Primary Drying: The Sublimation of Ice - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 102

Figure 3 Resistance to sublimation as function of cake thickness offered by different
excipients at an initial solution concentration of 5% w/w. Adapted from Pikal
the freeze-drier. This would then provide an estimate of DT, the
temperature difference between the shelf and the subliming ice front.
Not many studies on pharmaceutical preparations have been performed
in which all these parameters were carefully measured and documented.
According to Oetjen, for a typical freeze-drying process in which a
solution, containing 7% solids and contained in vials to a fill depth of
7 mm, is dried at 221C, the calculated heat transfer coefficient K v is
145 kJ (1Chm 2 ) 1 and the mass transfer rate is then 1.3 10 4 kg
(h m 2 mbar) 1 . Using this model system, it is instructive to evaluate and
compare the relative magnitudes of the three terms in Equation (2); they
are (from left to right) 2.33, 0.19 and 0.03, giving an estimated primary
drying time of 2.5 h. Thus, the first term on the right-hand side is dominant
and determines the drying time to an extent of ca. 90%. The fill depth is
thus seen to exert the major influence on the drying time: t s varies in a
linear manner with d and inversely with DT. This result would of course
argue against the approximation, discussed earlier, that the dried cake
offers no resistance to ice sublimation. The thermal conductivity of the
frozen solution appears to contribute little to the total heat transfer. Still
using this model, a 3-fold increase of the fill depth would lead to a 4-fold
increase of t s to ca. 10 h. Experimental tests with different food products