Geology Reference
In-Depth Information
following simple equation for estimating the velocity of
migration of the brine pocket
v
toward the warmer side
of the ice:
mechanism is well covered in the literature [
Weeks
and Ackley,
1982;
Petrich and Eicken,
2009;
Notz and
Worster,
2009;
Weeks,
2010].
Cox and Weeks
[1988] applied equations to calculate
the change in salinity of a given layer of ice due to the
brine expulsion mechanism. The equations were origi-
nally developed by
Cox and Weeks
[1986] to address
changes in salinity and porosity of ice core samples
immediately after extraction from the ice sheet and before
storage. Cores are usually exposed to colder air tempera-
ture upon extraction in the field (particularly in the polar
regions), and that is how brine expulsion as suggested by
the authors listed above becomes effective. During cool-
ing from temperature
T
1
to temperature
T
2
the amount of
brine expelled from an ice layer is measured by the ratios
of the ice salinities [
S
1
(
T
1
)/
S
2
(
T
2
)] as well as brine volume
V
b
(
T
1
)/
V
b
(
T
2
) according to the following equations (ratios
are always < 1):
D
mC
(2.38)
v
146
.
where
D
is the diffusion coefficient of the salts in the sea-
water,
C
is the salt concentration in the brine, and
m
is the
slope of the liquidus curve in the phase diagram.
If the temperature at the location of the brine pocket is
−6 °C, the theory gives a migration velocity 14.0
µ
m/h or
equivalent to almost 10 mm per month. It should also be
noted that brine pockets can migrate upward as well dur-
ing the early spring when the temperature gradient is
reversed.
Untersteiner
[1968] came to the conclusion that
brine pockets migrate by an average of 20 mm downward
near the ice surface, with an almost equal migration
upward during spring.
Weeks
[2010] presented an evalua-
tion of equation (2.38) in terms of migration velocities
observed at different ice temperatures.
Advection velocity of brine pockets caused by diffu-
sion is modeled using the assumption of sea ice being a
two‐component porous medium (pure ice and brine) and
presented in
Notz and Worster
[2009]. They found that
the speed of salt diffusion depends on the temperature
gradient in the bulk sea ice and independent of the geo-
metric distribution or interconnectedness of the brine
inclusions. They estimated also the typical advection
velocity of brine pockets to be 10
−9
m/s for a typical tem-
perature gradient of 10°C/m and a brine salinity of about
100‰. These results confirmed observations obtained by
Harrison
[1965] and
Jones
[1974]. In any case, brine
migrates with very small velocities and, therefore, this
mechanism may not be considered as an effective con-
tributor to ice desalination.
2. Brine Expulsion
The second mechanism of sea ice
desalination is brine expulsion. This mechanism was sug-
gested by
Bennington
[1967]. It is linked to the decrease in
bulk ice temperature and the associated decrease in the
volume of the brine pockets due to the solidification
of more water inside the brine pockets. Consequently,
salinity of brine remaining in the pockets is expected to
increase in order to maintain the phase equilibrium.
Since ice density is less than that of water, the frozen ice
inside the pocket occupies an approximately 10% greater
volume than that of water from which it was formed.
This mechanism was thought to increase the pressure
inside the pocket, which may ultimately cause cracks
around the pocket through which brine is expelled. While
most of the expelled brine is expected to flow downward
into the warmer ice medium, some may be expelled
upward in ice near the top surfaces. The brine expulsion
(2.39)
and
1
/
VT
VT
(
(
)
)
ST
ST
(
)
c
ST ST
i
(2.40)
b
2
b
1
exp
(
)
(
)
(
)
b
1
b
2
i
b
1
b
2
where
S
b
is brine salinity,
ρ
b
is brine density,
ρ
i
is pure
ice density (918 kg/m
3
), and
c
is a constant equal to
dρ
b
/
dT
,
which is 0.8 kg/m
3
. On the other hand, during warming of
ice (
T
2
>
T
1
), the above two equations take the form
ST
ST
(
(
)
)
1
(2.41)
i
2
i
1
(2.42)
Equations for calculating
S
b
and
b
are given in
Cox and
Weeks
[1986] and are included in sections 3.2 and 3.3,
respectively.
In general, brine expulsion is more pronounced in
the upper layer of sea ice, particularly in thin ice.
Cox
and Weeks
[1975, p. ii] concluded from their laboratory
experiments that brine expulsion was only important
during the first hours of ice growth and later became a
minor desalination process relative to gravity drainage.
Notz and Worster
[2009] calculated the brine velocity
caused by brine expulsion and found that it was less
than the typical growth rate of sea ice at the ice‐water
interface. Therefore, brine expulsion can only lead to
