Journal of Crystal Growth 213 (2000) 135}140

Ice con"guration near a growing ice lens in a freezing porous
medium consisting of micro glass particles
Kunio Watanabe *, Masaru Mizoguchi
Nougyo-Doboku, Faculty of Bioresources, Mie University, 1515 Kamihama Chyo, Tsu 514-8507, JapanDepartment of Biological and Environmental Engineering, The University of Tokyo, Tokyo 113-8657, Japan
Received 28 December 1999; accepted 17 February 2000
Communicated by T. Nishinaga

Abstract
To observe the formation of ice lenses, unidirectional freezing experiments were carried out using a water-saturatedporous medium made from micro glass particles. Knowledge of the ice con"guration in the vicinity of a growing ice lens isimportant for clarifying the mechanism of the formation of ice lenses. The ice con"guration in the vicinity of the warmest
ice lens in the freezing porous medium was investigated by combining Raman spectroscopy with the unidirectional
freezing experiments. No ice was found in any pore, warmer than the ice lens and the ice lens grows without penetrating
the warmer pores.  2000 Elsevier Science B.V. All rights reserved.
PACS: 81.10.A; 68.35.R; 64.70.D; 47.55.M
Keywords: Ice lens; Raman spectroscopy; Unidirectional freezing; Porous medium; Glass particles

1. Introduction
When porous media consisting of water and "neparticles, such as soil, are frozen unidirectionally,
the water sometimes forms regions of ice that arealmost devoid of particles [1,2]. These regions arecalled ice lenses, and repetition of the process results in the formation of intermittent layers of icelenses. The formation of ice lenses is recognized asa necessary condition for frost heave.

* Corresponding author. Tel.:#81-59-232-1211, ext. 2377;
fax: #81-59-231-9571.
E-mail address: kunio@dobokupc4.bio.mie-u.ac.jp (K.
Watanabe).

To clarify the mechanism of the formation of icelenses, it is important to observe the con"gurationof ice in freezing porous media. Kumai [3]observed the ice con"guration in frozen clay byscanning electron microscopy. Colbeck [4] directly
observed the freezing front in a water saturated,unconsolidated medium consisting of glass beads
a few millimeters in diameter. These observations,however, dealt only with freezing porous media in
which ice lenses did not form. Some models of theformation of ice lenses in freezing soil emphasize
the importance of ice growing in the frozen fringe,
which was assumed to consist of a network of poreice extending from the base of the warmest ice lensto a position at or near the 03C isotherm [5}7].
Direct observation of the ice con"guration in the0022-0248/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 3 5 3 - 5

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K. Watanabe, M. Mizoguchi / Journal of Crystal Growth 213 (2000) 135}140

Fig. 1. Electron micrographs of glass particles. The micrograph (a) is 10 times the magni"cation of (b).

vicinity of a growing ice lens, however, has not yet
been carried out.
In this study, we present the results of in situ
observations of ice lenses in a unidirectionallyfreezing porous medium consisting of water andmicro glass particles. The ice con"guration in thevicinity of a growing ice lens is revealed from theRaman spectra of the water-saturated pores formedby glass particles near the ice lens.

Table 1
Characteristics of the glass particles prepared
Mean diameter of particle (lm)Mean diameter of nanopore (nm)Speci"c nanopore volume (cm/g)Speci"c surface area (m/g)Speci"c gravity of particle (g/cm)Dry powder density (g/cm)Water content (g H O/g SiO )


9.7
3.3
0.30
150.5
2.12
0.791
0.790

2. Experimental procedures
2.1. Sample
The porous medium that we used consisted ofVycor glass particles, which formed a "ne powder.
Fig. 1 shows electron micrographs of a sample. The
particles were spherical with roughly the same diameters and their surface had nano-pores with a uniform diameter. Table 1 shows some characteristicsof the sample. The mean diameter of the particles
was estimated from the electron micrographs. The
mean diameter of the nano-pores and the speci"csurface area were determined by nitrogen adsorption. Fig. 2 shows the liquid water fraction in theFig. 2. Liquid-water fraction in the frozen porous medium measured by NMR technique.

K. Watanabe, M. Mizoguchi / Journal of Crystal Growth 213 (2000) 135}140

frozen sample measured using an NMR technique,which accurately measures the liquid water fractionin porous media [8]. Since all the water melt, theliquid water fraction of unfrozen sample remains
a constant value. More than 0.4 g/g of the water did
not freeze at !13C. This large amount of unfrozen
water will come from its high speci"c surface areaand presence of nanopores.
The water used was distilled, deionized and degassed. Water-saturated porous medium was prepared by placing the glass particles in a desiccatorwith water, evacuating the desiccator, allowing
a few days for the solid}vapor equilibrium to beestablished, adding liquid water, and allowing thesystem to equilibrate for a day. The preparedsample was placed into a sample cell, which consisted of two 26;76;1 mm glass slides and acrylic
spacers, and sealed with silicone, except for a small
hole on one side to relieve pressure. The insidevolume of the sample cell was 20;70;3 mm.
Two copper-constantan thermocouples with adiameter of 0.3 mm, calibrated with an accuracy of0.033C, were inserted into the sample cell tomeasure the temperature. Before the unidirectional
freezing experiment, the cell was initially cooled to23C.
2.2. Unidirectional freezing
The sample was frozen using the unidirectional
freezing apparatus shown in Fig. 3, which is basi-Fig. 3. Schematic illustration of the unidirectional freezing apparatus. A temperature gradient is established along the Z-axis.

137

cally the same as that designed by Nagashima andFurukawa [9]. The sample cell was placed in a Teflon cell holder. The opposite ends of the cell were
held at di!erent temperatures, ¹ and ¹ , by using&*
two copper blocks kept at constant temperatures
by Peltier thermoelements. This established a temperature gradient in the sample cell. A microscope
equipped with a charge-coupled device camera andvideo tape recorder system was placed above thecell and used to observe a growing ice lens. Imagesof a growing ice lens were captured at 1 min intervals. A computer divided the images into a 20-lm
grid and the growth rate of the ice lens was determined from the relative coordinates of the growthsurface. The temperature pro"le was traced on theimage using the locations and temperatures of thethermocouples, which were a few millimeters apartand sandwiched the growth surface. The temperature at the growth surface was estimated from thetemperature pro"le.

2.3. Raman spectroscopy
The Raman spectrum arising from translationallattice vibrations in ice Ih shows a molecular-optic
band peak at 225 cm\ [10,11]. If ice exists, thispeak should be observed. While the warmest icelens was growing, water in the vicinity of the growth surface was investigated using a Raman spectroscope (JOBIN YVON RAMANOR T64000),
which was placed above the sample cell. The
Raman spectroscope was calibrated to 0.1 cm\ byrecording the standard emission lines of neon. This
instrument was equipped with a charge coupleddevice detector that allows simultaneous recordingof the frequency range between 50 and 400 cm\.
The excitation energy for Raman emission wasproduced by an Argon ion laser using monochromatic radiation of 514.5 nm with an output of150 mW. The spectral resolution was 0.45 cm\ forall spectra. The incident laser beam was focused ona spot of the freezing sample 1 lm in diameter,
under a microscope. The time elapsed during eachmeasurement was 30 s. Since the ice lenses we observed grew less than 0.5 lm during each measurement, we neglected the growth of the ice lens during
the measurement period.

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K. Watanabe, M. Mizoguchi / Journal of Crystal Growth 213 (2000) 135}140

3. Results and discussion
3.1. Ice lenses in a porous medium consisting of glass
particles
When di!erent temperatures were applied toeither end of the sample cell, ice lenses formed, as
shown in Fig. 4. The black and white areas inFig. 4 are ice lenses and glass particles, respectively.
An ice lens initially appeared near the cold end of
the sample cell and grew with time. Once the ice
lens had grown a few 100 lm, it stopped growing
and a new ice lens then appeared in a place warmer
than where the previous ice lens was growing. Consequently, the ice lenses formed intermittent layers
perpendicular to the direction of heat #ow, which isfrom right to left in Fig. 4. The ice lenses thatformed later were thicker. Fig. 5 shows the change
in the thickness of the ice lens that formed at thewarmest place in the sample. The elapsed time wascounted from the beginning of formation of thewarmest ice lens. Initially, the warmest ice lens grew
rapidly, and then grew more slowly. After 300 min,the warmest ice lens was 1.2 mm thick. The temperature gradient near the warmest ice lens was0.253C mm\ and the temperature at the growthsurface of the ice lens was estimated to be!0.063C.

Fig. 4. Ice lenses in the porous medium consisting of glass
particles. Right-hand side is colder and left-hand side is warmer.
The ice lenses appears black since background can be seen
through the ice lenses, and the porous medium appear white.
The ice lenses grew from cold side and formed intermittent
layers in the direction perpendicular to heat #ow.

Fig. 5. Thickness of the warmest ice lens with time.

3.2. Raman spectra of water near the warmest
ice lens
In order to evaluate the in#uence of the sample
cell and glass particles on the Raman spectra, preliminary experiments were carried out using samples at room temperature and the temperature ofliquid nitrogen. No remarkable peaks arising fromthe sample cell and the glass particles were observed in the frequency range between 50 and400 cm\ from either sample (Fig. 7, Rand0R ).
*,Then, we measured the Raman spectra to observe
the peak at 225 cm\ in the vicinity of an ice lensthat had grown for 300 min. Fig. 6(a) shows a computer-processed image of the vicinity of the growthsurface of the ice lens monitored using the Ramansystem. The right side is colder and the left side iswarmer. The warmest ice lens appears black, and theglass particles appear as white circles. To measureeach pore, the diagnostic spot was moved in 0.4-lm
steps, as shown in Fig. 6(b), where d is the distancefrom the growth surface of the warmest ice lens.
Fig. 7 shows a series of the Raman spectra obtained from pores at distance d. The spectrum in theice lens (d(0) had a strong peak at 225 cm\,which indicated the existence of ice Ih. The peak
was also observed in the spectrum at the boundary
between a glass particle and the ice lens (d"0). On
the other hand, the spectrum at a warmer poremore than 5 lm away from the ice lens (d'5) had
no remarkable peak at 225 cm\, and was very
similar to that of the sample at room temperature
(R).
0

K. Watanabe, M. Mizoguchi / Journal of Crystal Growth 213 (2000) 135}140

Fig. 6. (a) Computer-processed image and (b) schematic illustration of the vicinity of the growth surface of the warmest ice lensmonitored using the Raman system. The diagnostic spot wasmoved in 0.4-lm steps for the measurement of each pore asshown in (b), where d is distance from the growth surface of thewarmest ice lens.

139Fig. 7. Raman spectra of pore water in the vicinity of thewarmest ice lens. d is distance from the growth surface of thewarmest ice lens in Fig. 6(b). R
and R are the Raman0*,
spectra of samples at room temperature and the temperature ofliquid nitrogen, respectively.

critical radius r* is given by the Gibbs}Thomsone!ect
3.3. Ice conxguration and proxle near the warmest
ice lens
If enough water reaches the growth surface of anice lens, the ice lens will keep growing. If there is notenough water, however, the ice lens will stop growing and another ice lens will start to form in a newlocation. Therefore, water near the growth surface
is important for ice lens formation. In our experiment, no ice larger than 1 lm was observed in poresat locations warmer than the ice lens. In nucleation,
only aggregates larger than a critical size are stableand grow to become the solid phase. The size of theaggregates depends on the temperature and decreases with the temperature. Assuming a cylindrical solid in liquid at a temperature of ¹, thec
¹r*",o q ¹ !¹(1)where c is the solid}liquid interfacial free energy,
o is the solid density, q is the latent heat of melting,and ¹ is the bulk melting temperature. Withc"29;10\ J m\, o "0.917;10 kg m\ andq"3.33;10 J kg\ [8], we obtain r*"0.026/(¹ !¹), where r* is measured in lm. Consequently, the calculated critical diameter at thepores warmer than the growth surface of the warmest ice lens, which had an estimated temperature!0.063C, is more than 0.87 lm. In addition, ice
formation is more di$cult in a pore than in bulk
water because of surface forces from surrounding

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K. Watanabe, M. Mizoguchi / Journal of Crystal Growth 213 (2000) 135}140

particles [8,12]. The estimated diameter only gives
the smallest value and suggests that no ice smaller
than about 1 lm exists in pores at positions warmer
than the warmest growing ice lens. Therefore, nopore ice exists in any location warmer than thegrowth surface of the warmest ice lens in the porous
medium consisting of glass particles with diameterof 9.7 lm and the ice lens grows without penetrating the warmer pores.
4. Conclusions
Unidirectional freezing experiments were carriedout on an uncon"ned, water saturated, uniform,
porous medium consisting of micro glass particles
with diameter of 9.7 lm. The formation of ice lenses
was observed in the porous medium. The Raman
spectrum of water was used to clarify the ice con"guration in the vicinity of the growing ice lens. No
ice was found in any pore warmer than the warmest
ice lens in the porous medium and the ice lens grew
without penetrating the warmer pores.
Acknowledgements
The authors wish to thank Dr. Y. Miyata andMr. Y. Minami for taking the electric micrographsand doing the pore size analysis, Ms. T. Ikeda,

Mr. H. Fukazawa and Dr. A. Hori for technicalsupport with the Raman spectroscopy and Dr. M.
Fukuda, Dr. T. Hondoh and Dr. T. Ishizaki foradvice on our main experiment.

References[1] J.G. Dash, H.-Y. Fu, J.S. Wettlaufer, Rep. Prog. Phys. 58(1995) 115.
[2] Y. Muto, K. Watanabe, M. Mizoguchi, T. Ishizaki, Proceedings of the Seventh International Conference on Permafrost, 1998, p. 783.
[3] M. Kumai, CRREL Report, Vol. 79}28, 1979.
[4] S.C. Colbeck, Soil Sci. 139 (1985) 13.
[5] R.D. Miller, Proceedings of the Third International Conference on Permafrost, 1978, p. 377.
[6] R.R. Gilpin, Water Res. Res. 16 (5) (1980) 918.
[7] J.M. Konrad, C. Duguennoi, Water Res. Res. 29 (1993)
3109.
[8] T. Ishizaki, M. Maruyama, Y. Furukawa, J.G. Dash,
J. Crystal Growth 163 (1996) 455.
[9] K. Nagashima, Y. Furukawa, J. Crystal Growth 171 (1997)577.
[10] P.T.T. Wong, E. Whalley, J. Chem. Phys. 62 (1975) 2418.
[11] H. Fukazawa, D. Suzuki, T. Ikeda, S. Mae, T. Hondoh,
J. Phys. Chem. B 101 (1997) 6184.
[12] Y.P. Handa, M. Zakrzewski, C. Fairbridge, J. Phys. Chem.
96 (1992) 8594.