Primary Drying: The Sublimation of Ice - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 99

sublimation. The reader is reminded that washing, hung out to dry on a
cold day, will freeze but will eventually dry, even without the need for a
vacuum pump. The real driving force for sublimation, DG s , is provided
by the water vapour pressure difference between the ice front and the
condenser surface. Since water vapour pressure is inversely proportional
to the temperature, it is in fact the temperature difference between the
ice front and the condenser surface that provides the driving force. This
demonstrates that DG s will be maximised by the choice of a formulation
with a high T g , combined with a condenser, which is able to operate at as
low a temperature as practically possible. The chamber pressure affects
the rate of sublimation, but not the driving force. For obvious reasons,
the chamber pressure must be maintained below the saturation vapour
pressure (SVP) of ice at the operating temperature.
8.3 Heat Transfer Mechanisms
The engineering principles and mechanisms of heat transfer that underlie
the supply of thermal energy to the frozen product have been discussed in
detail by Oetjen 7 and are only summarised here. Basically, the supply of
heat energy is made up of three distinct contributing mechanisms:
(i) Radiation from ''warm'' surfaces (''warm'' here refers to any
temperature above that of the subliming ice front).
(ii) Conduction within and between solid phases (heating plates,
glass vials, etc.).
(iii) Conduction within vapour phases produced by Brownian diffusion
and molecular collisions (can also be expressed as convection).
Radiation effects are governed by Stefan's law. They become significant
mainly near the walls and the door of the freeze-drier; they also depend
on the material of the surfaces, usually coated or uncoated metal. For a
radiating surface held at 301C and an ice front at 301C, the mass of ice
sublimed by radiation alone has been estimated to be only of the order
of 50 g (h m 2 ) 1 . 7
Contributions arising from heat transfer within and between phases
depend on the respective thermal conductivities of the materials, e.g. of the
heating shelves, aluminium plates, glass vials, the chamber pressure, and
the thermal conductivity of the frozen solution itself and of the portion of
the plug that has already been dried. The proportions of the last two
mentioned contributions change continuously during sublimation.
An approximate estimate of the effects of molecular collisions, i.e.
convection, on the sublimation rate can be derived with the aid of the