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

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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
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