| Dynamic and multi-dimensional in space mathematical models were constructed and solved in order to describe quantitatively the dynamic behavior of the primary and secondary drying stages of the freeze-drying of pharmaceuticals in trays and vials. The theoretical results were compared with the experimental data of the freeze-drying of skim milk, and the agreement between the experimental data and the theoretical results is good.; The problem of operating a tray freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem with the use of the rigorous unsteady state mathematical models for freeze drying in trays and vials which were developed in this work. The heat input to the material being dried and the drying chamber pressure are considered to be the control variables. Constraints are placed on the system state variables by the melting and scorch temperatures during primary drying, and by the scorch temperature during secondary drying. Necessary conditions of optimality for both the primary and secondary drying stages are derived and presented, and an approach for constructing the optimal control policies that minimize the drying times for both the primary and secondary drying stages is presented.; Also, a novel “dynamic pressure rise” method is developed as a remote sensing procedure for determining at different times during the primary drying stage of the freeze drying process (i) the temperature of the moving interface between the dried and frozen layers of the product, (ii) the position of the moving interface, (iii) the temperature of the bottom surface of the frozen layer of the product, and (iv) the temperature profile of the frozen layer of the product. |
