Numerical Solution of a Nonlinear Diffusion Model for Soybean Hydration with Moving Boundary

Abstract

Variable diffusivity and volume of the grains are taken into account in the diffusion model that describes mass transfer in soybean hydration. The variable space grid method (VSGM) was used to consider the increase in grain size, and the diffusivity was considered an exponential function of the moisture content. An equation for the behavior of the grain radius as a function of time was obtained by global mass balance over the soybean grain and the differential equation considered that the increase in radius happens due to the influence of the convective and diffusive fluxes at the surface of the grains. The model was solved by an explicit numerical scheme which presented satisfactory results. The results showed the behavior of moisture profiles obtained as a function of time and radial position and also showed how the grain radius increased with time and changed the solution domain of the diffusion equation.

Modeling of soybean hydration as a Stefan problem: Boundary immobilization method

“…In their work, the authors used the variable space grid method to include the space grid increase into the diffusion model, and reported a maximum deviation from the model prediction of 8.30% and a minimum deviation of 2.30%. The conclusion of improvement in the predictions was possible because the same set of experimental data, of moisture and radius over time, were used in the present work and in the work of Nicolin et al (). Although the improvement was moderate, it was mainly caused only by changing the method to include the spatial grid variation in the diffusion model.…”

“…The minimum distance identified was 1.71%, in the region where the bean radius practically does not change. The use of the boundary immobilization method improved the quality of the model predictions compared to the work of Nicolin et al () (Figure ). In their work, the authors used the variable space grid method to include the space grid increase into the diffusion model, and reported a maximum deviation from the model prediction of 8.30% and a minimum deviation of 2.30%.…”

“…It is possible to observe that the model predictions were very close to the experimental data. For the temperature of 10 °C, Nicolin et al () reported a maximum bean radius increase of 37.4% for soybeans of cultivar CD 202. In the present work, the predicted maximum increase for this temperature was 38.2%, as presented in Table .…”

“…For the validation of the proposed model, the data of moisture and radius over time were used for the temperatures of 10, 20, 30, 40, and 50 °C, obtained in the work of Nicolin et al (). This allowed one to compare the efficiency of the numerical method presented in this article when compared with the numerical method used in the work of Nicolin, Jorge and Jorge ().…”

“…The absorption or desorption of moisture by foods has been studied by several authors (Aguerre, Tolaba, & Suarez, ; Bello, Tolaba, Aguerre, & Suarez, ; Viollaz & Rovedo, ; Viollaz, Rovedo, & Suarez, ). In the analysis of the hydration of soybean grains and their increase in size caused by the diffusion of moisture, the works of Nicolin, Jorge, and Jorge (), Nicolin, Jorge, and Jorge (), Nicolin et al () and Nicolin, Jorge, and Jorge () stand out. In their works, the authors proposed the modeling, validation, and analysis of the results of Stefan problems and how this approach helps to better understand the soybean hydration process.…”