Mechanistic Modeling and Analysis of Thermal Radiation in Conventional, Microwave-assisted, and Hybrid Freeze Drying for Biopharmaceutical Manufacturing

TL;DR

This work addresses non-uniform drying in freeze-drying caused by thermal radiation, especially impacting edge and corner vials. It introduces a mechanistic two-stage primary-drying model augmented by a diffuse-gray radiation formulation and a radiation-network framework that accounts for radiation exchange among all surfaces, including multiple vials and chamber walls. The approach is validated against analytical solutions, Monte Carlo view-factor calculations, and literature experimental data for CFD, MFD, and HFD, demonstrating accurate prediction of temperatures, interface advancement, and drying times, with important insights on wall temperature and vial disposition. The study provides practical tools for design and optimization of freeze-dryer configurations, including a simplified and a data-driven hybrid variant, and delivers open-source MATLAB implementations to enable fast, accurate radiation analyses in industrial settings.

Abstract

In freeze drying, thermal radiation has a significant effect on the drying process of vials located near the corner and edge of the trays, resulting in non-uniformity of the products. Understanding and being able to predict the impact of thermal radiation are therefore critical to accurate determination of the drying process endpoint given the variation in heat transfer of each vial. This article presents a new mechanistic model that describes complex thermal radiation during primary drying in conventional, microwave-assisted, and hybrid freeze drying. Modeling of thermal radiation employs the diffuse gray surface model and radiation network approach, which systematically and accurately incorporates simultaneous radiation exchange between every surface including the chamber wall and vials, allowing the framework to be seamlessly applied for analyzing various freeze-dryer designs. Model validation with data from the literature shows accurate prediction of the drying times for all vials, including inner, edge, and corner vials. The validated model is demonstrated for thermal radiation analysis and parametric studies to guide the design and optimization of freeze dryers.

Figures (15)

• Figure 1: Schematic diagram of the freeze-drying process. The figure is adapted from Srisuma_2023_AnalyticalLyo.
• Figure 2: Three simple geometries where the view factor can be calculated analytically, including (a) a single vial, (b) two vials, and (c) three vials. The heating shelf and other equipment are omitted for clarity.
• Figure 3: Equivalent electrical network for thermal radiation exchange between two surfaces.
• Figure 4: Network representation for radiation exchange between the four surfaces for the three-vial case in Fig. \ref{['fig:SimpleGeometry']}c. The surface resistances are highlighted in blue, while the space resistances are shown in red.
• Figure 5: Flowcharts summarizing the calculation procedures for dynamic modeling of primary drying with the (a) radiation network and (b) simplified approaches.