Mass and heat transfer in vial freeze-drying of pharmaceuticals: role of the vial

J Pharm Sci. 1984 Sep;73(9):1224-37. doi: 10.1002/jps.2600730910.


Flow of water vapor is impeded by three barriers or resistances: resistance of the dried-product layer, resistance of the semistoppered vial, and resistance of the chamber. The relationship between heat flow and temperature difference may be described by a vial heat transfer coefficient which has contributions from three parallel mechanisms: (a) direct conduction from the shelf to the vial via points of direct contact between the vial and shelf, (b) conduction through the vapor between the vial bottom and the shelf, and (c) radiative heat transfer. This report describes experimental studies of the resistance of semistoppered vials, the resistance of the chamber, and vial heat transfer coefficients. Mass transfer through the semistoppered vial has significant contributions from both Knudsen- and viscous-flow mechanisms. Stopper and chamber resistances are of the same magnitude and are about a factor of 10 less than the dried product resistance. All three heat transfer mechanisms are significant, the relative contributions depending on both the chamber pressure and the type of vial. Vial heat transfer coefficients are sensitive to the geometry of the vial bottom, and even vials of nominally the same specifications may differ significantly in heat transfer characteristics. Vials from the same lot are relatively uniform in their heat transfer characteristics, the relative standard deviation of the vial heat transfer coefficient being only approximately 4%. The temperature distribution in the frozen product is adequately described by a constant temperature gradient in the vertical direction and the thermal conductivity of ice.

MeSH terms

  • Chemical Phenomena
  • Chemistry, Pharmaceutical
  • Chemistry, Physical
  • Drug Packaging*
  • Freeze Drying*
  • Gases
  • Hot Temperature
  • Pressure
  • Thermodynamics


  • Gases