Analysis of the composition of Brazilian black soybean seeds and mathematical modelling of intermittent drying and extraction of antioxidant compounds using fractional calculus

The present study aims to analyze the composition of black soybean seeds, evaluate the intermittent drying of black soybean seeds by fractional calculus, optimize the extraction conditions of the antioxidant compounds by varying the solvent ratio and the extraction time, fit traditional models of extraction kinetics, and compare with the fractional order model. Regarding the oil content, it is analyzed that black soybeans have a high lipid content (18.86%), an oil source of interest for research and industrial applications. Regarding drying, it was found that the first order model cannot be used to describe the kinetics of intermittent drying for black soybean seeds and the best kinetic fits were obtained with the Page and fractional order models, which can be applied in simulations of drying and dryer designs. Regarding the extraction process, ethanol/water 45/55 (v/v) solvent proportion obtained the highest antioxidant compound content during 1 h of extraction. So and MacDonald's and hyperbolic kinetic models presented the best fitting to experimental data. About the fractional order model, it is found that for extraction conditions with more significant amounts of water in the ethanolic solution, the α value obtained is less than 1, resulting in the phenomenon of subdiffusion. For the extraction condition with a low amount of water in the ethanolic solution, the α value was greater than 1, depicting a superdiffusion process.