Analytical solution and experimental validation of a model for hydration of soybeans with variable mass transfer coefficient

• A lumped parameter model was proposed to describe soybean hydration.
• The analytical and numerical solution for the model were obtained and compared.
• The analytical solution was validated with experimental and its parameters fitted.
• The results were compared with a simpler case of the model presented.
• A generalized analytical solution was proposed and discussed.

The hydration of soybeans was mathematically modeled using a lumped parameter model from the mass balance for water present in soybeans. The balance reveals that the water flow in the grains occurs through natural convection until the surface, while diffusion is responsible for the inside of the grains. In order to reflect the decrease in mass transfer, KS, as the concentration of water in the grains increases, the coefficient was assumed to present linear variation according to moisture following the approach by other authors. Such model had been numerically solved before; however, its analytical solution remained unknown. The analytical solution to the model was obtained and compared with both the numerical solution and the analytical solution to an elementary case of KS (constant) and validated against experimental data on moisture as a function of time for soybeans in cultivar CD 202 at different temperatures. This process confirmed that the analytical solution is correct and able to be applied in the simulation, analysis, optimization and projects of hydration units as well as any processes involving kinetics in accordance with the model studied. The parameters adjusted to both the numerical and the analytical solution were identical and grew exponentially with temperature. Finally, a generalized model was proposed to represent moisture as function of time and temperature using the results obtained in this study.