers of potentially low shear strength. It is generally agreed that increasing concentrations of solution
cause a significant reduction in the rate of frost heavein fine-grained soils.10,11
The freezing of water containing solute is based on
the same mechanism as that when crystal growth
excludes solutes.5 The first research into the dual
processes of solute rejection and redistribution was bymetallurgical engineers, and their work provides foun* To whom correspondence should be addressed. Tel: +81 59 232
1211 2377. Fax: +81 59 231 9571. E-mail: kunio@dobokuPc4.bio.
mie-u.ac.jp.
† Current address: Department of Biological and Environmental
Engineering, The University of Tokyo, Tokyo 113-8657, Japan.

dation material. For instance, when ice grows in asolution, solute is rejected from the growing ice surface,establishing a solute diffusion field near the ice surface
that depends on the rate of ice growth.12 This diffusion
field influences both the growth rate and shape of ice
crystals.13,14 When a solution freezes in a porous medium, the solute may be bound to nonmiscible particles,
such as clayey colloids or complexes, and these kinds ofparticles are also excluded from the surface of the ice
as it grows.15 The behavior of solute and particles nearice growth surfaces has recently been studied from anenvironmental perspective.16
Conte17 and Taber18 carried out the classic studies on
frost heave associated with the formation of ice lenses.
Later, study of frost heave became a major topic in civilengineering, and numerous theoretical and experimental studies were performed.19-24 Jackson et al.25 described ice lens growth, based on experimental data forparticle rejection from the surface of ice as it freezes.
Miller26 proposed a theory of secondary frost heave,
which considered the stress at each phase. This theory
is widely used, since it can explain the formation ofintermittent layers of ice lenses. However, it cannot
explain ice lens formation in some unconfined fineporous powder media.27 Recently, approaches to understanding the formation of ice lenses have appeared thatare based on intermolecular forces.28 Nevertheless,neither the redistribution of water and solute in thevicinity of ice lenses nor the impact of solute concentration on ice lens growth have been sufficiently verified.
Thus, the formation of ice lenses in saline porous
media is a complex natural phenomenon that remains
poorly understood. Knowledge of the effect of different
porous media, water content, and concentration andtype of solute on the growth of ice lenses is importantto gain a better understanding of the redistribution of
the water and solute. Here, we present the results of insitu observations of ice lenses in a unidirectionallyfreezing porous medium that consisted of glass microparticles saturated with different concentrations of
sodium chloride solution. The influence of solute concentration on the formation of ice lenses, and on the10.1021/cg005535i CCC: $20.00 © 2001 American Chemical Society
Published on Web 04/18/2001

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Watanabe et al.

Table 1. Characteristics of the Powdermean diameter of particle (µm)
mean diameter of nanopore (nm)specific nanopore volume (cm3/g)
specific surface area (m2/g)
specific gravity of particle (g/cm3)
dry powder density (g/cm3)
hydraulic conductivity (m/s)
mineral components

2.2
3.3
0.3
128.6
2.12
0.85
1.92 × 10-8
SiO2 (99.4%)
Na2O (little)
etc. (very little)

redistribution of water and solute due to ice lensing, isthen determined.
Materials and Methods
Sample. The porous medium that we used consisted ofVycor glass particles, which form a fine powder. Table 1 lists
some characteristics of the powder. The mean diameter of theparticles was estimated from electron micrographs; they were
spherical, of roughly equal diameter, and their surfaces werecovered with nanopores of uniform diameter. The mean
diameter of the nanopores and specific surface area were
determined by nitrogen adsorption. The saturated hydraulicconductivity represents an average over a length of 10 cm.
Using an NMR technique, we showed that the liquid-water/
total-water ratio in powder saturated with pure water at 80%
by mass was more than 40% at -1 °C.27
Distilled, deionized, and degassed water and sodium chloride of 99.9% purity were used. The saturated porous medium
was prepared by placing the glass particles in a sealed
chamber with the sodium chloride solution, evacuating thechamber, allowing a few days for solid-vapor equilibrium tobe established, and then adding solution and allowing thesystem to equilibrate for 1 day. The prepared sample consistedof unconfined particles, water, and solute and did not containany gases. The initial water content of each sample was 78 (2% by mass. The solute concentrations of the pore water inthe samples were 0, 0.005, 0.01, 0.015, 0.03, 0.05, and 0.1 mol
dm-3 (samples G000, G005, G010, G015, G030, G050, andG100, respectively). The prepared sample was poured into asample cell that consisted of two 26 × 76 × 1 mm3 glass slides
and acrylic spacers. The cell was sealed with silicon, except
for a small hole on one side to relieve pressure; its internal
volume was 20 × 70 × 3 mm3. Some sample cells included
two copper-constantan thermocouples, accurate to 0.03 °C,
to measure internal temperatures. An identical cell was
prepared containing only sodium chloride solution for comparison. The concentrations of the sodium chloride solutions
were 0, 0.03, 0.05, and 0.1 mol dm-3 (samples S000, S030,
S050, and S100, respectively). Each cell was cooled to 2 °C
before the unidirectional freezing experiment commenced.
Unidirectional Freezing Experiment. Each sample wasfrozen using a unidirectional freezing apparatus that wasbasically as designed by Nagashima and Furukawa13. Figure
1 shows a schematic illustration of the experiment. The sample
cell was sandwiched between a pair of copper blocks, each held
at a different constant temperature, TH ) 2.1 °C and TL )-4.0 °C, respectively, by Peltier thermoelements to establish
a temperature gradient, G ()0.21 °C mm-1). The effective
length of the temperature gradient was 32 mm. Once thetemperature gradient was established, the sample cell, connected to a translational stage with a computer-controlled
pulse motor, was pulled at constant rate Vc () 0.4 µm s-1)
through the temperature gradient; this continued for 10 000
s. After a short initial transition, the isotherms in the sample
advanced at a constant rate, Vf ) -Vc, under a fixed temperature gradient for a total distance of 4 mm. The temperature
gradient, G, was both monitored by the thermocouples in thesamples and deduced from the temperatures of the blocks
during the experiment.
A microscope equipped with a charge-coupled device cameraand videotape recorder system was placed above the cell andFigure 1. Schematic illustration of the unidirectional freezing
experiment. A temperature gradient was established along theZ axis. The solution-saturated powder was placed between two
glass slides and pulled at constant speed, Vc, through thetemperature gradient. The growth surface of the ice lenslagged behind the 0 °C isotherm.
used to observe the formation of ice lenses. Images were
captured at 1 min intervals; each was divided into a 12.5 µm
grid by computer, and the location of the ice lens was recorded.
In addition, the temperature of the ice surface was determinedby tracing the temperature gradient onto the image.
Measurement of Water and Solute Distributions. First,
we checked the water and solute migration in a sample kept
at 25 °C for 300 min. During this time, no significant redistribution of water or solute was observed.
After the sample was unidirectionally frozen with Vc ) 0.4µm s-1 for 4 mm, it was removed from the apparatus and cut
into slices a few millimeters thick, parallel to the growthsurface of the warmest ice lens. The sample was kept at an
ambient temperature of 2 °C during cutting. Any melting andwater migration in the sample during cutting was ignored,since only 1 min elapsed during this procedure. Each slice wasplaced into a dry oven for 24 h to measure the water content:
the ratio of the measured mass of the pure water divided bythat of the dry sample. Then, the slice was mixed with aquantity of deionized, distilled water equal in mass to thepowder in the sample, and the electric conductivity was measured. The amount of solute in the slice was then estimatedfrom the electrical conductivity, using a previously determinedcalibration curve. The molar concentration of the pore waterin the slice was then calculated.

Results and Discussion
Observation of Ice Lenses in Samples Frozen ata Constant Rate. Once a stable temperature gradientwas established, Vc ) 0.4 µm s-1 was applied to thesample. The freezing front remained virtually still inthe view field of the microscope throughout. Repeatedgeneration and growth of three to five layers of ice lenses
at the freezing front were observed. Figure 2 shows theice lenses observed in sample G000, while Vc wasapplied.32 Each ice lens appeared as a planar layer inthis porous medium, so we could clearly identify theboundary and location of the growing surface of the ice
lens.2,27 During the experiment, no air bubbles wereseen in the view field, suggesting that the sample
remained saturated during the experiment, since air
bubbles appear at the ice-water interface when wateris frozen at Vc ) 0.4 µm s-1.29
Under Vc, the layers of ice lenses had almost the same
thickness and spacing. Figure 3 shows the mean thickness of the ice lenses and the mean spacing between
them as a function of the initial solute concentration.

Water and Solute Distributions near an Ice Lens

Figure 2. Ice lenses observed in sample G000 while Vc ) 0.4µm s-1 was applied. The right-hand side is colder, and the lefthand side is warmer. The ice lenses appear black, since thebackground can be seen through the ice lenses, and the porous
medium appears white.

Figure 3. Mean thickness of ice lenses and mean spacing
between ice lenses as a function of the initial solute concentration of the pore water. Open circles show the mean thicknessof ice lenses, and solid circles show the mean spacing between
ice lenses.

The ice lenses were thinner when solute concentration
was high. Spacing was not uniform and not concentration-related. If we assume that the sum of the thicknesses of the ice lenses in a sample corresponds to theamount of frost heave, the results suggest that theamount of heave decreases with increasing soluteconcentration in the pore water. This agrees with theresults reported by Chamberlain.10
During freezing at Vc, the ice lenses that formed andgrew remained in essentially the same place in the view
field of the microscope, implying that they formed at aconstant temperature. The location in the view field
varied with the initial solute concentration. On completion of each experiment, we located the growth surfaceof the warmest ice lens in each sample (Figure 4). The
higher the concentration, the colder the location atwhich the ice lens formed. If we assume a linear
temperature gradient, G, in the sample, the temperature at the growth surface in the sample can be
determined from the right axis in Figure 4 by using thelocation of the surface and G ) 0.21 °C mm-1. The
dashed line in the figure indicates the molar freezing
depression of bulk sodium chloride solution. The temperature at the growth surface of the warmest lens islower than that at the ice-liquid water interface in a

Crystal Growth & Design, Vol. 1, No. 3, 2001 209

Figure 4. Location of the growth surface of the warmest ice
lens, when the sample was moved at 0.4 µm s-1 for 4 mm.
The left axis indicates the location of the growth surface of
the warmest ice lens (solid circle) and ice-liquid interface(cross). Zero on the axis equals the ice-liquid interface
observed in sample S000 (pure water), and negative values
refer to location on the cold side. The right axis indicates thetemperature at the growth surface, calculated from the linear
temperature gradient, G ) 0.21 °C mm-1. The dashed line
indicates the molar freezing depression of bulk sodium chloride
solution Tf, calculated using Tf ) iKfC, where C is the molar
concentration of the solution, i is the dissociation constant of
sodium chloride ()2), and Kf is the molar freezing point
constant ()1.86 °C mol-1).

solution at the same concentration. The slope of thetemperature at the growth surface approaches the slopeof the molar freezing depression curve when the soluteconcentration is high. These results suggest that soluteconcentration near the growth surface increases considerably above its initial value, because of solute rejection from the ice lens surface, and that this effect isparticularly apparent with a lower initial solute concentration. The results also suggest that the soluteconcentration near the ice surface may increase if there
are particles.
Any particle on the growth surface of an ice lens issubject to two counteracting forces: one attractive andone repulsive.2,28 The attractive force comes from viscous drag due to fluid flow around the particle, andthe repulsive force originates from intermolecular forces
between the ice lens, the particle, and the liquid water
film between them. An ice lens will keep growing if
the repulsive force is greater and will stop if theattractive force becomes greater. It is thought that therepulsive force depends on the solute concentration of
the water film between the ice lens and the particle.
The dependence of the thickness of the water film on
the solute has been investigated.30,31 In this context,
increasing the solute concentration of the pore water
causes ice lenses to develop at a colder location and be
thinner.
Water Redistribution near the Growth Surfaceof the Warmest Ice Lens. Figure 5 shows the distribution of the water content near the growth surface of
the warmest ice lens in a sample, just after the sample
was moved 4 mm. The region Z < -15 mm corresponds
to the region where the sample was first frozen, immediately after TH and TL were applied. In this region,
the water content in each sample rose slightly above
its initial value (∼0.78 g/g), while no ice lens wasobserved. In the region from Z ) -15 to -4 mm, where
the freezing front gradually advanced, nonuniform

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Crystal Growth & Design, Vol. 1, No. 3, 2001

Figure 5. Distribution of the water content near a growthsurface of the warmest ice lens, when Vc ) 0.4 µm s-1 wasapplied to the sample for 4 mm. The growth surface is locatedat Z ) 0. The left-hand side of the figure is colder, and theright-hand side is warmer.

Figure 6. Distribution of the solute concentration of porewater near the growth surface of the warmest ice lens.

layers of ice lenses were observed, and the water content
increased. In the region from Z ) -4 to 0 mm, whereVc was applied to the sample, a series of ice lenses ofvirtually identical thickness and spacing was observed(see Figure 2). The water content decreased withincreasing initial solute concentration. This change inwater content is derived from the dependence of ice lens
thickness on initial solute concentration, as shown in
Figure 3. There was a region of lower water content that
extended about 30 mm from the growth surface into theunfrozen area. Increasing the initial solute concentration increased the water content of this region anddecreased its length. These results indicate that water
migration from the unfrozen area to the freezing front
depends on initial solute concentration.
The saturated hydraulic conductivity of the powder,measured macroscopically, was 1.92 × 10-8 m s-1, whichis less than the growth rate of the ice lenses (0.4 × 10-6
m s-1). This implies that the supply of water to thegrowth surface of the ice lens lags behind its growth,causing a region of lower water content in the sample
as the ice lens grows.
Solute Redistribution near the Growth Surfaceof the Warmest Ice Lens. The solute concentration
distribution of pore water near the growth surface of
the warmest ice lens was calculated from the watercontent and the electric conductivity. Figure 6 shows
the distribution of solute concentration, using the same
Z axis as Figure 5. In the region where no ice lenses
were observed (Z < -15), the pore water retained its

Watanabe et al.

initial solute concentration. In the region where ice
lenses of uniform thickness were observed under Vc (-4mm < Z < 0 mm), no significant change in soluteconcentration was observed, while the water content
and electric conductivity values increased. The soluteconcentration of the pore water between ice lenses
became several times higher than the initial value,
presumably because the ice lenses almost totally rejected the solute. In the region Z ) 0-3 mm, the soluteconcentration of the pore water varied from sample tosample. For those samples in which the warmest ice lens
had grown sufficiently before freezing was stopped(samples G000, G010, G030, and G100), the soluteconcentration in this region was high, decreasing with
distance from the growth surface. Conversely, for samples
in which the warmest ice lens had only just started to
grow when freezing was stopped (samples G005, G015,
and G050), the solute concentration in this region was
low. These results suggest that the increased soluteconcentration near an ice lens is because of the growthof the ice lens. In the region from Z ) 3 to Z ) ∼30mm, the solute concentration of the pore water fell below
the initial value. The solute concentration of this region
increased, and its length decreased, with increasing
initial solute concentration, while in the warmer partof the sample the pore water retained the initial soluteconcentration.
When an ice grows in a solution, the diffusion length,l, of the solute in front of the ice-water interface isestimated to be l ) D/V by two-dimensional theory,
where D is the diffusion coefficient of the solute in thesolution and V is the movement velocity of the interface.
Since D for sodium chloride is about 1.5 × 10-9 m2 s-1
with solute concentrations of 0-5 mol dm-3, and thegrowth rate of the ice lens was ) 0.4 µm s-1, in thiscase l ) 3.8 mm. The solute that is rejected at thegrowth surface of the ice lens should therefore diffuse
within 4 mm of its surface, and outside 4 mm the soluteconcentration should reach equilibrium. In our experiment, when the ice lens had grown sufficiently (samples
G000, G010, G030, and G100), the solute concentrationin the region extending a few millimeters from thegrowth surface of the warmest ice lens into the unfrozen
part of the sample decreased with distance from the ice
surface. The length of the solute diffusion field causedby the growth of an ice lens was within this distance,
although we did not measure below 1 mm. On the other
hand, the solute concentration was lower than the initialvalue in a region extending about 30 mm into theunfrozen area from the ice surface. This redistributionof solute may arise not only from solute diffusion but
also from water migration due to ice lensing andinteractions between the solute and the particles.
Conclusions
Unidirectional freezing experiments were carried out
on an unconfined, uniformly sized, porous medium
consisting of glass microparticles saturated with sodium
chloride solution at different concentrations. The formation of ice lenses in the porous medium was observed
to depend on the initial solute concentration of the porewater. The distributions of water content and soluteconcentration near the growth surface of the warmest
ice lens in the porous medium were measured. When

Water and Solute Distributions near an Ice Lens

the initial concentration was high, thinner ice lenses
grew, and at lower temperatures. In a warmer, adjacentregion that extended about 30 mm into the unfrozen
area from the growing ice lens, the water content andsolute concentration fell below the initial value, whilein other unfrozen areas initial values were maintained.
The water content of this warmer region increased withhigh initial solute concentration, which also increased
the solute concentration of this region and decreased
its length.
The grain size of the samples that we used corresponds to that of silt. When dealing with water andsolutes in actual soil, it is important to consider migration due to ice lensing. Water and solute redistribution
in samples saturated with other solutions will bemeasured in the future.
Acknowledgment. We thank S. Akagawa and Y.
Y. Miyata for measuring the characteristics of the glass
particles.
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