Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature

Abstract

AbstractThe objective of this research was to evaluate the diffusion mechanism based on Fick's second law and anomalous diffusion modifying the drying operating conditions temperature (T) and relative humidity (RH) on apple slices (cv. Granny smith). Drying was performed at 30 °C, 40 °C, 50 °C and 30%, 50%, 70%RH based on a 32 experimental design. The drying curves were analyzed to determine the effective diffusion (Deff) using two methods: Fick's second law and anomalous diffusion model based on fractional calculus approach. Our results showed that the anomalous diffusion mechanism fit the experimental data better and revealed a super‐diffusive behavior (α > 1). Therefore, Deff values were estimated using the anomalous diffusion model with α = 1.735. With respect to the use of anomalous diffusion model solution based on fractional calculus at different operations conditions allow to get better fitting of drying data than second Fick's law model, even keeping the Arrhenius behavior of Deff with temperature.Practical applicationsDiffusion process is typically analyzed using models based on Fick's second law. However, several assumptions inherent in Fick's second law are not fulfilled in food materials (e.g., structural heterogeneity). In addition, Fick's second law does not consider structural variations during the drying process, and it is well known that fruits such as apples experience significant structural changes during drying. Fractional calculus is a tool for mathematically representing the anomalous diffusion of solutes whose movements can be faster or slower than postulated in Fick's second law due to food structure. In general, with second Fick's law model not good fitting to data are obtained, therefore the prediction capacity of the model is limited. Based on this, anomalous diffusion solution based on fractional calculus was applied. The results showed good fit the data to the model, and also by the time exponent (α) is possible to identify the kind of diffusion process.