ABSTRACT
Dynamic multi-dimensional mathematical models for the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes are presented for bulk freeze-drying on trays and for lyophilization in vials. The mathematical models account for the removal of free and bound water and can provide the position and geometric shape of the moving interface that separates the dried and frozen layers. The theoretical models presented here could be used in the design and scale-up of the freeze-drying process, as well as in the development of operating conditions and control strategies that could provide high drying rates and assure high quality for the pharmaceutical material being freeze-dried.
