Conduction, heating, freeze-drying

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

The total pressure during freeze drying may be measured by several methods, though only two are mostly used heat conductivity, and the membrane pressure difference gauge. Their operating principles and their advantages and disadvantages are described below. 

The thermal conductivity of ice and of dried products is relatively well known, but the surface heat transfer coefficient, Ksu during freezing and the total heat transfer coefficient K(ot during freeze-drying vary largely as described in the various chapters. Table 1.3 gives a survey of some data of interest in freeze-drying. 

The Li ions were introduced in two different ways either before or after Zr intercalation. The montmorillonite (Weston L-Eccagun) was first exchanged with NaCl (IN) and washed. Two montmorillonites with reduced charge were prepared following the Brindley and Ertem method (13). Part of the Na+ montmorillonite was first saturated with LiCl (IN) and washed. The Li+ clay thus obtained and Na+ clay suspension were stirred for 24 hours at 25°C and dried on glass plate. The films were then heated at 220°C for 24 h in order to allow Li diffusion in the clay structure. Two different Li concentrations (F=0.4 and F=0.6) were used. The Na Li+ modified montmorillonite were dispersed in water acetone solution (1/1). The ZrOCla, 8H2O solution was added to the Na+Li+ montmorillonite (0.02g.l l Zr/Clay=5.CEC). The suspension was stirred with NaOH solution (0.1 N) up to a OH/Zr ratio of 0.5. The final pH of the suspension was 1.85. After two hours of reaction at 40°C the Zr pillared clay was washed up to constant conductivity of the solution, freeze-dried and calcined at different temperatures up to 700°C (Eni-02 and EIII-03). 

Fig. 2. Heat-input methods Tor freeze-drying processes la) conduction, tb) radiation, (cl microwave. CC = cold condenser RHS = radiam-heat device...

To insure an undisturbed water vapor transport (see Section 1.2.4) the leak rate of a freeze-drying plant must allow BTM with sufficient accuracy. This applies for vapor pressures with ice temperatures ranging between -50 and -10 °C corresponding to 0.04—2.5 mbar. The pressure range for DR measurements is normally one decade below the above data and this has to be considered in the specification of the plant. All measurements discussed above have to be carried out with a capacitance vacuum gauge, because these instruments measure pressure independently of the type of gas. All vacuum gauges based on the change of heat conductivity as a function of pressure show a result which depends not only on the pressure of the gas mixture but also on the type of gas. Leybold AG [1.67] indicate that for instruments based on heat con-... 

Lyophilization (or freeze-drying) is a process utilized to convert a water-soluble material filled into a container to a solid state by removal of the liquid while frozen. The process requires the use of deep vacuums and careful control of temperatures. By conducting the process under reduced pressure, the water in the container converts from ice directly to vapor as heat is applied and is removed from the container by the vacuum. The dissolved solids in the formulation cannot undergo this phase change and remain in the container. At the completion of the cycle, the container will be returned to near atmospheric pressure stoppers are applied or fully seated and crimped as described above. Lyophilization is particularly common with biological materials whose stability in aqueous solution may be relatively poor. The time period in solution and the temperature of the solution are kept at a specified low temperature to prevent product degradation [35],... 

The limitations on heat transfer rates in conventionally conducted freeze drying operations have led early to the attempt to provide internal heat generation with the use of microwave power [21,22]. Theoretically, the use of microwaves should result in a very accelerated rate of drying because the heat transfer does not require internal temperature gradients and the temperature of ice could be maintained close to the maximum permissible temperature for the frozen layer without the need for excessive surface temperatures. 

Frozen Layer and Maximum Dry Surface Temperatures in Typical Freeze Drying Operation Conducted with Heat Input through the Dry Layer... 

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