Faculty of Mechanical Engineering, University of Maribor, Smetanova ulica 17, SI-2000 Maribor, Slovenia.
Eur J Pharm Biopharm. 2022 Jun;175:53-64. doi: 10.1016/j.ejpb.2022.04.010. Epub 2022 May 10.
Modeling lyophilization in a vial is frequently done on a single vial level. When setting up a numerical model, the main focus is on heat and mass transfer inside the lyophilizate, whereas the vapor dynamics in the headspace of the vial is taken into account simply through imposing the system pressure as a pressure boundary condition. The present paper offers a deeper insight into the interaction of the sublimated vapor flow and the corresponding vapor pressure conditions inside the headspace of a partially stoppered vial. This is achieved through a coupled numerical solution of the heat and mass transfer inside the product by means of a 0D model describing the frozen domain (ice) and the 3D fluid flow inside the vial geometry with the partially opened stopper, computed by means of Computational Fluid Dynamics. Due to low pressures, the slip flow regime within the continuum hypothesis has to be considered, leading to imposing velocity slip conditions at the solid walls. The 0D model is used for the computation of sublimation mass flow rate as well as heat transfer rate to the vial, with the results of the water vapor mass flow rate and the temperature communicated to the 3D CFD model as a new inlet boundary conditions for computation of compressible fluid flow dynamics inside the vial. The obtained CFD pressure field solution allows derivation of a pressure resistance model for a targeted vial stopper combination, which is then used in calculating the corresponding pressure drop in the headspace of the partially stoppered vial. The coupled CFD-0D model results are validated based on the results of dedicated experimental water runs on several vial and stopper geometries and show, that the vial geometry, but especially the installed stopper, alter the pressure field conditions inside the vial. The increased in-vial local vapor pressure values lead to a decrease of the mass flow rates and an increase of temperatures at the bottom of the product, which range from 0.6 K for the highest system pressure and up to 5.4 K for the lowest system pressure tested. The presented coupled model is suitable for the use in further studies of the impact of various vial forms as well as stoppers on the lyophilization dynamics in a vial.
在小瓶中进行冷冻干燥的建模通常是在单个小瓶级别上进行的。在建立数值模型时，主要关注的是冷冻干燥中的热量和质量传递，而小瓶瓶头空间中的蒸汽动力学则通过将系统压力作为压力边界条件来简单考虑。本文更深入地研究了部分塞住的小瓶瓶头空间中升华蒸汽流和相应蒸汽压力条件的相互作用。这是通过 0D 模型对产品内部的热传递和质量传递进行耦合数值求解来实现的，该 0D 模型描述了冻结域（冰），3D 流体流动则通过计算流体动力学（CFD）来计算带有部分打开塞子的小瓶几何形状内的流动。由于压力低，需要考虑连续体假设中的滑移流状态，从而在固体壁面施加速度滑移条件。0D 模型用于计算升华质量流量以及传递到小瓶的热量，水蒸气质量流量和温度的结果传达给 3D CFD 模型，作为计算小瓶内可压缩流体动力学的新入口边界条件。获得的 CFD 压力场解决方案允许为目标小瓶塞组合推导压力阻力模型，然后用于计算部分塞住的小瓶瓶头空间中的相应压降。基于针对几种小瓶和塞子几何形状进行的专用水运行实验结果验证了耦合 CFD-0D 模型的结果，并表明小瓶几何形状，但特别是安装的塞子，改变了小瓶内的压力场条件。增加的瓶内局部蒸汽压力值导致质量流量减少和产品底部温度升高，最高系统压力下的温度降低 0.6K，最低系统压力下的温度升高 5.4K。所提出的耦合模型适用于进一步研究各种小瓶形状和塞子对小瓶中冷冻干燥动力学的影响。
