Trelea Ioan Cristian, Passot Stéphanie, Marin Michèle, Fonseca Fernanda
UMR 782 Genie et Microbiologie des Procedes Alimentaires, AgroParisTech, INRA, 1 Avenue Lucien Bretignieres, 78850 Thiverval-Grignon, France.
J Biomech Eng. 2009 Jul;131(7):074501. doi: 10.1115/1.3142975.
Lyophilizing frozen pellets, and especially spray freeze-drying, have been receiving growing interest. To design efficient and safe freeze-drying cycles, local temperature and moisture content in the product bed have to be known, but both are difficult to measure in the industry. Mathematical modeling of heat and mass transfer helps to determine local freeze-drying conditions and predict effects of operation policy, and equipment and recipe changes on drying time and product quality. Representative pellets situated at different positions in the product slab were considered. One-dimensional transfer in the slab and radial transfer in the pellets were assumed. Coupled heat and vapor transfer equations between the temperature-controlled shelf, the product bulk, the sublimation front inside the pellets, and the chamber were established and solved numerically. The model was validated based on bulk temperature measurement performed at two different locations in the product slab and on partial vapor pressure measurement in the freeze-drying chamber. Fair agreement between measured and calculated values was found. In contrast, a previously developed model for compact product layer was found inadequate in describing freeze-drying of pellets. The developed model represents a good starting basis for studying freeze-drying of pellets. It has to be further improved and validated for a variety of product types and freeze-drying conditions (shelf temperature, total chamber pressure, pellet size, slab thickness, etc.). It could be used to develop freeze-drying cycles based on product quality criteria such as local moisture content and glass transition temperature.
冻干冷冻颗粒，尤其是喷雾冷冻干燥，越来越受到关注。为了设计高效且安全的冻干循环，必须了解产品床层中的局部温度和水分含量，但在工业中这两者都难以测量。传热传质的数学建模有助于确定局部冻干条件，并预测操作策略、设备和配方变化对干燥时间和产品质量的影响。考虑了位于产品板不同位置的代表性颗粒。假设在板中进行一维传递，在颗粒中进行径向传递。建立了温度控制搁板、产品主体、颗粒内部升华前沿和腔室之间的热和蒸汽传递耦合方程，并进行了数值求解。该模型基于在产品板两个不同位置进行的整体温度测量以及在冻干腔室中的部分蒸汽压测量进行了验证。发现测量值与计算值之间具有良好的一致性。相比之下，发现先前开发的用于紧凑产品层的模型不足以描述颗粒的冻干过程。所开发的模型是研究颗粒冻干的良好起点。它必须针对各种产品类型和冻干条件（搁板温度、腔室总压力、颗粒尺寸、板厚度等）进一步改进和验证。它可用于根据局部水分含量和玻璃化转变温度等产品质量标准来制定冻干循环。
