A mathematical model for the spray freeze drying process: The drying of frozen particles in trays and in vials on trays

A mathematical model is presented that can be used to study the heat and mass transfer mechanisms that determine the dynamic behavior of the primary and secondary drying stages of spray freeze drying (freeze drying of particle based materials) in trays and in vials on trays. Simulation results indicate that particle based materials require longer primary drying times than solution based materials (conventional freeze drying) due to (a) reductions in the heat and mass transfer capabilities of particle based materials, and (b) the development of a secondary porous dried layer near the surface of the lower heating plate during the primary drying stage of the spray freeze drying process. The results of spray freeze drying for the systems studied in this work indicate that the drying rate during the primary drying stage increases as (i) the product height decreases, (ii) the particle diameter increases, and (iii) the value of the packing porosity increases. The mathematical model presented in this work is considered to offer a necessary and essential capability that could be used for the design, optimization, and control of the spray freeze drying process as well as of a process involving the drying of frozen particles in packed beds.