Primary Drying: The Sublimation of Ice - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 101

collisions between gas molecules (convection), and this effect, in turn,
becomes more pronounced with increasing chamber pressure. Conduc-
tion effects are seen to contribute a higher proportion of heat transfer
for blown glass vials because their flat bottoms provide a better contact
with the shelf than do moulded glass vials.
The relative contributions of the differing heat transfer routes therefore
vary with pressure and with vial characteristics. A rise in chamber
pressure may lower the product temperature by increasing mass transfer
(sublimation) relative to heat input; this should be compensated by raising
the shelf temperature or, preferably, by adjusting the primary drying time.
The total sublimation time t s has been given as 107
t s ¼ (r.w 1 .DH s .w 0 1 .d)/{(1/K v ) þ (k.d/2) þ (DH s . w.d/2)}

(2)

where
r ¼ density of the frozen solution (kg/m 3 );
w 1 ¼ total water content (kg/kg);
w 0 1 ¼ mass fraction of ice, frequently taken as 0.9;
d ¼ fill depth (m);
k ¼ thermal conductivity of the frozen solution (kJ/1C.m.h);
K v ¼ heat transfer coefficient from the heat exchange fluid to the
subliming ice surface;
w ¼ water mass transfer (kg/h.m.Pa)
Equation (2) for t s has been derived subject to two simplifying
assumptions: (1) the dried cake does not offer any resistance to the
transport of water vapour, i.e. it has a high porosity and that the frozen
plug is non-porous; and (2) convective heat transfer within the dried
portion of the plug can be neglected. The first assumption is at odds with
some direct experimental results on the resistance of dried cakes to water
vapour permeation. 108,109 They are shown in Figure 3 and discussed in
more detail later. Altogether, these assumptions are said to introduce a
ca. 2% uncertainty into the estimate of t s .
Several experimental variables are required to enable Equation (2) to
be applied. They include:

the sum of heat transfer and thermal conductivity taken between
the shelf and the subliming ice front;
the thermal conductivity of the frozen plug;
the mass transfer (sublimation) rate.

It is also useful to have some knowledge of the actual magnitude of K v
and how it varies with temperature, pressure and the configuration of