Equivalence of models of freeze-drying

Abstract

Freeze-drying is a preservation process, consisting of two main stages: during the primary drying water is removed by sublimation; during the secondary drying chemically bound water is removed by desorption. Two different models of secondary drying are built. The first one consists of coupled heat and mass balances equations, the second one uses a modified Richards equation. Using scale transformations derived from the PDEs and the BCs, the first model is nondimensionalized. The model is further simplified by asymptotic reduction. It is proven that the reduced model is equivalent to the model that uses the modified Richards equation if the partial pressure of air is negligible compared to that of water vapor in the vials and in the chamber of the freeze-drier. This result shows that there is an opportunity for technology transfer, since solvers developed for modelling groundwater flows using Richards equations can also be used to model the economically important problem of freeze-drying.