Heat transfer in vial lyophilization.

Heat transfer in vial lyophilization has been studied experimentally and theoretically as a first step in developing a theoretical model for vial lyophilization. Heat transfer was studied by cooling and heating sealed vials containing water in a pilot scale freeze-dryer. The factors studied were bottom curvature of the vial, chamber pressure, fill volume, position on the shelf and the state of the water. A theoretical dynamic and two-dimensional axisymmetric model that comprised both the vial and its content was developed. It was constructed using physical models for thermal conductivity of gases at low pressure, thermal conduction and radiation. The coefficients in the model were based on physical constants and geometrical data and not assessed from experiments. The resulting differential equations were solved numerically. The theoretical model could well describe both heat transfer and heat accumulation in the vial. The dynamics of the corner vials could also be well modeled by adding heat transfer to the side of the vial. The effect of the curvature of the vial bottom, the heat accumulation in the glass vial and the heat transfer to the sidewalls of vials in the corner of the shelf all contributed to a significant radial influence on the heat transfer.