Mathematical modelling in simulate bulk density as a function of shrinkage and collapse mechanics during drying of food products

During drying, food products undergo several physical and structural changes. These changes have a direct impact on properties such as bulk density which is involved in heat and mass transfer processes. Therefore, the prediction of the bulk density as function of water content will be an interesting tool for the process optimization and as a quality indicator of dried food products. In the literature, several models are available to simulate density during drying. The majority of these models are empirical and very few are theoretical ones. However, so far no model has considered that the initial air volume existing at the beginning of the drying process could vary over time. In this study, a theoretical model to predict the bulk density of dried materials as a function of the moisture content was built based on the hypothesis of a variation in both initial and instantaneous porosities during drying. The present model involves two physical mechanisms namely collapse and shrinkage phenomena. The model was formulated as a constrained optimization problem and implemented and solved in Matlab. The new mathematical model was validated with the data obtained from open literature. The agreement with the experimental data and the present model was very good and does not depend on the product or on the technology used. The model was used to understand the mechanisms involved in the drying processes via the collapse and shrinkage functions. Discussions on the mathematical/optimization approaches used to solve the problem were also addressed. Thus, a similar methodology can be used to simulate the volume shrinkage coefficient as a function of moisture content during drying processes.