Table 1. Geometric definitions and relationships of ice structure. All units are SI.
Parameter
Functional relationship
Evaluated
G (grain size)
length/grain boundary intercepts
Φ (dihedral angle)
32
θ (contact angle)
0
σil, σal, and σiv (surface tension)
0.034, 0.075, 0.109 (Jm2)
VEINS
α
14
α = π/6-Φ/2
dv (vein width)
rv = dv/2 sinα
rv (radius of curvature of vein)
rv = dv/0.4838 (m)
3
Av = rv2
3 sin 2 α + sin 2α - 3α
Av = 0.0725 rv2 (m2)
Av (cross sectional area of vein)
2
l (length of veins per unit volume)a
l = 3/G2
RH (hydraulic radius)
2 vein area/vein circumference
RH = 0.2044 dv(m)
π rH
4
ki =
ki (permeability)
2G2 (1 + b 4 )
2
rAv = (dv / 2) (tan π / 6 - tan α / 2)
rAv (vein air-entry radius)
rAv = 0.2273 dv (m)
NODE
Rn (nodal volume/vein volume) b
13.89dv /G
rAn = (dv / 2) 3(3 ⋅ 8.61) / (4π)
rAn (node air-entry radius)b
rAn = 0.6357 dv (m)
LENS
2π
φ
φ 3
VL =
2 - 3 cos + cos3 rL
VL (volume of lens)c
0.0093 rL3 (m3)
3
2
2
(6
)(
)
3 + 3 / 4 2G
Sv (surface to volume ratio of ice grain)d
2.37/G
GROOVE (Fig. 8c)
β
sin1[(rgcos(Φ/2)/(ra + rg)]
Nye (1991b), bNye (1989), cNye and Mae (1972), dLliboutry (1996).
a
however, discarded the dirtier portions of her samples
sible at these molality levels.* The vein bulk molality
mv for the clean part of Sample A is then 6.46 105
before analysis. Contamination from the preparatory
moles kg1. Because of possible post-experimental con-
brine bath used to grow Sample A undoubtedly con-
tamination, we take mv as 1.00 106 moles kg1 for
tributed to the high concentration of Cl. For Sample
A, we assume that the Cl cations are located within
the clean part of Sample B, in line with Mader (1992b)
and closer to the value computed from Hanover tap
the ice lattice (Wolff 1996) and that an equal number of
Na+ anions are apportioned 50% each between grain
water.
boundaries and veins (Harrison and Raymond 1976).
Both samples also accreted impurities during post-
THEORY
experimental handling and sectioning (e.g., Fig. 4c).
Ice structure is determined thermodynamically from
The proportional impact of this contamination is greater
combined thermal and mechanical stresses in the ice.
for Sample B.
Interfacial surface tensions define the geometry of air
Because expelled impurities concentrate ahead of
and water inclusions. Table 1 summarizes the geometri-
the freezing front, they occur within a central core in
Sample A and towards the top of Sample B. Mader
(1992b) found that 89% of the impurities resided in
* In colder ice, the diffusivity of heat is much greater than the
diffusivity of salt and limits the diffusion of impurities. As tempera-
14% of the ice volume. With these proportions, the bulk
tures approach 0C and with increasing molality, however, latent heat
molality for the "clean" part of the sample is reduced
affects in ice lower its thermal diffusivity (Nye 1991a). Sample A
to a factor of 0.13 while that for the "dirty" part is
has a sufficiently high molality that thermal and salt diffusivities are
enhanced to a factor of 6.4. Here we assume that impu-
of the same magnitude for a temperature around 0.01C and thus
rities are immobile, although diffusion of solutes is pos-
some diffusion of solutes may occur.
4
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