Segments 1115 lost water, but C+(t) is still less than
periment 5 are plotted vs. the segment number i in Fig-
+
+
C0 . As a result C+(t) becomes less than C0 in every
ure 5a, where solid and open circles are the data points
+
+
of C0 and C+(t) respectively. The values of C0 are
section of V. The input of both water and Br to V must
nearly one in segments 114 because ice is absent
have come from the unfrozen part where the concen-
+
while the C0 increases with i in segments 1425 as the
tration of Br remained approximately at C0 during
the experiment. Suppose that unfrozen water and Br
content of ice increases.
The values of C+(t) vary in the unfrozen part (seg-
moved at the same rate. Then, C(t) must not be less
than C0. However, it is easy to see from Figure 5a that
ments 110), but they are not very far from one. How-
ever, the C+(t) increases sharply from segments 1523
C+(t) is less than one in segments 1116. This is obvi-
+
in comparison with C0 and as a result, the values of
ously contradictory. Therefore, we may conclude that
+
C+(t) become twice as great as the C0 values near the
Br must have moved faster than the unfrozen water in
segments 1116 where C+(t) is less than one.
cold end. There is an interesting trend that the values of
+
+
+
C+(t) become less than C0 in segments 1217. The
The features of C0 , C+(t) and Ca in experiment 5
+
behaviors of C0 and C+(t) described above can be seen
described above are common to experiments 68. In
experiment 6 (Fig. 5b) C(t) is less than C0 in segments
also in Figures 5bd, but become less pronounced as
the initial water content w0 increases.
1115, while in experiments 7 and 8 (Fig. 5c and d),
In Figure 5 the values of C+(t) fluctuate about one in
C(t) is less than C0 in segments 12 and 13. In Figure 5
+
+
Ca is greater than both C0 and C+(t) in the frozen
the unfrozen part, and the pattern of fluctuation ap-
part except for a few segments near the cold end.
pears to be more or less random. However, in the fro-
zen part near the 0C isotherm there is a common fea-
These data strongly indicate that Br moved faster
+
ture that C+(t) becomes less than C0 . It is clear from
than unfrozen water in the frozen part of the soil col-
Figure 4 that both water and Br moved from the
umns. In other words, the repulsion or negative ad-
sorption of Br by the negatively charged Morin clay
warmer to cooler parts in the soil columns. The com-
must have moved Br faster than unfrozen water.
mon feature described above indicates that unfrozen
water and Br may not move at the same rate.
Since the repulsion of anions is caused by the interac-
+
We will introduce a nondimensional quantity Ca
tion between anions and surfaces of soil particles, the
defined as
effect of anion repulsion on the transport of anions is
expected to become less pronounced with the increas-
+
Ca (i) = Ca (i) / C0
(10a)
ing unfrozen water content. This general trend can be
seen in Figure 5 with the increasing initial water con-
Ca (i) = Bi / Wi .
tent w0.
(10b)
It follows from eq 10b that Ca(i) is the (time) average
CONCLUSIONS
concentration of Br in water removed from the part Vi
The movement of water and Br was measured in
of a soil column during the experiment. It is easy to see
that the concentration of Br in water removed from Vi
unsaturated and partially frozen clay columns sub-
jected to linear temperature fields. Both water and Br
must be equal to C0 at the beginning and C(t) of seg-
ment i at the end of the experiment. The calculated val-
were found to move from the warmer to cooler parts
+
ues of Ca are plotted in Figure 5 in comparison with
in the columns. The data were analyzed under as-
+
C0 and C+(t).
sumption that Br is completely confined to unfrozen
In Figure 5, we may consider that the concentration
water in the frozen part of the columns.
of Br in the unfrozen part did not change significantly
The concentration of Br in water was found not to
from the initial concentration C0 during the experi-
change significantly from the initial concentration in
ment. However, in the frozen part, except for a few
the unfrozen part of the columns. However, the data
+
segments near the cold end, Ca is greater than both
from the frozen part of the columns strongly indicate
+
+
C0 and C+(t) in all cases. Since the features of C0 ,
that Br moved faster than unfrozen water because of
+
C+(t) and Ca common to experiments 58 are the
the repulsion of Br by the negatively charged sur-
most pronounced in experiment 5, we will examine ex-
faces of clay particles. The effect of anion repulsion
on the transport of Br in the frozen part of the col-
periment 5 below.
We will consider a part V of the soil column consist-
umns was found to become more pronounced with the
ing of segments 1118 (Fig. 2a and 5a). Since C + < 1
^
decreasing initial water content. It may be concluded
in V (Fig. 2a), every section of V lost Br during the
that the anion repulsion by clay surfaces plays a sig-
experiment. Since w+ > 1 in segments 1618, these
nificant role in the transport of Br in unsaturated and
three sections gained water during the experiment.
partially frozen clay.
9
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