5. Observation of freezing of dispersed glass beads in water (Exp. 3)

In this chapter, an ice growing surface in water with dispersed glass particles
was directly observed by using unidirectional freezing apparatus equipped withmicroscope, to clarify how the growth surface and each particle behave and what is thefactor that affect to the behavior.

In order to observe the behavior of each particle, themicroscope of this experiment had higher resolution than that used in the Exp. 1 and 2

5.1 Sample and method
Samples used here were three types of glass particles with different diametersof 2.2, 5.3 and 9.7 µm, which were mixed with distilled water and deaired.

Water

content of each mixture prepared was 1000g-water per 1g-glass particles.

In thisexperiment, sample cell had polyester spacers with thickness of 100 µm instead of 3
mm-thick spacer shown in figure 14.
capillary attraction.

The mixture was poured into the sample cell by

After the temperature gradient of 0.33 ˚C/mm was attained to thesample for half an hour, the cell was moved at a constant rate by the unidirectional
freezing apparatus.

Then the vicinity of ice growing surface was observed with amicroscope (100 magnification) until the cell was moved 5-mm distance. Table 3 lists
the condition of the sample moving rate Vs and the particle diameter d.
experiments were performed in the cold room with ambient temperature of 5.0 ˚C.

Table 3. Experimental conditions (Exp. 3).
Sample d (µm)
2
9.7
3
5.3
4
2.2

5.0
5.0

4.5

4.0
4.0
4.0Vs (µm/sec)
3.0
3.0 2.5
3.5 3.0 2.5- 89 -2.0
2.0
2.0

1.5

The5.2 Experimental results
Figure 27 shows the vicinity of ice growing surface in water with dispersed
glass particles.

In this figure, white points are glass particles and dashed line indicatesthe growth surface of ice.
unfrozen.

The right side of a dashed line is frozen area and the left is

In this experiment, the growth surface of ice stayed at the same location in

the visual field of microscope.

The behavior of the growth surface showed that thegrowth rate of ice was equal to the freezing rate and that the growth surface of ice kept
the same temperature.
Two kinds of ice formations were observed in this experiment.

Ice grew withpushing particles ahead at a low freezing rate (figure 27a) while it grew withencapsulating particles at a high freezing rate (figure 27b).

The former ice formation

shown in figure 27b might correspond to ice lensing in soil or fine particles bearingwater.

The latter ice formation shown in figure 27b might correspond to pore ice

formation in soil or fine particles bearing water.
Table 3 lists freezing rates for three kinds of glass particles to examine criteriawhether particles were encapsulated in ice or not.
that particles were pushed ahead by ice.

Underlines denotes the freezing rate

For the sample 2, ice grew with encapsulating

particles at the freezing rates of 4.0, 3.0 and 2.0 µm/sec while ice grew with pushingparticles ahead at the rate of 1.5 µm/sec.

The critical rate V c was affected by theparticle size.
In the freezing as shown in figure 27a, it was also observed that particles,
which had been pushed by ice growing surface, accumulated on the ice surface. And anew ice often started to grow beyond the layer of accumulated particles, which had acertain thickness.

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Fig. 27.

An image of the vicinity of ice growing surface in water with dispersed glass

particles.

The white points are glass particles and dashed line indicates the growthsurface of ice.

The right side of a dashed line is frozen area and the left is unfrozen.

Ice grew with pushing particles ahead at a low freezing rate (a) while it grew withencapsulating particles at a high freezing rate (b).

- 91 -Melt
Growt hRateFγVR
ViscousFlowFη
α

CrystalTemperature
gradientFig. 28.

Physical factors on a spherical particle ahead of the growing surface of ice

crystal.

- 92 -5.3 Discussion
The relationship of particle diameter, freezing rate and solute concentration to
the freezing of water containing particle has studied by Chernov et al. (1977), Pötschkeand Rogge (1989), Körber et al. (1992).
a particle trapping phenomena.

Körber et al. has shown the criterion for such

According to their theory, an isolated particle pushedto an advancing ice front is subject to two counteracting forces (figure 28): an attractive
and a repulsive force.

The attractive force comes from viscous drag due to fluid flow

around the particle, which favors entrapment (d <<R):Fη = 6πηVgR

Rd - a0,(26)

where η is coefficient of viscosity, V g is the rate of ice growing, a0 is average moleculardistance in liquid, d is the distance between ice growing surface and a particle, and R is
radius of the particle. The repulsive force originates from van der Waals forces:

Fγ = 8πa20 ∆γ

R3d2 (d+2R)2,(27)

where ∆γ is the difference of surface energy between particle-liquid water and liquidwater-ice.

The balance of the two forces determines whether the particle isencapsulated or not.

When F γ > F η, ice will grow without encapsulating of a particle.

In this case, liquid water film between the particle and ice growing surface will keep
constant thickness.

If we assume that these forces are equal (equation (26) = (27)),

critical freezing rate Vc whether the particle is encapsulated or not would be given by

VC =4 ( d - a0) a02∆γ R .
3η d2 (d + 2R) 2(28)- 93 -

The critical freezing rate Vc is increased with increasing the particle radius R.
Our experimental results can be explained by Körber's theory, although thesample 4 was out of range to apply it.

It can be considered that ice formation withpushing particles ahead is essentially the same ice formation as shown in ice lensing
observed in Exp. 1 and 2. In fact, we often found that a new ice started to grow beyond
the layer of accumulated particles shown in Figure 27a after the particles had
accumulated to a certain thickness.

Although details of the phenomenon were notexamined, the new ice growth in the Exp. 3 must be related to the ice lensing in Exp. 1and 2.

Therefore, it is suggested that the critical rate whether ice lensing will occur ornot, can be derived from the critical freezing rate Vc.
the forces around only one particle.

However, this theory deals with

In soil or micro-particles, where particles interacts

each other, multi-body effect should be considered.

Since these reasons, equation (28)does not explain the ice lensing as it is.

5.4 Summary
In this chapter, the behavior of growth surface of ice and particle near thesurface was observed by using the unidirectional freezing apparatus.

The criteria forexclusion and encapsulation of glass particles during ice formation with respect toparticle size and freezing rate was shown.

The relations of particle size and freezing

rate to the critical freezing rate was explained by Körber's theory. Since the ice lensing
is considered to be essentially same as the ice formation with pushing particle ahead, it
is suggested that critical freezing rate is important factors to make ice lensing model.

- 94 -