∆T = 0.13 2.978 mNaCl
water interactions and as a consequence only dem-
onstrates qualitatively what might occur in a soil.
2
0.211 mNaCl (icesolution)
(3)
For example, Frolov and Komarov (1993) demon-
strated that NaCl solutions in soil remain unfro-
zen to temperatures lower (24C) than the eutectic
R2 = 1.000
for pure NaCl (21.2C, Fig. 2), presumably due to
∆T = 42.37 12.082 mNaCl
capillary effects.
Banin and Anderson (1974) examined solute
2
+ 3.131 mNaCl (solutionNaCl . 2H2O) (4)
effects on freezing-point depression by comparing
the freezing points of soils, with and without NaCl
R2 = 0.964
additions. They found excellent agreement be-
tween experimental measurements and a theoret-
and
ical solute model at low NaCl concentrations and
a small but consistent underestimate (1020%) of
Wu = mBi/mBf
(5)
the experimental freezing point at higher NaCl
concentrations. Suleimanov and Andronova (1990),
∆T = freezing-point depression
where
using a similar theoretical solute model, reported
mNaCl = NaCl molality
a similar underestimate of the measured freezing
Wu = fraction of unfrozen water
point. Both studies suggested that this discrepan-
mBi and mBf = initial and final molalities.
cy was due to the inhomogeneous distribution of
salt in water because of the negative adsorption of
Equation 5 assumes the precipitation of a pure ice
anions (anion repulsion) near negatively charged
phase. At 10 and 20C, the corresponding NaCl
surfaces, which resulted in abnormally high salt
molalities are 2.77 and 4.94 mol kg1, respectively
concentrations in the bulk solution.
(eq 3). Therefore, the unfrozen water contents at
Yong et al. (1979) developed an unfrozen soil
10 and 20C for a solution that was initially 1.0
water model that explicitly accounts for negative
mol kg1 are 0.361 (1.0/2.77) and 0.202 (1.00/4.94),
salt adsorption using diffuse double-layer theory.
respectively (eq 5). Conversely the frozen percent-
This model showed excellent quantitative agree-
ages are 63.9 and 79.8%. If the initial NaCl solu-
ment with a montmorillonite soil sample but only
tion was 0.01 mol kg1, then the unfrozen fraction
qualitative agreement for kaolinite and grundite
at 20C would be 0.00202 (0.01/4.94), with a fro-
soils. This discrepancy was attributed to the mod-
zen percentage of 99.8%. Clearly the concentration
el requirement for interlamellar migration of
of salts in the solution phase during the freezing
water in soil freezing, which is a reasonable
process, because of salt exclusion from the ice
assumption for montmorillonite but not for kaolin-
phase, can substantially alter the freezing point
ite or grundite. Yong et al. (1979) also pointed out
and unfrozen water contents of solutions.
examples where pure solution theory contradicts
The NaClH2O phase diagram also demon-
experimental measurements. For example, the
strates that an NaCl aqueous solution with an ini-
unfrozen water content at subfreezing tempera-
tial concentration < 5.17 m will not precipitate
tures first decreases with the addition of salt to a
NaCl . 2H2O until the temperature drops to 21.2C
minimum value around 103 mol L1, then increas-
and the NaCl molality increases to 5.17 mol kg1
es with increasing salt concentration, as would be
(the eutectic point). On the other hand, if the ini-
predicted from pure solution theory. There are
tial NaCl molality is > 5.17 mol kg1, then
strong interactions among soil surface area,
NaCl . 2H2O will be the initial phase to precipitate
charged surfaces, soil salts and moisture that con-
and ice will not form until the temperature drops
trol freezing-point depression and unfrozen water
to 21.2C and the NaCl concentration decreases
content of soils. A model that can describe these
to 5.17 mol kg1.
interactions quantitatively over a broad range of
For soils the major factors influencing the freez-
salt concentrations does not exist at present.
ing-point depression and unfrozen water contents
A number of papers have reviewed the physics
are temperature, adherence of water to soil parti-
of moisture movement in freezing and frozen soils
cles and solute concentrations (Hoekstra 1969,
(Hoekstra 1969, Anderson and Morgenstern 1973,
Anderson and Morgenstern 1973, Perfect et al.
Miller 1980, Perfect et al. 1991). This is a broad field,
1991, Frolov and Komarov 1993). The pure NaCl
much studied and for the most part beyond the
H2O phase diagram (Fig. 2) neglects soil solid
scope of this review. For the purposes of this re-
3
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