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Fractional Calculus As A Mathematical Tool To Improve The Modeling Of Mass Transfer Phenomena In Food Processing

Research Scholar

Ricardo Simpson, Food, Agriculture, and Biological Engineering (Chile)
Jaques Nunez, Co-Researcher
Sudhir Sastry, Faculty Mentor


Ricardo Simpson is currently a professor in the Chemical and Environmental Engineering Department at the Universidad Técnica Federico Santa María, in Chile. He earned a degree in biochemical engineering from P. Universidad Católica de Valparaíso in 1980, a master's in food science and technology from Oregon State University in 1990 and a doctorate in food science from Ohio State in 1993. Since obtaining his PhD, Simpson has been an extremely prolific scientist and collaborator in the food industry, not only in Chile but internationally as well. His contributions are summarized in more than 70 peer-reviewed publications (as author or co-author).

What is the issue or problem addressed in your research?

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.

What methodology did you use in your research?

Our hypothesis is that the diffusion process within food materials which are non-Fickian, i.e. 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.

What are the purpose/rationale and implications of your research?

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.