Multicomponent diffusion modeling and simulation in prato cheese salting using brine at rest: The finite element method approach

Bona, Evandro; Silva, Rui Sérgio S.F. da; Borsato, Dionísio; Silva, Luiz Henry M.; Fidelis, Dayanne Aline de Souza

doi:10.1016/j.jfoodeng.2006.02.041

Cited by 21 publications

(23 citation statements)

References 30 publications

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“…Most research publications on mass transfer in cheese are using Fick's model with some specific geometries [10]. Diffusion coefficients in food matrices can be evaluated by different methods involving defined geometries and well-defined experimental conditions (steady or transient state and boundary conditions).…”

Section: Using Fick's Law Solutions To Estimate Diffusion Coefficientsmentioning

confidence: 99%

“…Simal et al [70] and Bona et al [9,10] described a mathematical procedure to obtain the diffusion coefficients of different species (salt and water) that simultaneously diffuse in cheese in such a situation that each mass flux is affected by the existence of the others. The correspondent local mass balances combined with Fick's law were simultaneously solved in one dimension [70] or in three dimensions using a numerical finite 488difference method [9,10].…”

Section: Generalized Fick's Modelmentioning

confidence: 99%

“…The correspondent local mass balances combined with Fick's law were simultaneously solved in one dimension [70] or in three dimensions using a numerical finite 488difference method [9,10]. Indeed, with the development of high-performance computers, it is possible to simulate a process close to reality using three-dimensional geometries and numerical techniques such as the finite element method (FEM) [9,10].…”

Section: Generalized Fick's Modelmentioning

confidence: 99%

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Determination of the diffusion coefficients of small solutes in cheese: A review

Floury

Jeanson

Aly

et al. 2010

Dairy Sci. Technol.

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-In cheese technology, the mass transfer of small solutes, such as salt, moisture and metabolites during brining and ripening, is very important for the final quality of the cheese. This paper has the following objectives: (i) to review the data concerning the diffusion coefficients of solutes in different cheese types; (ii) to review the experimental methods available to model the mass transfer properties of small solutes in complex matrices such as cheese; and (iii) to consider some potential alternative approaches. Numerous studies have reported the transfer of salt in cheese during brining and ripening. Regardless of the type of cheese and its composition, the effective diffusion coefficients of salt have been reported to be between 1 and 5.3 × 10 −10 m 2 ·s −1 at 10-15°C. However, few papers have dealt with the mass transfer properties of other small solutes in cheese. Most of the reported effective diffusion coefficient values have been obtained by macroscopic and destructive concentration profile methods. More recently, some other promising techniques, such as nuclear magnetic resonance, magnetic resonance imaging or fluorescence recovery after photobleaching, are currently being developed to measure the mass transfer properties of solutes in heterogeneous media at microscopic scales. However, these methods are still difficult to apply to complex matrices such as cheese. Further research needs to focus on: (i) the development of nondestructive techniques to determine the mass transfer properties of small solutes at a microscopic level in complex matrices such as cheese; and (ii) the determination of the mass transfer properties of metabolites that are involved in enzymatic reactions during cheese ripening. cheese / mass transfer / diffusion / modelling / solute Article published by EDP SciencesRésumé -Détermination des coefficients de diffusion de petits solutés dans le fromage : une synthèse. En technologie fromagère, le transfert de petits solutés, tels que le sel, l'eau et les métabolites au cours du saumurage et de l'affinage, joue un rôle majeur sur la qualité finale du fromage. Cette revue bibliographique a pour objectifs principaux : (i) de faire le bilan des valeurs publiées des coefficients de diffusion de différents solutés dans les fromages ; (ii) de passer en revue les méthodes expérimentales disponibles pour déterminer les propriétés de transfert des petits solutés dans des milieux complexes comme le fromage ; (iii) de considérer les méthodes alternatives potentiellement applicables aux fromages. Dans la littérature, de nombreuses études ont été publiées au sujet du transfert de sel dans les fromages au cours du saumurage et de l'affinage. En fonction du type de fromage et de sa composition, les coefficients de diffusion effectifs du sel sont compris entre 1 et 5,3 × 10 −10 m 2 ·s −1 à des températures comprises entre 10 et 15°C. Très peu d'études concernant les propriétés de transfert d'autres petits solutés dans les fromages ont été publiées. La plupart des coefficients de diffusi...

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Section: Using Fick's Law Solutions To Estimate Diffusion Coefficientsmentioning

confidence: 99%

Section: Generalized Fick's Modelmentioning

confidence: 99%

Section: Generalized Fick's Modelmentioning

confidence: 99%

See 1 more Smart Citation

Determination of the diffusion coefficients of small solutes in cheese: A review

Floury

Jeanson

Aly

et al. 2010

Dairy Sci. Technol.

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show abstract

“…Nine samples of the cheese were salted in static condition for 5 hours (BONA et al, 2007) in a brine mixture consisting of 13.59 g NaCl.100 g -1 NaCl+KCl+water and 5.06 g KCl.100 g -1 NaCl+KCl+water at 10 ± 1 o C using an adapted domestic refrigerator (CONTINENTAL 560 L). Twenty liters of brine were prepared according to a literature procedure (FURTADO, 1991), which suggested a saline concentration of 20% (w/w) and an average pH of 5.5 (adjusted with HCl).…”

Section: Saltingmentioning

confidence: 99%

“…In general, for fully dissociable ions such as Na + and K + , the values of the cross coefficients are ten times lower than those of the main coefficients (GERLA; RUBIOLO, 2003;MEDINA-VIVANCO et al, 2002). Several authors have studied diffusion in food using the Fick's laws for binary and ternary systems, including diffusion during the salting of Prato cheese (BONA et al, 2007) and Pategras cheese (GERLA; RUBIOLO, 2003); salting (ZORRILLA; RUBIOLO, 1994a) The Finite Element Method (FEM) is a set of powerful numerical techniques for solving differential equations frequently used in food science, which allows the simulation of systems under realistic conditions (WANG; SUN, 2003). The FEM can provide solutions for differential equations that simulate phenomena such as heat and/or mass transfer, radiation, fluid dynamics, and elasticity, as well as chemical and biological processes responsible for the loss of food quality (MARTINS, 2006).…”

Section: Ripeningmentioning

confidence: 99%

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

Bona¹,

Silva²,

Borsato³

et al. 2010

Ciênc. Tecnol. Aliment.

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Mathematical modeling of NaCl and KCl diffusion in mozzarella cheese using static and stirred brine

et al. 2020

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Multicomponent diffusion modeling and simulation in prato cheese salting using brine at rest: The finite element method approach

Cited by 21 publications

References 30 publications

Determination of the diffusion coefficients of small solutes in cheese: A review

Determination of the diffusion coefficients of small solutes in cheese: A review

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

Mathematical modeling of NaCl and KCl diffusion in mozzarella cheese using static and stirred brine

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