Simultaneous Transfer of Na+, K+, and Fe2+ Ions During Salting of Precooked Mushroom (Agaricus bisporus): Mathematical Modeling, Optimization, and Experimental Validation

Abstract

The champignon mushroom has no antinutritional factors that can affect iron bioavailability. It is considered a functional food and can provide health benefits by presenting bioactive components. The simultaneous transfer of Na + , K + and Fe 2+ in the pre-cooked mushroom (Agaricus bisporus) was modeled and simulated by the finite element method (FEM). The Biot number, cross and main diffusion coefficients were determined by the super modified simplex optimization method by minimizing the percentage errors. The errors between experimental and simulated data were 5.66% for NaCl, 5.36% for KCl and 8.26% for Fe 2+ in the static brine and 3.11% for NaCl, 3.30% for KCl and 15.34% for Fe 2+ in stirred brine. With the obtained model, it was possible to verify the influence of the film formed on the surface of the mushroom during the diffusion of ions, as well as the increase of ferrous ion adsorption when using the salting system with stirring.

Application of artificial neural networks in the study of Mozzarella cheese salting

“…The solute diffusion occurred under isothermal conditions (20 °C) and cheese contraction during salting was not considered. To evaluate the influence of the film formed on the Mozzarella cheese surface, in the static and dynamic salting systems, the Cauchy boundary condition was considered (Bona et al, 2007;Bordin et al, 2020) instead of Dirichlet boundary conditions, in which the concentrations obtained on the surface of the cheese immediately after dipping are the same as those of brine (Chung, 1978). The finite element formulation followed the procedures established by Cremasco et al (2019) and Angilelli et al (2015).…”

“…It was used a computer Intel® Core ™ i7-4790 CPU© 3.60 GHz, 32 GB RAM and 250 GB HDD. Table 1 shows the values of the Main and cross coefficients, mass transfer coefficient (h m ) in the film, the relationship between the mass transfer coefficient (h m /λ m ) and the Biot number determined by the finite element method using COMSOL Multiphysics® software, with the application of simplex optimization coupled with the desirability functions, during the diffusion process in the static and dynamic system (Bordin et al, 2020). All simulations were performed using a 3D geometry modeling, with time-dependent solver Backward Differentiation Formula (BDF) with extremely fine tetrahedral finite element mesh, and the continuum was divided into 44,275 tetrahedral elements with a convergence criterion of 10 -4 .…”

3D Simulation and Artificial Neural Networks Application in the Diffusion Study of Champignon Mushroom/Solution Interface During the Salting

“…The cross coefficients being smaller than the main coefficients means that the gradient diffusion is more important than the diffusion due to the interference from a solute in the flow of the other one. 12,25,26 The main diffusion coefficient for potassium was slightly higher than the sodium coefficient. The results were expected since they consider that the diffusion of salts in biosolids takes place within the occluded water presenting higher diffusion coefficients for the potassium ions.…”