Freezing time estimation

Jones G J 1984 On estimating freezing times during tissue rapid freezing J. Microsc. 136 349-60... 

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Recently SFD has attracted the attention of formulation scientists. Spray-freeze drying of aqueous solutions of pure proteins or protein/sugar combinations (Maa et al. [5]) produced larger, more porous particles than those prepared by SD. When the modeling of SFD process is concerned, a mathematical model based on a steady-state heat-transfer condition has been derived by Maa and Prestrelski [6] that can be used to estimate the freezing time in liquid nitrogen, for instance. 

For the non-isothermal cases the freeze-off time, t/, may be estimated by the method described in Example 5.11. 

Fig. 1.80.3. Course of the freeze drying after the product has been frozen as per Fig. 1.80.1 (bottom). Nomenclature as in Figs. 1.80.1 and 1.80.2. The rise of T is different. The optima) time frame for the change from MD to SD can not be estimated from the Tpr plot (Fig. 7 from [ 1.631).

With Eq. (3), it is also possible to estimate Ksu. The uncertainties are the differences between the freezing of the product around the temperature sensor and in the undisturbed product, the position of the sensors, the correlation between time and temperature and occasionally also the actual amount of frozen water. From Fig. 1.4, the estimated Ksu is... 

With Eq. (3), itis also possible to estimate KsuThe uncertainties are the differences between the freezing of the product around the temperature sensor and in the undisturbed product, the position of the sensors, the correlation between time and temperature and occasionally also the actual amount of frozen water. From Figure 1.4.1, the estimated Ksu is approximately 480 kj/m2 h °C with a possible error of 10% and maximum error of 20%. Such high values can only be expected if the vials are carefully selected for their uniformity, especially with respect to a very even and flat bottom. Otherwise, the /< u can be much smaller, e.g. 230 kj/m2 h °C as calculated from data shown in Table 1.4.1. 

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