Mathematical modeling of multicomponent NaCl and KCl diffusion process during the salting of pre-cooked champignon mushrooms

Bordin, Mirian Souza Prado; Borsato, Dionísio; Cremasco, Hágata; Galvan, Diego; Silva, Lívia Ramazzoti Chanan; Romagnoli, Érica Signori; Angilelli, Karina Gomes

doi:10.1016/j.foodchem.2018.01.188

Cited by 21 publications

(32 citation statements)

References 16 publications

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“…Simplex optimization begins with the delimitation of lower and upper limits for each factor that will be controlled. Simplex optimization was performed in three fundamental steps: initial simplex; coordinate of reflection and coordinate of the motion vector, according to the methodology described by Bona et al 10 and Bordin et al 5 In the initial simplex, the algorithm suggests combinations of values of rate constants, that were used in the simulations of the reaction in geometry 0D. After establishing the initial simplex, the molar conversion values for each simplex were obtained with the FEM application.…”

Section: Resultsmentioning

confidence: 99%

“…The multiphysics platform simulation based on the finite element method (FEM) is an analytical methodology that has been highlighted in science areas. 5,6 FEM is used to solve differential equations using a variational formulation or a residual weight procedure, where a partial differential equation is transformed into a system of ordinary differential equations, when the problem is time dependent. Several authors have used the simulation by finite elements, coupled to optimization methods and desirability functions, to determine parameters such as diffusion coefficients, laminar and Biot number.…”

Section: Introductionmentioning

confidence: 99%

“…Several authors have used the simulation by finite elements, coupled to optimization methods and desirability functions, to determine parameters such as diffusion coefficients, laminar and Biot number. 5,7,8…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling of the Transesterification Reaction by Finite Elements: Optimization of Kinetic Parameters Using the Simplex Sequential Method

Galvan¹,

Chendynski²,

Mantovani³

et al. 2020

J. Braz. Chem. Soc.

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The use of biodiesel as fuel has been presented as a viable alternative in the search for renewable energies. It can be produced from the transesterification reaction of vegetable oils with methanol in the presence of sodium or potassium hydroxide as catalysts. In the present research, the transesterification reaction of soybean oil was modeled considering the three steps of the direct and reverse reactions following a second order general kinetics by the finite element method using the COMSOL Multiphysics ® software. The values of rate constants were determined using the simplex optimization method coupled with the desirability functions. The optimized rate constants for the forward reactions were 0.250 × 10 −6 (k 1f), 1.137 × 10 −6 (k 2f) and 3.134 × 10 −6 (k 3f); and for the reverse reactions were 0.202 × 10 −6 (k 1r), 0.884 × 10 −6 (k 2r) and 0.219 × 10 −6 (k 3r) all in m 3 mol −1 s −1. The kinetic model proposed for the reaction can be simulated by the finite element method (FEM) under realistic conditions.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mathematical Modeling of the Transesterification Reaction by Finite Elements: Optimization of Kinetic Parameters Using the Simplex Sequential Method

Galvan¹,

Chendynski²,

Mantovani³

et al. 2020

J. Braz. Chem. Soc.

Self Cite

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“…The finite element method (FEM) is used to solve differential equations using a variational formulation or residual weight procedure, where a partial differential equation is transformed into a system of ordinary differential equations for a time dependent problem. 16 Several authors 17,18 have used finite element simulation coupled with optimization methods and desirability functions to determine mass transfer parameters.…”

Section: Introductionmentioning

confidence: 99%

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

Bordin

Cremasco

Galvan

et al. 2020

J. Braz. Chem. Soc.

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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.

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“…Salting by immersion in a solution containing sodium chloride is one of the oldest and most commonly used treatments for food preservation, since this salt not only has antimicrobial activity, but also promotes chemical and nutritional changes, enhancing the flavor, texture, color and regulating moisture in the final product (Thibaudeau et al, 2015). Various types of foods, such as meat, fish, eggs, cheese, olives, pickles, potatoes, carrots, among others, are still obtained through the use of this preservation process (Dixit et al, 2018;Bordin et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Influence of film coefficient during multicomponent diffusion – KCl/NaCl in biosolid for static and agitated system using 3D computational simulation

et al. 2019

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The influence of film coefficient formed during the diffusion of inorganic salts (NaCl and KCl) in biosolids was studied using a 3D computer modeling by Finite Elements Method (FEM) in CDMSDL Multiphysics ® software combined with SDM-type Artificial Neural Networks (ANN). Such tools have shown that the influence of the film formed in the biosolid/solution interface occurs in a heterogeneous manner and is due to the matrix geometry, the type of system (agitated or static) and the ion size (Na + or K +). The influence of film coefficient was more pronounced for K + ion, and for a static system. Comparing the geometry of biosolids, ion diffusion was more pronounced in the (Y±) axis in relation to other axes, X (±) and Z (±), as well as in between the poles (±) of this axis. FEM simulation associated with SDM-type ANN were efficient tools to evaluate this complex and unknown biophysical phenomenon.

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Mathematical modeling of multicomponent NaCl and KCl diffusion process during the salting of pre-cooked champignon mushrooms

Cited by 21 publications

References 16 publications

Mathematical Modeling of the Transesterification Reaction by Finite Elements: Optimization of Kinetic Parameters Using the Simplex Sequential Method

Mathematical Modeling of the Transesterification Reaction by Finite Elements: Optimization of Kinetic Parameters Using the Simplex Sequential Method

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

Influence of film coefficient during multicomponent diffusion – KCl/NaCl in biosolid for static and agitated system using 3D computational simulation

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