aqueous solutions, which is most often assumed in contaminant-transport models, even
though water at 25C under atmospheric pressure has a density of 997.02 kg m3, a relative
change of 2.98% from its maximum. At the triple point of water (0.01C), liquid water has a
density of 999.78 kg m3, a relative change of 0.022% from its maximum.
Supercooled water
Speedy (1987) has presented equations that have been fitted to the thermodynamic
properties of supercooled water. His equation for the density of water is
1 (n) n+1
ρ = ρs exp-Ts ∑
Bα ε
+ 2Cα ε1/2 ,
(4)
n= 0 n + 1
where ρs is a reference density and both Bαn) and Cα are empirical parameters, the values of
(
which are presented in Table 1. A global fit of eq 4 to the density data of Hare and Sorensen
(1987) yielded the following parameter estimates:
ρs
0.901 532 859 3
Cα
0.001 176 165 2
Bα0)
(
0.003 844 238 2
Bα1)
(
0.015 727 076 1
Bα2)
(
0.074 406 461 4
Bα3)
(
0.140 643 265 3
The largest deviation of the fitted curve from measured data is 0.20%.
Viscosity
The viscosity of liquid water increases exponentially with decreasing temperature.
While the International Association for the Properties of Water and Steam (IAPWS) has
released an elaborate expression for calculating the viscosity of water as a function of pres-
sure and temperature, a much simpler expression may be used accurately for common
pressures and temperatures between 40 and 25C. Experimental viscosity data have been
fitted to the empirical VogelTammannFulcher (VTF) equation:
B
v = v0 exp
(5)
t + t0
where ν0 = 0.028 556 Pa s
B = 509.53C
t = temperature (C)
t0 = empirical constant equal to 123.15C.
A modification of this equation is able to fit the available data more closely:
B
B3
B2
v = v0 exp 1 +
+
(6)
.
t + t0 (t + t0 )2 (t + t0 )3
where ν0 = 0.000 046 01 Pa s
B1 = 3068.6C
B2 = 3.3775 105 C2
B3 = 1.4781 107 C3.
This relation is plotted in Figure 3, showing its agreement with measured values.
In the temperature range of 35C to 0C, the viscosity of supercooled water may be
fitted to Speedy's (1987) limiting-temperature empirical equation (eq 3). This relation is
presented in Figure 4.
6
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