An asymptotic model for the primary drying stage of vial lyophilization

Asymptotic methods are employed to analyse a commonly used one-dimensional transient model for coupled heat and mass transfer in the primary drying stage of freeze-drying (lyophilization) in a vial. Mathematically, the problem constitutes a two-phase moving boundary problem, in which one of the phases is a frozen porous matrix that undergoes sublimation, and the other is a low-pressure binary gaseous mixture. Nondimensionalization yields a model with 19 dimensionless parameters, but a systematic separation of timescales leads to a reduced model consisting of just a second-order differential equation with two initial conditions for the location of a sublimation front; the temperature and gas partial pressures can be found a posteriori. The results of this asymptotic model are compared with those of earlier experimental and theoretical work. Most significantly, the current model would be a computationally efficient tool for predicting the onset of secondary drying.