Mathematical models of the process of submlimationand optimization of lyophilization modes

Abstract

The purposeof this study is to analyze methods of mathematical modeling for calculating the stage of primary sublimation, as the most important stage in lyophilization technology. Presented are mathematical formulas, equations for the calculation of heat and mass transfer processes, during the removal of 90 % of all frozen ice. A model is considered that takes into account the contribution of all thermal effects, including the transient energy balance, taking into account the heat transfer through the side wall of the vial and radiation, even if they are present in a small amount. The mathematical model can be used to optimize the lyophilization cycle, and also as tools for technological monitoring (using sensors based on models). The model considered in the article is a one-dimensional nonstationary state model in which the correct comprehensive transient energy balance has been introduced to describe the heat transfer through the glass of the vial, and the results are estimated using experimental data. The equations used in the simulation describe the mass and energy balances in the dried layer, taking into account the rate of adsorption/desorption of water at the interface, mass and heat transfer at the sublimation interface, as well as the energy balance of heat transfer in the wall of vials, shelf and other factors affecting the process of sublimation. Conclusions are made on the presented mathematical models and the characteristic of the direction of the process of optimization of primary sublimation in lyophilization technology is given.