(convection), while in low-pressure (higher vacuum) conditions,
heat transfer by gaseous conduction is reduced and energy input to
the product is predominantly by radiative heat transfer, which is a
relatively inefficient mechanism. As a general rule of thumb, in
order to provide sufficient heat input through gaseous conduction
while also allowing for some sublimation cooling and temperature
gradients within each product container, the chamber will typically
be maintained at between one-third and one-half of the pressure
that equates to the vapor pressure of the ice in the product at its
measured (or calculated) temperature, as defined by standard vapor
pressure tables; however, chamber pressure may be subject to more
rigorous optimization as part of a Quality by Design (QbD)
approach [24].
Vapor Differential Pressure
and Drying Efficiency
To sustain freeze-drying it is necessary to establish a pressure gradient from a product (higher pressure), to condenser, and finally
vacuum pump (lower pressure) so that water migrates from the
product to the condenser as drying progresses. Although the temperature of the product must be higher than that of the condenser
to ensure a net migration of water from the product, the system
driving force represents the difference in vapor pressure (VP) rather
than the difference in temperature between product and condenser
and can be calculated as the difference in VP between the two. For
example, product at À20
C has a VP ¼ 0.78 Torr and with the
condenser at À40
C (equivalent to a VP of 0.097 Torr), driving
force will be 0.78–0.097 or 0.683 Torr. Little improvement in
driving force is achieved by operating the condenser at À70
C.
(VP ¼ 0.002 Torr, providing a VP differential of 0.78 [product]—
0.002 [condenser] of 0.778 Torr.) The example illustrates that
greater sublimation efficiency is derived by increasing product temperature rather than reducing condenser temperature, and the
selection of suitable excipients that enable high-processing temperatures to be used during freeze-drying without compromising
product quality plays an important role in process and cycle
development.
Heat and Mass Transfer
The essence of the freeze-drying process depends on maintaining a
critical balance between the conversion of ice into water vapor by
sublimation under vacuum and the removal of that vapor from the
frozen mass. To maintain sublimation, heat energy is applied to the
product to compensate for sublimation cooling. However, the heat
extracted from the drying product as water vapor must carefully
balance the amount of energy added to the product.
Unless this equilibrium can be maintained, the product temperature will either decrease, thereby reducing drying efficiency, or
increase, which may compromise product quality by inducing melt
or collapse. This critical balance between product warming to
increase drying rate and vapor extraction is defined by the heat
Principles of Freeze-Drying
113
heat transfer by gaseous conduction is reduced and energy input to
the product is predominantly by radiative heat transfer, which is a
relatively inefficient mechanism. As a general rule of thumb, in
order to provide sufficient heat input through gaseous conduction
while also allowing for some sublimation cooling and temperature
gradients within each product container, the chamber will typically
be maintained at between one-third and one-half of the pressure
that equates to the vapor pressure of the ice in the product at its
measured (or calculated) temperature, as defined by standard vapor
pressure tables; however, chamber pressure may be subject to more
rigorous optimization as part of a Quality by Design (QbD)
approach [24].
Vapor Differential Pressure
and Drying Efficiency
To sustain freeze-drying it is necessary to establish a pressure gradient from a product (higher pressure), to condenser, and finally
vacuum pump (lower pressure) so that water migrates from the
product to the condenser as drying progresses. Although the temperature of the product must be higher than that of the condenser
to ensure a net migration of water from the product, the system
driving force represents the difference in vapor pressure (VP) rather
than the difference in temperature between product and condenser
and can be calculated as the difference in VP between the two. For
example, product at À20
C has a VP ¼ 0.78 Torr and with the
condenser at À40
C (equivalent to a VP of 0.097 Torr), driving
force will be 0.78–0.097 or 0.683 Torr. Little improvement in
driving force is achieved by operating the condenser at À70
C.
(VP ¼ 0.002 Torr, providing a VP differential of 0.78 [product]—
0.002 [condenser] of 0.778 Torr.) The example illustrates that
greater sublimation efficiency is derived by increasing product temperature rather than reducing condenser temperature, and the
selection of suitable excipients that enable high-processing temperatures to be used during freeze-drying without compromising
product quality plays an important role in process and cycle
development.
Heat and Mass Transfer
The essence of the freeze-drying process depends on maintaining a
critical balance between the conversion of ice into water vapor by
sublimation under vacuum and the removal of that vapor from the
frozen mass. To maintain sublimation, heat energy is applied to the
product to compensate for sublimation cooling. However, the heat
extracted from the drying product as water vapor must carefully
balance the amount of energy added to the product.
Unless this equilibrium can be maintained, the product temperature will either decrease, thereby reducing drying efficiency, or
increase, which may compromise product quality by inducing melt
or collapse. This critical balance between product warming to
increase drying rate and vapor extraction is defined by the heat
Principles of Freeze-Drying
113