The anomalous diffusion model based on a fractional calculus approach applied to describe the rehydration process of dried vegetal food matrices

The rehydration process has been traditionally modeled by Fick's second law; however, due to the poor goodness of fit, empirical models such as Peleg's and Weibull models have been implemented. The aim of this work was to demonstrate that the anomalous diffusion model based on fractional calculus can be used to model rehydration process and simultaneously provide a phenomenological understanding of the process. The food matrices assessed were aloe vera, apple, Chilean papaya, and bell peppers rehydrated at 20, 40, and 60 degrees C. The results showed that the anomalous diffusion model was not only able to improve the goodness of fit of rehydration data (R-2 >.99), but also that D-eff can be used under different temperatures given the goodness of fit of the Arrhenius model (R-2 >.88) compared with empirical and Fick's models. Finally, an anomalous diffusion model based on fractional calculus can be successfully used to model the rehydration process in food materials. Practical Applications The novelty of this research is based on the implementation of the anomalous diffusion model that has the simplicity and accuracy of empirical models (e.g., Peleg's model) but with the advantage of a physical interpretation and predictive capacity. Furthermore, although the anomalous model has already been successfully tested in the dehydration process, this is the first time that it has been validated in a rehydration process. Due to the predictive capacity of the anomalous under different operation conditions, the food industry not only could estimate processing time with high accuracy, but also optimize the rehydration process.

Automated summary

This study demonstrated that the anomalous diffusion model based on fractional calculus can improve the goodness of fit in rehydration data and be used under different temperatures. The model provides a better fit than empirical and Fick's models and offers predictive capacity for optimizing the rehydration process in the food industry.