Hidratação de grãos de soja : influência das condições de contorno e da variação de volume sobre modelos matemáticos

Abstract

The hydration process is an important step in the production of soybean protein. These proteins are used primarily to the production of soy-based foods. For the description of the hydration of soybeans phenomenological mathematical models of distributed parameters can be used. These models consider elementary steps of mass transfer and include spatial variations of the properties described. In the solution of such models partial differential equations are generated that require an initial condition and two boundary conditions to be solved. The boundary conditions are usually set in the center and at the surface of the grain. There are different approaches to what happens in terms of surface boundary condition and three of them are generally used: equilibrium moisture immediately reached, moisture behaving as a first order process with respect to time and equality of diffusive and convective flows. It is interesting to use the boundary condition that describes what is really happening on the surface so that there is a good fit. Beyond the boundary conditions, the hypothesis that the volume and diffusivity vary during hydration were also explored. There are indications that the diffusivity has an exponential dependence with moisture in soybean hydration and the volume of the grain undergoes a variation of up to 30% by the end of hydration. In this context, three boundary conditions on the surface were tested and it was assessed which gives the best fit to the experimental data at constant volume while Hsu's model was solved for the cases of constant and variable volume. All models considered the exponential dependence of diffusivity with moisture. The best fit was obtained for the boundary condition of equal flows on the surface at constant volume. The diffusivity showed significant changes with position, humidity and temperature. Comparing the cases of constant and variable volume using Hsu's model, the fits were similar, but the diffusivities obtained showed orders of magnitude of 10 times difference suggesting that the constant volume hypothesis leads to an estimation of parameters without physical reality.