from Figure 2 that both water and Br moved from the

warmer to cooler parts in the soil columns. The unfro-

(5)

zen part (segments 110) of soil columns lost both wa-

0

ter and Br . It is interesting that a few segments in the

frozen part near the 0C isotherm also lost both water

and Br and that the minimum value of *C * + appears in

^

(6)

these frozen segments.

0

where *t*0 is the duration of the experiment (22 days).

If we assume that Br is transported mainly by the

movement of unfrozen water, the mass flux *F*B of Br is

We will consider the balance of water and Br in the

given as

part of soil columns *V*i consisting of segments 1*i*. We

will assume that the initial dry density of each segment

(7)

is equal to the final dry density of each segment mea-

sured at the end of the experiment. The loss of water *W*i

where *C*i is the concentration of Br in unfrozen water

from the part *V*i during the experiment is calculated as

for segment *i*. From eq 6 and 7 we obtain

(

)

(3)

(8)

0

where *v *is the volume of each segment and ρj and *w*j are

the dry density and the water content of segment *j *re-

For a special case in which *C*i remains constant at the

spectively. Similarly, the loss of Br , *B*i, from the part *V*i

initial value *C*0, from eq 5 and 7 we obtain

during the experiment is calculated as

(9)

(

)

^

^

(4)

It follows from eq 9 that both *W*i and *B*i attain their

maxima at the same segment. This obviously did not

^

where *C*j is the Br content of segment *j*.

occur in our experiments.

The calculated values of *W*i for experiments 14 are

Since Br is excluded from growing ice and is con-

plotted together with those for experiments 58 in Fig-

fined to unfrozen water, the concentration of Br , *C*i,

must be a nondecreasing function of *i *for *i *≥ 10 when a

ure 3, where open circles are the data points from ex-

periments 14, while solid circles are the data points

linear temperature field is established at the beginning

from experiments 58. For instance, in Figure 3a the

of experiments. Because of the Br exclusion from ice,

calculated values of *W*i for experiment 1 are plotted to-

gether with those for experiment 5. Experiments 1 and

a result, the segment number of the maximum *B*i be-

5 are conducted under the same conditions, except that

comes greater than that of the maximum *W*i.

Br is absent in experiment 1. Suppose that the soil was

The Br ion may not be completely confined to un-

packed uniformly in each column and that Br does not

frozen water. However, let us assume this complete

affect the movement of unfrozen water. Then it is an-

confinement, as it appears to be a good approximation.

ticipated that the calculated values of *W*i for experiment

We will also assume that the phase equilibrium of wa-

1 should be equal to those for experiment 5. Since the

ter holds true in the experiments. Then, the unfrozen

uniform packing of soil is quite difficult, Figure 3 indi-

water content is approximated by the equilibrium un-

cates that the level of Br content used in experiments

frozen water content determined by the nuclear mag-

58 does not significantly affect the mobility of unfro-

netic resonance technique on a separate sample of

zen water.

Morin clay. Under these assumptions the con-

The calculated values of *W*i and *B*i for experiments

centrations of Br in unfrozen water at both the begin-

58 are presented in Figure 4. It is easy to see from

ning and the end of the experiments were calculated.

these figures that both *W*i and *B*i attain their maxima

The results of calculations for experiments 58 are

and that the segment number of the maximum *B*i is

presented in Figure 5, where nondimensional quanti-

+

greater than that of the maximum *W*i. Let *F*w(*i*) and

ties *C*0 and *C*+(*t*) are defined as the concentrations of

Br in unfrozen water divided by *C*0 at the beginning

from segment *i *to segment *i *+ 1, then *W*i and *B*i are

and the end of the experiment respectively. For in-

+

given as

stance, the calculated values of *C*0 and *C*+(*t*) for ex-

5

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