Physical bases of freezing point measurement using ... - Boschung

E. Bornand
Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 273
Physical bases of freezing point measurement using
active and passive probes
Boschung Mecatronic AG, Route d’Englisberg 21, CH-1763 Granges-Paccot, Switzerland
etienne.bornand@boschung.com
ABSTRACT
Active and passive probes implanted in the pavement are used to forecast the formation of icy slipperiness such
as glazed frost, rime, etc., and to determine the road conditions. The active probe owns an element able to freeze
the aqueous solution laying on its surface. It measures the freezing temperature via the latent heat of fusion
which is released during the crystallization. The passive probe - which cannot artificially freeze the solution -
measures different physical properties such as the temperature, the conductivity, the permittivity of the solution,
from which road parameters are deduced. The degree of protection of the road, given by the salt content, is
deduced from the freezing temperature and the thickness of the solution.
Keywords : active probe, passive probe, saline aqueous solution, freezing temperature, supercooling, latent heat
of fusion, salt content, electrical conductivity, permittivity, Peltier effect, thermoelectric cooler.
1. INTRODUCTION
The formation of icy slipperiness such as glazed frost, rime, etc., on the roads may have
diverse origins such as cooling of the wet pavement, streaming followed by cooling, freezing
rain, etc. If chemicals have been spread on the pavement, the freezing point will be lower
than 0 °C. The goal of the active and passive probes is on one hand to predict the imminence
of ice formation and to trig in the Road Maintenance Center the required warning in function
of the degree of urgency, and on the other hand to measure the actual protection rate of the
road.
2. ACTIVE PROBES
An active probe is characterized by the fact that the aqueous solution laying on its
surface can be cooled and frozen by an artificial means.
2.1 Principle of operation
The principle of operation of the Boschung's patented active probe for the measurement
of the freezing temperature is based on the variation of enthalpy associated with the
solidification of the aqueous solution.

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 274
2.1.1 Nucleation of ice
Nine allotropic varieties of ice do exist, however only ice Ih exists under pressures
lower than 200 MPa and temperatures greater than those of liquid air. It crystallizes in the
hexagonal system (spatial group P 63/mmc) and is then the only ice that exists in the natural
state.
Ice may form either by the freezing of liquid water (producing for instance glazed frost)
or by deposition from the vapor phase (producing for instance rime). In both cases, the
initiation of the ice phase occurs by the nucleation of a small ice embryo. Under certain
conditions, water can be cooled well below 0 °C and yet remains in the liquid state. Water in
such a metastable state is said to be supercooled. If the nucleation of the ice phase occurs on
foreign particles (impurities, dust particles, gaseous bubbles, etc.), the ice is said to form by
heterogeneous nucleation. If foreign particles do not play a role in the nucleation, the ice
phase must be initiated by water molecules combining together to form an ice embryo which
can grow spontaneously. In this case, the ice is said to form by homogeneous nucleation. It is
interesting to note that vibrations also initiate the crystallization of supercooled water. The
nucleation of ice is discussed in detail in [Hobbs 1974].
2.1.2 Latent heat of fusion
The change in enthalpy dH associated with a change in phase of a material at constant
pressure p is given by :
dH = dU + pdV (1)
where dU and dV are the changes in internal energy and volume of the material respectively.
The latent heat of fusion Lf of ice is defined as the change in enthalpy when a unit mass of ice
is converted isothermally and reversibly into liquid water. In this case, the term p dV is small
compared to the other two terms in equation (1), so that Lf is equal to the change in internal
energy. The latent heat of fusion of ice at 0 °C and standard atmospheric pressure is
333.5 kJ/kg. For a discussion about this subject, see [Hobbs 1974].
To melt ice, latent heat of fusion has to be supplied (endothermic transformation), while
when water is frozen, an amount of heat equal to the latent heat of fusion is released
(exothermic transformation).
2.1.3 Scenario of the measurement
Instead of considering the cooling of pure water, let us consider first the behavior of a
saline aqueous solution during cooling from an initial temperature T0, as illustrated in the
figure 1. As pointed out by [Franks 1982], initially the solution supercools, until nucleation
takes place at the temperature Tbc and crystal growth begins. Since the latent heat cannot be
removed fast enough, the temperature rises to the melting temperature Tm. In the vicinity of
the growing ice crystals, the concentration of salt increases, reducing the local Tm, and

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 275
therefore retarding further freezing. The accumulation of heat now being the limiting factor,
ice continues to grow slowly at a constant rate. The temperature stays at Tm as far as the heat
generation is greater or equal than the heat withdrawal. When the rate of cooling becomes
greater than the rate of latent heat liberation, the temperature once again begins to fall. When
all the water has frozen, the rate of cooling depends on the thermal conductivity of the
solidified system. The temperature is then lowered until the asymptotic temperature Ta is
reached.
In the case of the cooling of pure water, the behavior is comparable to the one of an
aqueous saline solution, with the differences that Tm will be precisely 0 °C and the freezing
will not be retarded by the phenomenon described above.
The active probe achieves such a cooling and measures Tm by means of a thermocouple
or a platinum RTD 1 . The cooling is stopped as soon as Tbc is reached. Note that in the rest of
the text, for reasons of more common usage in our field, Ts (temperature of solidification, or
freezing point temperature 2 ) will be used instead of Tm.
The shape of the cooling curve is the same whatever the deicing product my be, salt or
deicers specially used on the airports such as ethylene glycol.
supercooling
T
Tm
T0
T bc
T a
0
beginning of
crystallization
Figure 1 : behavior of a saline aqueous solution during cooling.
2.2 Cooling performances
The cooling of water at the surface of a probe, schematically represented in figure 2, is
performed by a thermoelectric cooler (TEC). Heat is pumped through an metallic conductor
and is rejected through a heat sink. The isolation between the cold and hot sides is achieved
by an insulator. For the measurements of cooling performances, as shown in the figure, the
1 RTD = resistive temperature detector.
2 In some documents, the freezing point temperature is named GT (Gefrier Temperatur).
t

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 276
temperature was measured at the center of the surface of the probe, i.e. at the bottom of the
water, by a thermocouple.
H2O
Figure 2 : schematic representation of the cooling system.
T
thermocouple
cooler
body
insulator (plastics)
thermoelectric cooler
heat sink
Table 1 gives an example of computed cooling performances obtained with a
commercial TEC. i is the current supplied to the TEC, U the voltage 3 , Qin the electric power,
Qc the cooling power, Qh the rejected heating power and COP the coefficient of performance.
Heat power and COP depend of course on the temperatures Tc and Th of the cold and hot sides
of the TEC. In this example, Tc = - 19.1 °C and Th = 5.9 °C. The operation principle of
electronic refrigeration is described in Appendix A.
i [A] U [V] Qin [W] Qc [W] Qh [W] COP
1.5 1.4 2.1 1.7 3.8 0.80
2 1.8 3.5 2.6 6.2 0.74
2.5 2.1 5.3 3.4 8.7 0.63
3 2.5 7.5 3.9 11.5 0.53
3.3 2.7 9.0 4.2 13.2 0.47
3.9 3.2 12.3 4.5 16.8 0.37
Table 1 : cooling performances of a commercial TEC 4 .
3 Note that the symbol U is used for the internal energy (§ 2.1.2) as well as for the voltage!
4 MELCOR CP 1.0-31-05L.

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 277
For the currents listed in table 1, measurements of the cooling of pure water are shown
in figure 3. The water thickness is 0.5 mm and its volume is about 80 mm 3 . As discussed in
§ 2.1.3, the peaks of the curves originate from freezing. They reach the temperature of 0 °C.
T [°C]
10
5
0
-5
-10
-15
-20
-25
-30
3.3 A
3.9 A
0 20 40 60 80 100 120 140 160 180
t [s]
1.5 A
2 A
Figure 3 : influence of the current on the cooling rate of pure water.
2.5 A
The times t-15 and t-20 necessary to lower the temperature of 15 °C, respectively 20 °C,
are reported versus the current in figure 4, as well as the temperature difference between T0
and Ta. With the low current of 1.5 A, cooling of more than 20 °C is reached. This means that
even with low supplied power, effective cooling can be achieved.
t [s]
140
120
100
80
60
40
20
0
1 1.5 2 2.5 3 3.5 4
i [A]
Figure 4 : performances of cooling of the probe.
34
32
30
28
26
24
22
20
T 0 - T a [°C]
3 A
t -15 [s]
t -20 [s]
T 0 - T a [°C]

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 278
3. PASSIVE PROBES
While active probes are able to artificially create solidification of an aqueous solution,
passive one's do not. With this kind of probes, road conditions are deduced from
measurements of physical properties of the solution. The parameters which can be measured
are the following 5 :
3.1 Temperature
The temperature of the pavement is measured by means of a thermocouple or a
platinum RTD.
3.2 Electrical properties
The electrical properties which can be measured are the electrical conductivity σ and
the permittivity (or dielectric constant) ε.
To measure the electrical conductivity, the van der Pauw method [van der Pauw 1958]
can be used.
The permittivity of a material is given by :
ε = ε0εr , (2)
where ε0 = 8.85419 · 10 -12
C V -1
m -1
is the permittivity of free space and εr the relative
permittivity of the material. Dielectric and conduction properties may be investigated by
measuring the impedance Z of the material as a function of the electrical frequency. εr is
expressed by :
εr( ω) = εr′ − iεr′′
. (3)
ω is the applied angular velocity of the electric signal and ε r ′ and εr ′′ are the real and
complex parts of the relative permittivity 6 . The loss angle δ is :
The electrical conductivity is connected to the permittivity by :
εr
tgδ
=
ε
′′
′ . (4)
r
σ = ω ε ε′′
. (5)
Water is a polar material, i.e. constituted by dipoles. At low frequencies, its
permittivity ε r ′ can be greater than 100. The electrical properties of liquid water are discussed
5 None exhaustive list.
6
εr ′ is a measure of how much energy is stored in the material and εr ′′ a measure of how much energy is lost.
0 r

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 279
in [Franks 1972], those of pure ice in [Hobbs 1974, Jaccard 1959, Ruepp 1973, Franks 1982]
and those of aqueous electrolyte solutions in [Horvath 1985, Franks 1973]. Data are given in
[Zaytsev and Aseyev 1992, Barthel et al. 1995].
4. DISCUSSION
4.1 Utilization of active and passive probes
As we have seen, the first goal of the active probe is to measure the freezing
temperature. However it allows also to measure the surface temperature Tr of the road. In that
case, stabilization between cycles would have to be performed. It is interesting to note that the
surface temperature of the road could be difficult to measure with only one probe. As shown
by Scharsching [Scharsching 1991] its value is not homogeneous on all the surface of the
road. The location of the probe has to be chosen with care.
It is also possible to use in the same vicinity all together an active an a passive probe,
the first one measuring Ts and the second one 7 Tr. The last possible configuration is to use
only a passive probe, in conjunction with meteorological sensors (relative humidity,
precipitation, etc.).
4.2 Salt content
For the road's winter maintenance executive, the knowledge of the freezing temperature,
as important it could be, is nevertheless not sufficient. Due to precipitation, streaming or
evaporation, the amount of water on the pavement, and then the concentration of chemical
and the freezing temperature, may vary. The parameter which can be used to characterize the
protection rate of the road is the salt content. As it will be shown, it can be deduced from the
freezing temperature and the thickness of the solution. The example of spreading solid
sodium chloride as anti-icing treatment will be considered.
The quantity of salt spread by the service vehicle can be chosen to give a salt content s
comprised between 5 and 40 g/m 2 . After the salting, the mass mNaCl of salt laying on an area A
of the pavement is given by :
m = s⋅
A . (6)
NaCl
If salt is diluted in a certain amount mH 2 O of water (in order of simplification, the salt
content on the area A is kept constant), the weight concentration c of NaCl will be :
mNaCl
c =
m + m
NaCl H2O m
=
m
NaCl
tot
, (7)
7 The passive probe has to be placed far enough from the active one in order to be not influenced by it.

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 280
with m = m + m .
tot NaCl H2O The volumetric properties of aqueous sodium chloride solutions are for instance given
in [Rogers and Pitzer 1982]. For temperatures close to 0 °C, the specific volume ν (in cm 3 /g)
can be fitted by :
2
ν( c) = 0. 653c − 0. 704 c+
0. 999
It is then possible to compute the thickness e of the solution :
e =
c ⋅ m
A
. (8)
ν( ) tot . (9)
It remains to express the freezing temperature Ts corresponding to the considered salt
concentration. Ts is of course given by the phase diagram of the NaCl - H2O mixture [Zaytsev
and Aseyev 1992] represented in figure 5.
T s [°C]
0
-5
-10
-15
-20
-25
c
0 0.05 0.1 0.15 0.2 0.25 0.3
Figure 5 : NaCl - H2O phase diagram. Eutectic coordinates are ceutectic = 0.2331
and Ts min = -21.12 °C.
In order to compute the freezing temperature, the curves have been fitted. The one with
negative slope (c ∈ [0, 0.2331]) is approximated by the following polynomial :
3 2
T ( c) =−470. 65c −32. 625c −57.
232 c
s
while the one with positive slope (c ∈ [0.2331, 0.266]) is approximated by :
, (10)
3 2
Ts( c) =− 531, 791c + 393, 483c − 96, 251c+ 7, 770. 5 . (11)

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 281
Let us consider now a road where a salt content of 20 g/m 2 has been spread. Table 2
gives the freezing temperatures for different thicknesses of the solution. From -13.9 °C for a
thickness of 0.1 mm, the freezing temperature increases very quickly to -2.3 °C for a
thickness of 0.5 mm!
e [mm] Ts [°C]
0.1 -13.9
0.2 -6.1
0.3 -3.9
0.4 -2.9
0.5 -2.3
Table 2 : dependence of the freezing temperature on the thickness of the solution
for a salt content of 20 g/m 2 .
Freezing temperatures are reported versus the thickness of the solution for different salt
contents in figure 6. When e increases, the phase diagram of figure 5 is gone through from the
right to the left, or in other words, in the direction of decreasing NaCl concentrations.
T s [°C]
0
-5
-10
-15
-20
-25
5 g/m 2
e [mm]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
10 g/m 2
20 g/m2
30 g/m 2
40 g/m 2
Figure 6 : dependence of Ts on the thickness of the solution for different salt contents.
For a given salt constant, the thickness eopt of the solutions which gives the best
protection of the road, i.e. the NaCl concentration of the eutectic, is given by :
e
opt [mm]
ν ( 0. 233)
⋅ s
-3
=
= 3.73⋅10 s 2 . (12)
[ g/m ] 0. 233

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 282
eopt , which is rather weak, is represented in figure 7.
e opt [mm]
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Figure 7 : dependence of eopt on s.
0 10 20 30 40
s [g/m 2 ]
Knowing e and Ts, the salt content can be calculated by :
cT ( s)
⋅ e
s =
ν
( cT ( ) )
where c(Ts) is approximated by the following polynomial :
s
, (13)
−63−42−2 cT ( ) =−6. 211⋅10 ⋅T −4. 637 ⋅10 ⋅T −1807 . ⋅10 ⋅T
s s s
4.3 Accuracy of the measurement of the freezing temperature
s
. (14)
While the accuracy of the measurement of Ts by an active probe is mostly given by the
accuracy ΔT of the sensor which measures the temperature during the cooling, the one of a
passive probe is dependent of the function T = T( x , x , x , K, x , K , x ) used to compute
s s 1 2 3 i n
the freezing temperature. In that case, the absolute error is given by :
ΔT
s ≅
i=
1
n
Ts
∑ x
∂
∂
i
Δ x , (15)
where the xi are the different variables which are measured and Δxi their absolute errors. In
other words, the accuracy of a passive probe is a sum of errors depending of the different
parameters themselves and their absolute error. If for instance a passive probe is able to
measure the salt concentration and the thickness of the solution, it can be understood that
errors on c and e (due to the measurements themselves, pollutants, etc.) will affect the
i

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 283
computation (13) of the salt content. Therefore it comes that the accuracy of active probes is
better than that of passive ones.
5. CONCLUSION
The physical principles of the freezing point measurement by active and passive probes
have been discussed. Whatever the deicing product may be (NaCl, CaCl2, MgCl2, ethylene
glycol, etc.), the active probe measures truly Ts, with a good accuracy. The measurement of
this same parameter with a passive probe is less accurate. In addition, this kind of probe
requires parametrizations of the software and can require the use of meteorological data. By
contrast, the passive probe is cheaper than the active one.
ACKNOWLEDGMENTS
The author would like to thank J. Heierli for helpful discussions and P. Francey for
performing the measurements of the cooling performances of the probe.

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 284
Appendix A - Peltier cooling
In the active probe, the freezing of the solution is artificially created by a TEC, which is
a solid state heat pump that utilizes the Peltier effect. It consists of a number of p- and n-types
pairs (couples) of a semiconductor material 8 [Goldsmid 1986] connected electrically in series
and sandwiched between two ceramic plates, i.e. connected thermally in parallel. As shown
schematically in figure A.1, when powered by a DC power supply, current i causes heat to
move from one side of the TEC to the other. This creates of course a cold side and a hot side 9 .
The rejected heating power Qh, greater than the heat Qc pumped in the cold side, is given by :
Qh = Qc + Qin = Qc + U ⋅ i . (A1)
Tc and Th are the temperatures of the cold and hod side of the TEC.
U
i
TEC
Figure A1 : schematic representation of the principle of the Peltier pumping.
Qc does not increase linearly with the current. The yield of the TEC is defined by the
coefficient of performance (COP) :
Qc
Qc
COP = =
Q U ⋅i
in
Qc
Qh
Tc
Th
. (A2)
For the same TEC and temperatures Tc and Th than those considered in § 2.2, figure A2
shows the COP versus the current. The current giving the maximum coefficient of
performance COPmax is named the optimal current iopt.
8 The best semiconductor for thermoelectric refrigeration at ordinary temperatures is bismuth telluride, Bi2Te3.
9 If the direction of the current is inverted, the cold and hot sides are also inverted. It is then possible to cool or
to heat the solution at the surface of the probe.

REFERENCES
Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 285
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1.0
0.8
0.6
0.4
0.2
0.0
0 0.5 1 1.5 2 2.5 3 3.5 4
i [A]
Figure A2 : dependence of COP on current for a commercial TEC 10 ,
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