CRREL REPORT 95-3

Transport of Tracer 

Br in

Frozen Morin Clay in Response to

Temperature Gradients

Yoshisuke Nakano February 1995

1

2

3

3

4

5 6

4
For conversion of SI metric units to U.S./British customary units of measurement

consult Standard Practice for Use of the International System of Units (SI), ASTM

Standard E380-89a, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa. 19103.

Cover: Experimental apparatus.

Abstract

The movement of water and Br was measured in unsaturated and partially

frozen soil columns subjected to linear temperature fields. Both water and

 Br moved from the warmer to cooler parts in the columns. The data were

analyzed under the assumption that Br is confined to unfrozen water. It

was found that the negative adsorption of Br by clay surfaces plays a significant role in the transport of Br in frozen Morin clay and that Br tends to

move faster than unfrozen water.
US Army Corps

of Engineers®

Cold Regions Research &

Engineering Laboratory

CRREL Report 95-3

Transport of Tracer 

Br in

Frozen Morin Clay in Response to

Temperature Gradients

Yoshisuke Nakano February 1995

Prepared for

OFFICE OF THE CHIEF OF ENGINEERS

Approved for public release; distribution is unlimited.
PREFACE

This report was prepared by Dr. Yoshisuke Nakano, Chemical Engineer, of the Applied Research Branch, Experimental Engineering Division, U.S. Army Cold Regions Research and Engineering Laboratory. Funding was provided by DA Project 4A161102AT24, Research in Snow, Ice

and Frozen Ground; Work Package 125, Frozen Ground Processes; Work Unit AT24-SC-F01,

Physical Processes in Frozen Soil; and the Strategic Environmental Research and Development

Program (SERDP).

The author thanks P.H. Miyares, formerly of CRREL, for his work in analyzing the concentration of 

Br by ion chromatography. He also thanks Dr. Thomas Jenkins and Dr. Yin-Chao Yen, both

of CRREL, for technically reviewing this report.

The contents of this report are not to be used for advertising or promotional purposes. Citation of

brand names does not constitute an official endorsement or approval of the use of such commercial

products.

ii
CONTENTS

Preface ........................................................................................................................... ii

Nomenclature ................................................................................................................ iv

Introduction ................................................................................................................... 1

Experiment .................................................................................................................... 2

Results of experiments .................................................................................................. 3

Analysis of data ............................................................................................................. 5

Conclusions ................................................................................................................... 9

Literature cited .............................................................................................................. 10

ILLUSTRATIONS

Figure

1. Apparatus .............................................................................................................. 2

2. Nondimensional contents of water w+ and Cˆ + versus the segment number i

for experiments 5–8 ........................................................................................ 4

3. Comparison of Wi

 values from experiments both with and without Br ............. 6

4. Calculated values of Wi

 and Bi for experiments 5–8 ............................................ 7

5. Values of Cˆ

0

+ , C t + ( ) and Ca+ of experiments 5–8 .............................................. 8

TABLE

Table

1. Experimental conditions ....................................................................................... 3

iii
iv

NOMENCLATURE

Bi loss of 

Br from a part Vi

 of a soil column

b positive constant

C concentration of 

Br in unfrozen water

C+ C/C0

Ca(i) average concentration of 

Br in unfrozen

water removed from a part Vi

 of a soil

column during the experiment

Ca

+ Ca(i)/C0

C0 concentration of 

Br in distilled water that

was mixed with dry soil to make soil columns

C0

+ concentration of 

Br in unfrozen water

divided by C0 at the beginning of the

experiments

Ci concentration of 

Br in unfrozen water for

segment i

Cl solute concentration in the liquid phase

Cs solute concentration in the solid phase

Cˆ 

Br content, weight of Br per unit weight of

dry soil

Cˆ + ˆ / C Cˆ

0

Cˆ

0 initial 

Br content

FB(i) mass flux of 

Br from segment i to segment

i + 1

Fw(i) mass flux of water from segment i to

segment i + 1

k effective segregation coefficient

k0 value of k when u = 0

T temperature

Tc temperature at the cold end of a soil column

Tw temperature at the warm end of a soil

column

t time (days)

t

0 22 days

u growth rate of a solid phase

Vi part of a soil column consisting of segments

1 through i

v volume of each segment

Wi loss of water from a part Vi of a soil column

w content of water (including ice) based on

the dry weight of soil

w+ w/w0

w0 initial water content

wi content of water (including ice) of segment

i based on the dry weight of soil

ρ dry density of soil

ρa average ρ over all segments

ρi dry density of soil in segment i

σ standard deviation
Transport of Tracer Br in Frozen Morin Clay

in Response to Temperature Gradients

YOSHISUKE NAKANO

INTRODUCTION

The transport of solutes in frozen or freezing soils is

important for both engineering and scientific reasons.

The presence of salts is known to drastically alter the

mechanical properties of frozen soils (Sego et al. 1982,

Hivon 1991). It is also known that the presence of salts

tends to reduce the rate of frost heave in fine-grained

soils (Konrad 1990). The migration of fertilizer and

pesticides during annual freezing is a subject of considerable interest in agronomy (Gray and Granger

1986).

The phenomenon of freezing soils that contain solutes is complex and poorly understood. Inasmuch as

solutes tend to be excluded from growing ice, they are

confined to the domains of unfrozen (interfacial) water. The transport process of solutes depends mainly on

the transport of unfrozen water, but it also is influenced by the diffusion or dispersion of solutes and

complex interactions of solutes with the surfaces of

soil particles and ice. The amount of unfrozen water in

frozen soils generally increases with the increasing

concentration of solutes (Banin and Anderson 1974).

Since the mobility of unfrozen water tends to increase

with the increasing unfrozen water content (Nakano

1991), the two transport processes of solutes and unfrozen water mutually depend on each other. Because

of this mutual dependence, the transport of solutes in

frozen soils is more complex than that in unfrozen

soils.

The rate of solute transport is anticipated to be great

where the rate of water transport is great. Since the

transport of water is closely coupled with the phase

change of water in freezing soils and solutes tend to be

excluded from growing ice, the solute redistribution is

expected to be most rigorous near a freezing front.

Therefore, the solute redistribution near a freezing

front has attracted the attention of researchers. Mahar et

al. (1983) investigated salt redistribution during freezing of gravel saturated with a salt solution of a known

concentration. They found that a distinct freezing interface did not exist. Instead, a zone of partially frozen

gravel with a high unfrozen water content beginning at

the depressed freezing point isotherm (freezing front)

was observed. It was also found that the salt concentration in unfrozen water increases toward the lower temperatures and that the content of salt in the frozen part of

gravel was less than the initial content (Mahar et al.

1983).

When the solidification occurs from the melt containing impurities, the composition of the solid phase

generally differs from that of the coexisting melt. This

phenomenon, called segregation or redistribution

among researchers of crystal growth, has been studied

extensively. Analyzing the process of redistribution,

Burton et al. (1953) obtained a quantitative description

(BPS theory) of an effective segregation coefficient k

given as

 

k C C k k ke bu = = +− [ ] ( ) −

s 00 0 / / l 1 (1)

where Cs and Cl = solute concentrations in the solid

and liquid phases, respectively, adjacent to the solid/liquid interface

k0 = value of k when the growth rate u of

the solid phase is zero

b = positive number that depends on a

given system.

Weeks and Lofgren (1966) showed the validity of BPS

theory applied to the problem of freezing salt so
lutions. By freezing columns of sand saturated with a

NaCl solution at constant rates, Baker and Osterkamp

(1989) found that BPS theory approximately holds true.

Konrad and McCammon (1990) conducted step freezing

tests on a saturated clayey silt with various salinities.

They found that the rate of cooling is the main factor

controlling solute redistributions and that there is a

threshold rate of cooling of 3°C/day above which no redistribution takes place (k = 1).

The flow of aqueous solutions through unfrozen porous media has been investigated extensively (Nielsen et

al. 1972). In saturated systems, the flow of a solute is

described as the sum of a convective term and a diffusive

term. The diffusive term is equivalent to Fick’s law of

diffusion where the diffusivity coefficient includes the

effect of both molecular diffusion and hydrodynamic

dispersion. Such a description is not accurate for finegrained soils with small water contents because the interaction between solutes and surfaces of soil particles becomes significant. It has been shown experimentally that

a soluble salt and water in which it is dissolved move at

different rates through fine-grained soil (Biggar and

Nielsen 1962, Krupp et al. 1972). For example, when a

CaCl2 solution containing 36Cl and 3H is passed through

soils, the 36Cl appears earlier in the effluent than the 3H.

This behavior can be explained by anion repulsion or

negative adsorption of salt by the negatively charged soil

particle surfaces.

While it has been anticipated that the phenomenon of

anion repulsion is important in the transport process of

solutes in frozen soils, no supporting data are available.

The objective of this study is to examine experimentally

the transport of the Br ion in unsaturated and partially

frozen soil. The content of Br was intentionally kept low

so that the transport of unfrozen water would not be altered significantly by Br. This study also aims to find

the effect of interactions between Br and surfaces of

soil particles.

EXPERIMENTS

Experiments were conducted in which closed soil

columns, initially with the uniform dry density and the

uniform contents of water and Br, were subjected to a

constant and linear temperature gradient. The apparatus

used in the experiments is shown in Figure 1.

The apparatus consists of four parts made of aluminum: an upper plate, a lower plate and two end plates.

The upper and lower plates are approximately 23 cm

long × 20 cm wide × 5 cm thick. Four grooves with a

rectangular cross section, 20.32 cm long × 1.27 cm wide

× 0.625 cm deep, were machined on the upper surface of

the lower plate. The center lines of these grooves, which

are parallel to the longer side of the plate, are spaced 3.8

cm apart. Grooves for O-ring seals were also machined

around each rectangular groove in the upper plate so that

when the upper and lower plates are bolted together,

four closed empty spaces of rectangular column shape

are formed to be used as containers of soil.

Each of the two end plates has a 2.54-cm hole drilled

into it, through which an antifreeze mixture from a temperature-controlled bath is circulated. The two end

plates are positioned by four bolts. Two sides of the upper and lower plates bolted together have a small taper

that matches the taper of the end plates so that the bolted

upper and lower plates smoothly slide into the spaces

created by the two end plates, with assured close contact. The four aluminum parts, when assembled, are

thermally insulated by foam plastic. A row of 10 copperconstantan thermocouples is placed with equal spacing

through the upper plate along the centerline of each

groove to measure and record temperatures in a soil

sample.

The soil selected for the experiment, called Morin

clay, is a marine-deposited clay obtained from the

Morin brickyard, Auburn, Maine. Morin clay is a nonswelling clay with a specific surface area of 60

1–Upper plate 4–Inlet and outlet of an antifreeze mixture

2–Lower plate 5–Groove

3–End plates 6–O-ring

2

Figure 1. Apparatus.

1

2

3

3

4

5 6

4
tioning a soil column into 25 segments with ideally

equal lengths, they serve as an indicator of uniformity in

packing and accuracy in sectioning.

In Table 1 Tw is the temperature at the warm end of a

soil column while Tc is the temperature at the cold end

of a soil column. For all the experiments, the same linear temperature field was applied; the duration of experiments was 22 days. In the last column of Table 1 is

given the concentration of Br in distilled water C0 that

was mixed with dry soil to make the soil columns. In

experiments 1–4, distilled water without Br was mixed

with dry soil, while 400 μg/g Br was used in experiments 5–8. Experiments 1–4 were conducted to find the

effects of Br on the transport of unfrozen water by comparison with experiments 5–8, where Br was used.

The results of experiments 5–8 are presented in Figure 2, where nondimensional quantities w+ and Cˆ + are

defined as

w ww + = / 0 (2a)

ˆ ˆ / C CC + ˆ = 0 (2b)

where w is the measured water (including ice) content at

the end of experiments, while w0 is the initial uniform

water content. The unit of water content is the weight of

water and ice per unit weight of dry soil. Cˆ is the measured Br content. The unit of Br content is the weight

of Br per unit weight of dry soil.

In Figure 2 the nondimensional quantities w+ and

Cˆ + are plotted versus the segment number i that is assigned 1–25 from the warm end to the cold end. The

linear temperature field imposed is also shown in these

figures. The 0°C isotherm is located at the interface between segments 10 and 11 so that the temperatures of

segments 1–10 are positive while those of segments 11–

25 are negative.

It follows from the definitions of eq 2a and 2b that

w+ and Cˆ + would be one if unfrozen water and Br did

not move at all during the experiments. It is clear

m2/g and a specific gravity of 2.75 g/cm3. This clay

was used in the experiments reported by Nakano and

Tice (1990). For a given dry density ρ and initial water

content w0, the exact amounts of oven-dry Morin clay

and distilled water containing 400 μg/g of Br as KBr

were weighed to be packed into a groove. Mixing thoroughly the weighed soil and water, we allowed the

mixture to set for a few days to attain moisture equilibration. After all four grooves were packed with soil

samples, we bolted together the upper and lower plates

to seal each of four soil columns with a rectangular

cross section and froze them down to about –15°C.

An experiment began by placing the bolted upper

and lower plates into the space between the two end

plates. A stable and linear temperature field was usually established within 1 hour by adjusting the temperatures of the two baths. After a specified time

passed, the bolted upper and lower plates were brought

into a coldroom with its temperature being set at –

10°C. The two plates were separated and each sample

was quickly sectioned into a total of 25 segments with

equal lengths. Each segment was placed in a glass

weighing bottle and oven-dried. The water content and

the dry density of each segment were determined

gravimetrically. The concentration of Br of each segment was determined using the Dionex Ion Chromatography Model 2010i.

RESULTS OF EXPERIMENTS

The test conditions of the experiments are presented in Table 1. For all of these experiments, we

aimed to maintain the average dry density of the soil

columns at about 1.45 g/cm3, although the uniform

packing of soil in each column was quite difficult. We

examined the uniformity of the soil columns by using

the measured dry density of all segments after each experiment. The mean ρa and the standard deviation σ of

dry density ρ are given in Table 1. Although these values are affected by errors associated with rapidly sec3

Table 1. Experimental conditions.

Temperature Temperature

Experiment w0 ρa Tw Tc gradient duration C0

no. (%) (g/cm) σ (°C) (°C) (°C/cm) (days) (μg/g)

1 22.5 1.48 0.13 1.00 –1.50 0.120 22 0.0

2 25.0 1.45 0.10 1.00 –1.50 0.120 22 0.0

3 27.5 1.46 0.07 1.00 –1.50 0.120 22 0.0

4 30.0 1.45 0.12 1.00 –1.50 0.120 22 0.0

5 22.5 1.44 0.11 1.00 –1.50 0.120 22 400

6 25.0 1.46 0.14 1.00 –1.50 0.120 22 400

7 27.5 1.47 0.13 1.00 –1.50 0.120 22 400

8 30.0 1.43 0.08 1.00 –1.50 0.120 22 400
4

0.4

0.8

1.2

1.6

2.0

– 1.6

– 0.8

0

0.8

1.6

0 4 8 12 16 20 24

i

w+

, C+ ^ T (°C)

= 22 (d)

= 25 (%)

t 

w0

 

w+

C

^ +

T

0.4

0.8

1.2

1.6

2.0

– 1.6

– 0.8

0

0.8

1.6

0 4 8 12 16 20 24

i

w+

, C+ ^ T (°C)

= 22 (d)

= 30 (%)

t 

w0

 

w+

C

^ +

T

0.4

0.8

1.2

1.6

2.0

– 1.6

– 0.8

0

0.8

1.6

0 4 8 12 16 20 24

i

w+

, C+ ^ T (°C)

= 22 (d)

= 27.5 (%)

t 

w0

 

w+

C

^ +

T

a. Experiment 5.

b. Experiment 6.

c. Experiment 7.

d. Experiment 8.

Figure 2. Nondimensional contents of water

w+ and Cˆ + versus the segment number i for

experiments 5–8.

0.4

0.8

1.2

1.6

2.0

– 1.6

– 0.8

0

0.8

1.6

0 4 8 12 16 20 24

i

w+

, C+ ^ T (°C)

= 22 (d)

= 22.5 (%)

t 

w0

 

w+

C

^ +

T
from Figure 2 that both water and Br moved from the

warmer to cooler parts in the soil columns. The unfrozen part (segments 1–10) of soil columns lost both water and Br. It is interesting that a few segments in the

frozen part near the 0°C isotherm also lost both water

and Br and that the minimum value of Cˆ + appears in

these frozen segments.

ANALYSIS OF DATA

We will consider the balance of water and Br in the

part of soil columns Vi consisting of segments 1–i. We

will assume that the initial dry density of each segment

is equal to the final dry density of each segment measured at the end of the experiment. The loss of water Wi

from the part Vi during the experiment is calculated as

Wv w w j

j

i

i 0j = − ( ) =

∑ρ

1

(3)

where v is the volume of each segment and ρj and wj are

the dry density and the water content of segment j respectively. Similarly, the loss of Br, Bi

, from the part Vi

during the experiment is calculated as

Bv CC j

j

i

i 0j = − ( ) =

∑ρ

1

ˆ ˆ (4)

where Cˆ

j is the Br content of segment j.

The calculated values of Wi for experiments 1–4 are

plotted together with those for experiments 5–8 in Figure 3, where open circles are the data points from experiments 1–4, while solid circles are the data points

from experiments 5–8. For instance, in Figure 3a the

calculated values of Wi for experiment 1 are plotted together with those for experiment 5. Experiments 1 and

5 are conducted under the same conditions, except that

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

packed uniformly in each column and that Br does not

affect the movement of unfrozen water. Then it is anticipated that the calculated values of Wi

 for experiment

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

uniform packing of soil is quite difficult, Figure 3 indicates that the level of Br content used in experiments

5–8 does not significantly affect the mobility of unfrozen water.

The calculated values of Wi and Bi for experiments

5–8 are presented in Figure 4. It is easy to see from

these figures that both Wi and Bi attain their maxima

and that the segment number of the maximum Bi is

greater than that of the maximum Wi. Let Fw(i) and

FB(i) be mass fluxes of water and Br, respectively,

from segment i to segment i + 1, then Wi and Bi are

given as

5

W F i dt

t

i w

0

= ∫

0

( ) (5)

B F i dt

t

i B

0

= ∫

0

( ) (6)

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 FB of Br is

given as

F i CF i B iw () () = (7)

where Ci is the concentration of Br in unfrozen water

for segment i. From eq 6 and 7 we obtain

B C F i dt

t

i iB

0

= ∫

0

() . (8)

For a special case in which Ci remains constant at the

initial value C0, from eq 5 and 7 we obtain

 Bi = C0Wi . (9)

It follows from eq 9 that both Wi and Bi attain their

maxima at the same segment. This obviously did not

occur in our experiments.

Since Br is excluded from growing ice and is confined to unfrozen water, the concentration of Br, Ci

,

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

linear temperature field is established at the beginning

of experiments. Because of the Br exclusion from ice,

Ci increases with i in segments where ice is present; as

a result, the segment number of the maximum Bi becomes greater than that of the maximum Wi

.

The Br ion may not be completely confined to unfrozen water. However, let us assume this complete

confinement, as it appears to be a good approximation.

We will also assume that the phase equilibrium of water holds true in the experiments. Then, the unfrozen

water content is approximated by the equilibrium unfrozen water content determined by the nuclear magnetic resonance technique on a separate sample of

Morin clay. Under these assumptions the concentrations of Br in unfrozen water at both the beginning and the end of the experiments were calculated.

The results of calculations for experiments 5–8 are

presented in Figure 5, where nondimensional quantities C0

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

Br in unfrozen water divided by C0 at the beginning

and the end of the experiment respectively. For instance, the calculated values of C0

+ and C+(t) for ex-
6

0 4 8 12 16 20 24

i

w = 22.5 (%) 0 

Br+

 

0

Wi (g)

0.2

0.4

0.6

i

0

Wi (g)

0.2

0.4

0.6

0 4 8 12 16 20 24

w = 25 (%) 0 

Br+

 

i

0

Wi (g)

0.2

0.4

0.6

0 4 8 12 16 20 24

w = 27.5 (%) 0 

Br+

 

i

0

Wi (g)

0.2

0.4

0.6

0 4 8 12 16 20 24

w = 30 (%) 0 

Br+

 

a. Experiment 1 with 5.

b. Experiment 2 with 6.

c. Experiment 3 with 7.

d. Experiment 4 with 8.

Figure 3. Comparison of Wi values from experiments both with and without Br .
7

i

= 22 (d)

= 22.5 (%)

t 

w0

 

Wi

Bi

0

T > 0° C

Wi (g), Bi (mg)

0.2

0.4

0.6

0 4 8 12 16 20 24

i

= 22 (d)

= 25 (%)

t 

w0

 

Wi

Bi

0

T > 0° C

Wi (g), Bi (mg)

0.2

0.4

0.6

0 4 8 12 16 20 24

i

= 22 (d)

= 27.5 (%)

t 

w0

 

Wi

Bi

0

T > 0° C

Wi (g), Bi (mg)

0.2

0.4

0.6

0 4 8 12 16 20 24

i

= 22 (d)

= 30 (%)

t 

w0

 

Wi

Bi

0

T > 0° C

Wi (g), Bi (mg)

0.2

0.4

0.6

0 4 8 12 16 20 24

a. Experiment 5.

b. Experiment 6.

c. Experiment 7.

d. Experiment 8.

Figure 4. Calculated values of Wi

 and Bi

for experiments 5–8.
8

i

= 22 (d)

= 22.5 (%)

t 

w0

 

C+

 

0

C+ (t)

C+

 

a

0

2

4

T > 0° C

5

3

1

C0, C (t), Ca

 + + +

0 4 8 12 16 20 24

i

C0, C (t), Ca

 + + +

= 22 (d)

= 27.5 (%)

t 

w0

 

C+

 

0

C+ (t)

C+

 

a

0

2

4

T > 0° C

5

3

1

0 4 8 12 16 20 24

i

C0, C (t), Ca

 + + +

= 22 (d)

= 30 (%)

t 

w0

 

C+

 

0

C+ (t)

C+

 

a

0

2

4

T > 0° C

5

3

1

0 4 8 12 16 20 24

i

C0, C (t), Ca

 + + +

= 22 (d)

= 25 (%)

t 

w0

 

C+

 

0

C+ (t)

C+

 

a

0

2

4

T > 0° C

5

3

1

0 4 8 12 16 20 24

a. Experiment 5.

b. Experiment 6.

c. Experiment 7.

d. Experiment 8.

Figure 5. Values of C0

+ , C+(t) and Ca+ of experiments 5–8.
Segments 11–15 lost water, but C+(t) is still less than

C0

+ . As a result C+(t) becomes less than C0+ in every

section of V. The input of both water and Br to V must

have come from the unfrozen part where the concentration of Br remained approximately at C0 during

the experiment. Suppose that unfrozen water and Br

moved at the same rate. Then, C(t) must not be less

than C0. However, it is easy to see from Figure 5a that

C+(t) is less than one in segments 11–16. This is obviously contradictory. Therefore, we may conclude that

Br must have moved faster than the unfrozen water in

segments 11–16 where C+(t) is less than one.

The features of C0

+ , C+(t) and Ca+ in experiment 5

described above are common to experiments 6–8. In

experiment 6 (Fig. 5b) C(t) is less than C0 in segments

11–15, while in experiments 7 and 8 (Fig. 5c and d),

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

part except for a few segments near the cold end.

These data strongly indicate that Br moved faster

than unfrozen water in the frozen part of the soil columns. In other words, the repulsion or negative adsorption of Br by the negatively charged Morin clay

must have moved Br faster than unfrozen water.

Since the repulsion of anions is caused by the interaction between anions and surfaces of soil particles, the

effect of anion repulsion on the transport of anions is

expected to become less pronounced with the increasing unfrozen water content. This general trend can be

seen in Figure 5 with the increasing initial water content w0.

CONCLUSIONS

The movement of water and Br was measured in

unsaturated and partially frozen clay columns subjected to linear temperature fields. Both water and Br

were found to move from the warmer to cooler parts

in the columns. The data were analyzed under assumption that Br is completely confined to unfrozen

water in the frozen part of the columns.

The concentration of Br in water was found not to

change significantly from the initial concentration in

the unfrozen part of the columns. However, the data

from the frozen part of the columns strongly indicate

that Br moved faster than unfrozen water because of

the repulsion of Br by the negatively charged surfaces of clay particles. The effect of anion repulsion

on the transport of Br in the frozen part of the columns was found to become more pronounced with the

decreasing initial water content. It may be concluded

that the anion repulsion by clay surfaces plays a significant role in the transport of Br in unsaturated and

partially frozen clay.

9

periment 5 are plotted vs. the segment number i in Figure 5a, where solid and open circles are the data points

of C0

+ and C+(t) respectively. The values of C0+ are

nearly one in segments 1–14 because ice is absent

while the C0

+ increases with i in segments 14–25 as the

content of ice increases.

The values of C+(t) vary in the unfrozen part (segments 1–10), but they are not very far from one. However, the C+(t) increases sharply from segments 15–23

in comparison with C0

+ and as a result, the values of

C+(t) become twice as great as the C0

+ values near the

cold end. There is an interesting trend that the values of

C+(t) become less than C0

+ in segments 12–17. The

behaviors of C0

+ and C+(t) described above can be seen

also in Figures 5b–d, but become less pronounced as

the initial water content w0 increases.

In Figure 5 the values of C+(t) fluctuate about one in

the unfrozen part, and the pattern of fluctuation appears to be more or less random. However, in the frozen part near the 0°C isotherm there is a common feature that C+(t) becomes less than C0

+ . It is clear from

Figure 4 that both water and Br moved from the

warmer to cooler parts in the soil columns. The common feature described above indicates that unfrozen

water and Br may not move at the same rate.

We will introduce a nondimensional quantity Ca

+

defined as

C i Ci C a a0

+ ( ) ( )/ = (10a)

Ci BW a ii () / . = (10b)

It follows from eq 10b that Ca(i) is the (time) average

concentration of Br in water removed from the part Vi

of a soil column during the experiment. It is easy to see

that the concentration of Br in water removed from Vi

must be equal to C0 at the beginning and C(t) of segment i at the end of the experiment. The calculated values of Ca

+ are plotted in Figure 5 in comparison with

C0

+ and C+(t).

In Figure 5, we may consider that the concentration

of Br in the unfrozen part did not change significantly

from the initial concentration C0 during the experiment. However, in the frozen part, except for a few

segments near the cold end, Ca

+ is greater than both

C0

+ and C+(t) in all cases. Since the features of C0+ ,

C+(t) and Ca

+ common to experiments 5–8 are the

most pronounced in experiment 5, we will examine experiment 5 below.

We will consider a part V of the soil column consisting of segments 11–18 (Fig. 2a and 5a). Since Cˆ + < 1

in V (Fig. 2a), every section of V lost Br during the

experiment. Since w+ > 1 in segments 16–18, these

three sections gained water during the experiment.
LITERATURE CITED

Baker, G.C. and T.E. Osterkamp (1989) Salt redistribution during freezing of saline sand columns at constant

rates. Water Resources Research, 25: 1825–1831.

Banin, A. and D.M. Anderson (1974) Effects of salt

concentration changes during freezing on the unfrozen

water content of porous materials. Water Resources

Research, 10: 124–128.

Biggar, J.W. and D.R. Nielsen (1962) Miscible displacement: II. Behavior of tracers. Soil Science Society

of America Proceedings, 26: 125–128.

Burton, J.A., R.C. Prim and W.P. Slichter (1953) The

distribution of solute in crystals grown from the melt.

Part I, Theoretical. Journal of Chemical Physics, 21:

1987–1991.

Gray, D.M. and R.J. Granger (1986) In situ measurements of moisture and salt movement in freezing soils.

Canadian Journal of Earth Science, 23: 696–704.

Hivon, E.G. (1991) Behavior of saline frozen soils.

Ph.D. Dissertation, Department of Civil Engineering,

University of Alberta, Edmonton, Canada (unpublished).

Konrad, J.M. (1990) Segregation potential-pressuresalinity relationships near thermal steady state for a clayey

silt. Canadian Geotechnical Journal, 27: 203–215.

Konrad, J.M. and A.W. McCammon (1990) Solute partitioning in freezing soils. Canadian Geotechnical Journal, 27: 726–736.

Krupp, H.K., J.W. Biggar and D.R. Nielsen (1972)

Relative flow rates of salt and water in soil. Soil Science

Society of America Proceedings, 36: 412–417.

Mahar, L.J., R.M. Wilson and T.S. Vinson (1983)

Physical and numerical modeling of uniaxial freezing in

a saline gravel. In Proceedings, 4th International Conference on Permafrost, July 17–22, Fairbanks, Alaska.

Washington, D.C.: National Academy Press, p. 773–778.

Nakano, Y. (1991) Transport of water through frozen

soils. In Proceedings, 6th International Symposium on

Ground Freezing. Rotterdam: Balkema, p. 65–70.

Nakano, Y. and A. Tice (1990) Transport of water due to

a temperature gradient in unsaturated frozen clay. Cold

Regions Science and Technology, 18: 57–75.

Nielsen, D.R., R.D. Jackson, J.W. Cary and D.D.

Evans (1972) Soil Water. Madison, Wisconsin: ASASSSA, p. 175.

Sego, D., T. Schultz and R. Banasch (1982) Strength

and deformation behavior of frozen saline sand. In

Proceedings, 3rd International Symposium on Ground

Freezing, 22–24 June, Hanover, N.H., U.S.A. USA Cold

Regions Research and Engineering Laboratory, p. 11–

18.

Weeks, W.F. and G. Lofgren (1966) The effective solute distribution coefficient during the freezing of NaCl

solutions. Institute of Low Temperature Science, Physics

of Snow and Ice, 1: 579–597.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

6. AUTHORS

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

 REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS 15. NUMBER OF PAGES

16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

 OF REPORT OF THIS PAGE OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and

maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,

including suggestion for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington,

VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

For conversion of SI units to non-SI units of measurement consult Standard Practice for Use of the International System of Units (SI),

ASTM Standard E380-93, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa. 19103.

February 1995

Transport of Tracer Br in Frozen Morin Clay PR: 4A161102AT24

in Response to Temperature Gradients WP: 125

WU: AT24-SC-F01

Yoshisuke Nakano

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road CRREL Report 95-3

Hanover, New Hampshire 03755-1290

Office of the Chief of Engineers

Washington, D.C. 20314-1000

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161.

12

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

The movement of water and Br was measured in unsaturated and partially frozen soil columns subjected to linear temperature fields. Both water and Br moved from the warmer to cooler parts in the columns. The data were analyzed under the assumption that Br is confined to unfrozen water. It was found that the negative adsorption of Br by clay surfaces plays a significant role in the transport of Br in frozen Morin clay and that Br tends to move faster than unfrozen

water.

Clay Ion transport

Frost heave Temperature gradients