Effects of variable diffusivity on soybean hydration modelling as a Stefan problem

Abstract

The diffusion of moisture in soybean grains is usually followed by two physical facts related to the presence of water: the increase in grain size due to water accumulation and the increase in permeability, as more water is absorbed. In order to increase the physical meaning of the proposed model those two phenomenological facts were inserted in the classical Fick's Second Law of Diffusion. The increase of the grains was taken into account by considering the radius of the grains as a moving boundary of the diffusion system (characterizing a Stefan problem). The increase in permeability was taken into account by considering an exponential dependence of the diffusivity with the moisture content. The behaviour of the main parameters was analyzed with the temperatures. The moisture profiles were calculated for the moving boundary problem as well as the behaviour of the radius of the grains as a function of time. The results showed good agreement with experimental reality of soybean hydration process.

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

“…In grains such as soybeans, such a result is consistent since temperature and moisture increase tend to soften the bean structure, making the mass transfer easier. The classical behavior of this result remains, even if the grain size variation, caused by the diffusion of moisture, is taken into account in the proposed model (Coutinho, Omoto, Conceição, Andrade, & Jorge, ; Coutinho, Omoto, dos Santos Conceição, Andrade, & Jorge, ; Nicolin et al (); Nicolin et al (); Nicolin, Jorge and Jorge (); Nicolin et al, ).…”

“…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.…”

Vegan tempeh burger: prepared with aged bean grains fermented by Rhizopus oligosporus inoculum

“…Hydration is understood as a physical process related to tegument permeability and the properties of grain's constituent colloids. Water absorption rate depends on chemical composition, permeability of integument and the presence of water in liquid or gaseous forms in the medium where process is occurring (Nicolin, Jorge, & Jorge, 2017). Cavariani et al (2009) affirm that tegument permeability affects the soybean hydration rate due to variations in thickness, composition, cultivar, and place of production.…”