Determination of pressure resistance of a partially stoppered vial by using a coupled CFD-0D model of lyophilization

Abstract

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.