Investigação de modelos fenomenológicos aplicados à hidratação de soja convencional e transgênica - Nicolin, Douglas Junior (2015)
Phenomenological models were developed to describe the hydration kinetics of both conventional and transgenic soybean. A lumped parameter model was developed at first which considered the mass transfer coefficient as a linear function of moisture content. The model was validated with moisture experimental data and compared with its simpler version present in literature. An analytical solution was obtained to the proposed model and the results were better than the simpler version which considered constant mass transfer coefficient along the whole hydration process. A distributed parameter model was also developed based on Fick's Second Law of Diffusion to model the hydration kinetics of both conventional and transgenic cultivars. In order to increase the physical reality of the model it was considered that the size of the grains in which the diffusion equation is valid increased by applying the Variable Space Grid Method (VSGM), turning the problem into a moving boundary problem, which is mathematically known as Stefan problem. Two cases were considered: diffusion equation with constant diffusivity and diffusion equation with diffusivity as a function of moisture content. The proposed models described satisfactorily the tendencies of moisture content experimental data as a function of time and the models provided both the profiles for the new radial positions which arose as the grains increased and the behavior of the radius of the grains as a function of time as one of the results from the solution of the model. The constant diffusivity model presented better results than the variable diffusivity one as could be observed by Akaike test. The best model was used to obtain diffusivities for another six transgenic cultivars. The deviation between calculated values and radius experimental data was due to the irregular increase of the seed coat of the soybean grain in a preferential direction after a certain time of immersion. A two moving boundaries model was also developed. The first moving boundary is a hydration front which moves towards the center of the grains and that reaches the center when the whole grain has equilibrium moisture content. The second moving boundary is the radius of the grain itself and it moves until reaching a maximum value when the steady state is also reached. Through the consideration of pseudo steady state hypothesis it was possible to obtain analytical expressions which related the two moving boundaries to time and it was possible to demonstrate that there were differences between dynamic and pseudo steady state predictions of the behavior of the moving boundaries. The models developed in the present work, specially the distributed parameter models, can be used to model mass or heat diffusion processes in spherical systems which suffer variation in the size of their size during the diffusion process.