CFD based determination of sublimation mass flux for lyophilization inside a vial

In the case of computational models of lyophilization in a vial, the intensity of drying is to a large extent controlled by the pressure conditions above the drying surface, as the drying driving force is the pressure difference between the saturation vapour pressure at the sublimation interface and the vapour partial pressure above the drying substance. In majority of studies, the effect of the vial and the rubber stopper geometry on the pressure conditions inside the vial is either neglected or taken into account by an estimated additional vapour pressure increase inside the vial. As the pressure conditions depend on the flow of sublimated solvent inside the vial-stopper conduit geometry, but are experimentally difficult to determine, a dedicated CFD analysis of flow conditions inside the vial-stopper channel was performed. The influence of imposing of the no-slip and slip conditions on the solid surfaces on the pressure drop in the system was studied and the effect of the increased partial pressure of the solvent on the sublimation rate was evaluated for the starting phase of the lyophilization by implementing the Stefan’s one sided diffusion model. The computational results show, that the effect of the additional flow resistance due to the vial conduit and the stopper is most significant at lowest system temperatures, with as much as 30% increase in vapour pressure inside the vial.