Use of 3D mathematical modelling to understand the heat transfer mechanisms during freeze-drying using high-throughput vials

Abstract

• A 3D steady model predicts heat flows during sublimation in vials inside a well plate. • Time evolution is studied by adding mass transfer to a 3D steady heat transfer model. • Gas conduction and radiation from the chamber cause heat flow variations among vials. • Heat flow variations between vial positions diminish as sublimation occurs. • Well plates reduce heat flow variations between vial positions during sublimation. Screening potential vaccine formulations during freeze-drying is a time-consuming task. High-throughput systems, consisting of small vials inside aluminium well plates, can accelerate formulation selection. However, heat transfer variations among vials due to the edge effect can entail deviations in the final product quality and bias results. This work investigates how the vial position in the well plate impacts the heat flow received during the primary drying step of freeze-drying. Two 3D steady-state models were proposed and compared to evaluate the effect of time passing. One model, called the distilled water model , represents vials containing only a frozen layer at the beginning of primary drying. A second model, called the product model , represents vials containing frozen and dried product layers after drying has progressed (up to half of the product dried). Heat transfer models were validated using heat flows determined by gravimetric analysis during sublimation tests (shelf temperatures −40 and −15 °C, chamber pressures from 4 to 65 Pa). At the beginning of primary drying, the distilled water model indicated that vials facing a chamber wall received heat flows up to 25% greater than those in the centre of the well plate. As sublimation progressed ( product model ), the dried product layer resistance to mass transfer tended to counterbalance the impact of the chamber wall.