Fractional Calculus as a Mathematical Tool to Improve the Modeling of Mass Transfer Phenomena in Food Processing

Research, innovations and applications in the food industry are always delayed relative to other areas of engineering, in part because modeling, simulation and optimization of food processes face additional challenges due to the nature of biological materials. In addition, researchers and scientists in other engineering fields tend to have better mathematical training in relation to researchers in biological sciences. Our hypothesis is that the diffusion process within food materials which are non-Fickian, that is, anomalous, can be characterized using a fractional calculus formulation. There is currently strong experimental and theoretical evidence that the diffusion process in food materials generally departs from the Fickian diffusion model which comes from the random walk displacement of the diffusants. In biological materials the heterogeneity due to the cellular structure produces regions in which the diffusants can travel anomalous length distances or be stopped in compartments, which produces a departure from the expected results of the random walk, resulting in anomalous diffusion. The introduction and application of fractional calculus to the field of food science/engineering could lead to many uses, primarily in heat and mass transfer processes. Fractional calculus is a powerful tool for solving and understanding complex natural phenomena; therefore, we believe it is necessary to exploit it to the utmost to obtain realistic and practical solutions for the mass transfer phenomena and to demonstrate its potential to other food science/engineering problems.