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glassy product skin at the surface of the frozen solution. It is seen,
therefore, that formulation details, as well as cooling rates, can mark-
edly affect the subsequent ice sublimation process. It has been sug-
gested
110
that the actual ice sublimation rate, as expressed in an idealised
form by Equation (1), may well be lower in practice by factors in excess
of three orders of magnitude for small ice crystals that are completely
coated by glassy films of freeze-concentrated solution. In summary,
therefore, rapid cooling results in small ice crystals (a large specific ice
surface area) and provides a uniform texture in the dried product, but
because of lack of ice connectivity, such crystals are also likely to reduce
the sublimation rate to an economically unacceptable degree. Coarse
structures are usually preferred because they favour ice sublimation, the
downside being that, depending on the solid content, product ''skins''
may develop at the surface of the advancing ice front.
The actual drying (sublimation) time t
s
is thus seen to depend on the
following quantities:
Fill depth (m)
Density of the frozen product (kg m
3
)
Water content of product solution (kg kg
1
)
Latent heat of sublimation at the particular drying temperature (kJ
kg
1
)
Temperature difference between shelf and ice front (1C)
Total heat transfer coefficient from shelf to sublimation front [kJ (m
2
h
deg)
1
]
Thermal conductivity of frozen product [kJ (m h deg)
1
]
Fraction of frozen water (usually 4 0.9)
Permeability (i.e. porosity) of dried product to water vapour [kg (m h
Pa)
1
]
8.5
Interplay of Pressure, Temperature and Time
The complex relationship between chamber pressure and temperatures
of shelf and product, and its impact on the sublimation rate, is illus-
trated in Figure 6 for a recombinant protein preparation.
111
Let us
assume that T
g
for such a composition is -201, so that the drying
conditions must be set to ensure that the product temperature does not
exceed this value at any time during the primary drying cycle. The
sublimation rate corresponding to point A, at a chamber pressure of 40
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