AI 中文总结
针对冻干初级干燥中的微塌陷现象，提出群体平衡模型直接模拟孔径演变并关联传质阻力，以矩方法保持计算效率，实验验证表明可预测中间温度且速率常数可能为材料参数。
AI 中文摘要
在药物冷冻干燥的初级干燥步骤中，众所周知，无定形辅料在接近其玻璃化转变温度时容易发生“微塌陷”。现有的针对该现象的建模方法通常要么回避该区域，要么通过实验上繁重的经验评估来评估由此产生的传质阻力下降。在本工作中，我们正面处理该现象，开发了一个群体平衡模型，用于描述冻干饼在微塌陷过程中的孔径分布，并将孔径与传质阻力相关联。通过采用矩方法和插值闭合处理群体平衡，我们使模型的计算负担与文献标准的初级干燥模型相当。对于文献中一个传质阻力在干燥过程中明显随产品温度变化的例子，我们将群体平衡模型拟合到高和低产品温度的情况，并表明它可以以相同的精度模拟中间情况。传质阻力表达式的有效性通过另一组文献数据得到验证，其中对于没有微塌陷的配方，事后测量了孔径分布；该模型仅需拟合一个参数即可在这些情况下获得与事后经验评估相当的产品温度预测精度。最后，针对一种配方在多种条件下进行的复杂多实验拟合，在产品温度上取得了定量一致，表明微塌陷行为的速率常数可能是一种材料参数，与具体的多孔几何形状无关。
英文摘要
In the primary drying step of pharmaceutical freeze drying, it is well known that amorphous excipients are prone to "microcollapse" as they approach their glass transition temperature. Existing modeling approaches for this phenomenon generally entail either avoidance of this regime or an experimentally burdensome empirical assessment of the resulting drop in resistance to mass transfer. In this work, we approach the phenomenon head-on by developing a population balance model for the pore size distribution of a freeze-dried cake during microcollapse and relating the pore size to mass transfer resistance. By treating the population balance with the method of moments and an interpolative closure, we keep the model's computational burden on par with the literature-standard model for primary drying. For a literature example when mass transfer resistance clearly varies as a function of product temperature during drying, we fit the population balance model to cases with high and low product temperature and show that it can then simulate intermediate cases with equal accuracy. The validity of the expression for mass transfer resistance is demonstrated with another literature data set, where pore size distributions were measured after the fact for a formulation without microcollapse; only a single parameter from this model needs to be fit to those cases to yield predictive accuracy in product temperature on par with post-hoc empirical assessment. Finally, a sophisticated multi-experiment fit for one formulation across a range of conditions yields quantitative agreement in product temperatures, suggesting that the rate constant for microcollapse behavior may be a material parameter and independent of the precise porous geometry.
Comments31 pages and 18 figures (counting graphical abstract). Originally submitted to International Journal of Heat and Mass Transfer
