Freeze-dried layer permeability

The concept of permeability introduces another overall parameter often used to characterize globally the morphology of porous media with respect to gas flow. Thus, for interpreting the sublimation data during freeze-drying processes, the water vapor permeability, denoted by K, is classically defined by the following relationship (Darcy s law)  

Equation 3.3 shows that Kis inversely proportional to the water vapor mass transfer resistance, previously defined by Eq. 3.1. 

From the above relationship, it is possible to estimate the experimental values of K from experimental values of the primary drying rate, denoted by m, over the sublimation period corresponding to the freeze-dried layer thickness, Idry, by the following relationship  

Nakagawa et al. (2007a) interpreted the dependence of the water vapor mass transfer permeability of the dried layer on ice crystal morphologies by using this relationship for different nucleation temperatures. The increase in the nudeation temperature was expected to increase the water vapor mass transfer permeability of freeze-dried materials and to contribute to acceleration of the primary sublimation rates during freeze-drying. 

The experimental values of permeability, Kejip, plotted in Fig. 3.20 correspond to mean values of dried layer thickness, of about 3 and 4 mm for the mannitol and 

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On the other hand, the dried cake permeability values were theoretically estimated by the same authors from values of the mean size of the ice crystals by assuming that the freeze-dried cake texture could be represented by a bundle of capillary tubes (mean diameter, denoted ore)- Under conditions of molecular flow in the Knudsen regime (Kn = 4) this theoretical freeze-dried layer permeability, denoted by K odei. was estimated by the following equations ... 

D Quast, M Karel. Dry layer permeability and freeze-drying rates in concentrated fluid systems. Journal of Food Science 33 170, 1968. 

If the freeze-drying process is controlled by water vapor mass transfer through the freeze-dried layer - for example in the case of dried cake of very low permeability or for very favorable heat transfer conditions - the drying rate for one vial is proportional to the mean driving force P - Pc) - that is, to the water vapor pressure difference between the sublimation front interface and the drying chamber - and controlled by the freeze-dried cake mass transfer resistance, denoted J p, which is inversely proportional to the dried layer permeability defined by Darcy s law. Inthiscaseitholds ... 

Values of the permeabilities of the freeze-dried layer derived from the previously mentioned modeling are presented in Fig. 3.10. They dearly explain the well known influence of the freezing protocol - more precisely of the nudeation temperature - on the duration of the subsequent sublimation step as also observed experimentally (compare with Section 3.3.1.2). 

The primary characteristic necessary for a liner, cover, or cutoff wall is low permeability, which essentially enables them to slow down the seepage or diffusion of chemicals. Clay is therefore the main material used to construct these containment systems. The thickness and chemical compatibility of containment systems are of concern in assessing the performance of a system. For example, clay liners are constructed as a simple liner that is 2 to 5 ft thick. In composite and double liners, the compacted clay layers are usually between 2 and 5 ft thick, depending on the characteristics of the underlying geology and the type of liner to be installed. Regulations specify that the clay used can only allow water to penetrate at a rate of less than 1.2 in./yr. However, the effectiveness of clay liners can be reduced by fractures induced by freeze-thaw cycles, drying out, and the presence of some chemicals. 

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