Sublimation interface

The frozen product, with a temperature difference of about 2°C between the ice in the bottom of the vial and the ice at the sublimation interface. 

Sublimation (or Primary Drying). For the sublimation phase of the process, the frozen material usually is subjected to a vacuum of about 4.6 millimeters of mercury. The ice-crystal sublimation process can be regarded as comprised of two basic processes (l)Heal transfer, and (2) mass transfer. In essence, heat is furnished to the ice crystals to sublime them he generated waler vapor resulting is transferred out of the sublimation interface. Thus, it is evident thal sublimation will be rare-limited by both resistances to heat and mass transfer as they occur within the material. 

As the sublimation interface recedes in (he material (Fig. 2). (he dry layer presents a resistance to the flow of water vapor and a pressure difference must exist between the ice interface and the surface of the dry... 

Tire rate of heat input to the frozen material is a function of the operating-vacuum method of heal transfer and the properties of ihe dried product. The operating vacuum determines the pressure difference and. in turn, the rate of mass transfer, which must be in balance with the rate of heat input. Otherwise, either melting will occur at the sublimation interface and the purpose of freeze-drying will be defeated or the sublimation temperature will decrease and the cost of processing will increase. 

The heal required for sublimation (1200 Btu per pound of ice 664 kilogram-calories per kilogram of ice) can be supplied by conduction, radiation, electric resistance, microwave, or infrared heating. Three methods of heal input that have been investigated extensively are shown in Fig. 2. Depending on the method of heal transfer, the temperature gradient between Ihe sublimation interface and the heat source is limited by Ihe maximum temperature which can be tolerated on Ihe surface of the dry... 

Drying Rates. Drying a frozen material proceeds initially at a constant rate with rapid evolution of water vapor. As Ihe sublimation interface recedes within the product, water-vapor evolution decreases. This is the start of the falling-rate period. When only bound water remains within the cellular structure of the product, the desorption period begins. During the constant-rate period, the sublimation rate can be expressed in terms of the heat of sublimation of ice and the heat-rale equation ... 

The overall heat-transfer coefficient U depends upon the properties of the dry product and the method of heal transfer. The heat-transfer rate A is influenced by the mechanical design of the heating elements and the conditioning of the frozen mass. The temperature gradient AT is limited by the maximum allowable temperatures al the sublimation interface and dry-layer surface. In the constant-rate period, the lirst one-half to two-thirds of the drying cycle, about 8fl + of the water is removed. 

However, a slowing down of ice sublimation will be observed if the total pressure in the chamber becomes too close to the pressure above the sublimation interface [9,10,12], Indeed, for an efficient removal of water vapor from the containers, a sufficient pressure differential must exist between the ice-vapor interface and the chamber. The total pressure above the ice-vapor interface is approximately equal to the saturated vapor pressure of ice at the temperature of the, sublimation front, as the head space contains mostly water vapor [10-12], Therefore, the pressure gradient that promotes water removal will no longer exist if the pressure level of the calibrated leak exceeds the saturated vapor pressure of ice at the target product temperature. 

Sublimation always starts at an open surface and then moves inwards into the sample. After some of the ice is sublimated, the sample exhibits two distinct regions, namely the dry layer (from which ice crystals have sublimated) and the frozen layer (where ice crystals are still present). These two regions meet at the so-called ice interface , sublimation interface , freeze-drying interface or, simply, interface . 

Where Ti is the dried layer temperature, T2 is the frozen layer temperature, is the mass transfer flux of the water vapour, Cj is the bound water and H is the sublimation interface. The different parameters of the model are presented in [12], In this work, we use a simplified equation to describe the dynamic of the mass flux based on the diffusion equations of Evans. The equation is given by the following expression ... 

Where po and pn is the partial pressures of water vapor at z=0 and z=H(f) respectively. The pressure boundary condition at the top surface of the material being dried is defined as a constant pressure inside the drying chamber, and the vapor pressure at the sublimation interface is defined as an equilibrium vapor pressure according to the temperature of the interface. 

For more the details about the MPC CB software and the operations conditions, the reader can refer to [12]. The optimal minimization of the drying time rmder constraints may be equivalent to define the performance index as the maximization of the velocity of the sublimation interface. Since MPC CB solves a rninirnization problem, the objective function is ... 

FIGURE 12.1 Diagram of a material on a tray during freeze drying. The variable X denotes the position of the sublimation interface (front) between the freeze-dried layer (layer I) and the frozen material (layer II). 

In the secondary drying stage, there is no frozen (II) layer, and thus there is no moving sublimation interface. The secondary drying stage involves the removal of bound water. The thickness of the dried (I) layer is L, and the energy... 

It should be noted that an increase in pressure will increase feie but at the expense of resistance to mass transfer, which is also increased. Hence, the mass flux is reduced and consequently the temperature of the sublimation interface and of the frozen layer is increased. Thus, the thermal conductivity increases but the temperature driving force is decreased. 

The uniformly retreating ice-front model was tested by Sandall et al. (SI) against actual freeze-drying data. The model satisfactorily predicted the drying times for removal of 65-90% of the total initial water (SI, Kl). The temperature 7 of the sublimation interface did remain essentially constant as assumed in the derivation. However, during removal of the last 10-35% of the water, the drying rate slowed markedly and the actual time was considerably greater than the predicted for this period. 

Chouvenc et al. (2004a) was compared with the predictions of the two previously quoted MTM models. The position of the sublimation interface and the thickness of the dry layer, denoted were estimated as functions of time by simple mass balances. Chouvenc et al. (2004a) observed that the Rp values derived from the three models were similar for < 6 mm and slightly lower than the few literature values. Moreover, experimental data correlation lines pass close to the axis origin, so that no significant crust effect was present in the experimentally investigated crystalline system (mannitol), in contrast to what is observed with concentrated vitreous systems that can present relatively large crust effects. 

Milton et al. (1997) proposed the manometric temperature measurement (MTM) the transient pressure response is mathematically modeled under the assumption that four mechanisms contribute to the pressure rise, namely the direct sublimation of ice through the dried product layer at a constant temperature, the increase in the ice temperature due to continuous heating of the frozen matrix during the measurement, the increase in the temperature at the sublimation interface when a stationary temperature profile is obtained in the frozen layer and, finally, the leaks in the chamber. The four contributions are considered purely additive the values of the thickness and of the thermal gradient are needed but they are not known exactly. The values of the vapor pressure over ice, of the product resistance and the heat transfer coefficient at the vial bottom are determined with regression analysis. 

Thermodynamic equilibrium is assumed at the subliming interface moreover, at the beginning of the PRT the heat fluxes at z = 0 (interface) and at z = Lg.ozen (bottom of the vial) are assumed to be equal, thus K, can be derived by equating the boundary conditions from Eqs. 4.6 and 4.7, both taken at t = to ... 

Liu ef al. (2008) can be used to calculate the exergy losses, but some assumptions of these authors have been removed as their validity appears to be questionable for example, that the vapor pressure at the sublimation interface is equal to the chamber pressure. The exergy losses due to heat transfer during primary drying h) calculated from the temperature profile in the dried layer (see Fig. 5.1) ... 

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