Analytical Prediction of Water Activity Evolution for Shelf Life Modeling of Packaged Dehydrated Foods

This study investigates the performance of different Moisture Sorption Isotherm (MSI) equations in predicting the shelf life of dehydrated fish powder, packaged in materials of different water vapor barrier properties. Fish soup powder, produced from salmon by-products, packed in polylactic acid (PLA) and multilayer PET/PE/EVOH/PE pouches and stored under controlled temperature (20°C-50°C) and relative humidity (21%-51%) conditions was used as case study. Water transfer, lipid oxidation, and color change were monitored to assess quality degradation during storage as a function of temperature and water activity (a_w). The GAB (Guggenheim-Anderson-de Boer) model provided the best fit across the entire a_w range, while BET (Brunauer, Emmett, and Teller) and the linear MSI were applicable in the lower a_w region (< 0.65). MSI models were incorporated into the moisture transport equation governing water vapor exchange through the packaging film, and the resulting differential equation was solved in closed form: fully explicit in time for the linear model, and as an explicit relationship between time and water activity for BET and GAB, the latter reported here for the first time. This analytical solution based on the GAB MSI obviates the need for numerical solution algorithms and facilitates calculations. This further enabled product quality prediction, based on lipid oxidation and browning kinetics, demonstrating a tool for selecting packaging materials and estimating shelf life of low-moisture foods at variable storage conditions. PRACTICAL APPLICATIONS: This study provides a practical tool for predicting the shelf life of low-moisture foods by combining moisture sorption isotherms with analytical solutions of water transfer equations. The proposed approach can assist food manufacturers in selecting appropriate packaging materials based on their barrier properties and expected storage conditions. It also enables faster and less labor-intensive shelf life estimation compared to traditional experimental methods.