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

Journal of Food Engineering

Volumn 79, Issue 3, 2007, Pages 771-778

  Bona, Evandro ^a   Silva, Rui Sérgio S F da ^a   Borsato, Dionísio ^a   Silva, Luiz Henry M ^b   Fidelis, Dayanne Aline de Souza ^a  

^a STATE UNIVERSITY OF LONDRINA   (Brazil)

^b School of Apucarana   (Brazil)

Author keywords

Generalized Fick's second law; Three dimensional modeling and simulation

Indexed keywords

COMPUTER SIMULATION; DIFFUSION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; QUALITY CONTROL;

GENERALIZED FICK'S SECOND LAW; PARTIAL SUBSTITUTION; THREE-DIMENSIONAL MODELING;

FOOD PRODUCTS;

EID: 33750147872     PISSN: 02608774     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfoodeng.2006.02.041     Document Type: Article

References (40)

1. Bickford W.B. A first course in the finite element method (1990), Irwin, Boston 649p
2. Bona, E. (2004). Mixed salting with NaCl and KCl in prato cheese: Modeling of multicomponent diffusion applying the finite element method. 120p. Dissertation (Master in Food Science) - Universidade Estadual de Londrina, Londrina (in Portuguese).
3. Bona E., Borsato D., Silva R.S.S.F., and Herrera R.P. Aplicativo para otimização empregando o método simplex seqüencial. Acta Scientiarum 22 5 (2000) 1201-1206
4. Bona E., Borsato D., Silva R.S.S.F., and Silva L.H.M. Difusão multicomponente durante a salga mista de queijo prato. Ciência e Tecnologia de Alimentos 25 2 (2005) 394-400
5. Brebbia C.A., and Ferrante A.J. The finite element technique: An introduction for engineers (1975), Ed. UFRGS, Porto Alegre 410p
6. Chung T.J. Finite element analysis in fluid dynamics (1978), McGraw Hill, New York 378p
7. Cline A.K., Moler C.B., Stewart G.W., and Wilkinson J.H. An estimate for the condition number of a matrix. SIAM Journal of Numerical Analysis 16 (1979) 368-375
8. Cussler E.L. Multicomponent diffusion (1976), Elsevier, Amsterdam 176p
9. Davis P.J., and Polonsky I. Numerical interpolation, differentiation and integration. In: Abramowitz M., and Stegun I. (Eds). Handbook of mathematical functions (1965), Dover Publications, New York 875-924
10. Derringer G., and Suich R. Simultaneous optimization of several response variables. Journal of Quality Technology 12 4 (1980) 214-219
11. Dongarra J.J., Bunch J.R., Moler C.B., and Stewart G.W. LINPACK users' guide (1979), SIAM, Philadelphia
12. EdAkin J. Finite element analysis for undergraduates (1986), Academic Press, London 319p
13. Fitzgerald E., and Buckley J. Effect of total and partial substitution of sodium chloride on the quality of cheddar cheese. Journal of Dairy Science 68 12 (1985) 3127-3134
14. Furtado M.M. A arte e a ciência do queijo (1990), Editora Globo S.A., São Paulo 297p
15. Guinne T.P., and Fox P.F. Salt in cheese: physical, chemical and biological aspects. In: Fox P.F. (Ed). Cheese: Chemistry, physics and microbiology Vol. 1 (1984), Elsevier Applied Publ. Science, New York 31-35
16. Heldman D.R. Predicting the relationships between unfrozen water fraction and temperature during food freezing using freezing point depression. Transactions ASAE 17 (1974) 63
17. He F.J., and Macgregor G.A. Potassium intake and blood pressure. American Journal of Hypertension 12 (1999) 849-851
18. Huebner K.H., Thorton E.A., and Byron T.G. The finite element method for engineers. 3rd ed. (1995), John Wiley & Sons, New York
19. Katsiari M.C., Voutsinas L.P., Alichanidis E., and Roussis I.G. Manufacture of kefalograviera cheese with less sodium by partial replacement of NaCl with KCl. Food Chemistry 61 1/2 (1998) 63-70
20. Lindsay R.C., Hargett S.M., and Bush C.S. Effect of sodium/potassium (1:1) chloride concentrations on quality of cheddar cheese. Journal of Dairy Science 65 3 (1982)
21. Lomauro G.L., and Bakshi A.S. Finite element analysis of moisture diffusion in stored foods. Journal of Food Science 50 (1985) 392-396
22. Lombardi A.M., and Zaritzky N.E. Simultaneous diffusion of citric acid and ascorbic acid in prepeeled potatoes. Journal of Food Process Engineering 19 (1996) 27-48
23. Luna J.A., and Bressan J.A. Mass transfer during brining of cuartirolo argentino cheese. Journal of Food Science 51 3 (1986) 829-831
24. Lynch N. In search of the salty taste. Food Technology 41 11 (1987) 82-86
25. Naveh D., Kopelman I.J., and Pflug I.J. The finite element method in thermal processing of foods. Journal of Food Science 48 (1983) 1087-1093
26. Onsager L. Theories and problems of liquid diffusion. Annals of the New York Academy of Sciences 46 (1945) 241
27. Payne M.R., and Morison K.R. A multi-component approach to salt and water diffusion in cheese. International Dairy Journal 9 (1999) 887-894
28. Pinto J.C., and Lage P.L.C. Métodos numéricos em problemas de engenharia qui{dotless}́mica (2001), Rio de Janeiro, e-papers 317p
29. Puri V.M., and Anantheswaran R.C. The finite-element method in food processing: a review. Journal of Food Engineering 19 (1993) 247-274
30. Rapacci M. Efeito da substituição do cloreto de sódio por cloreto de potássio nas caracteri{dotless}́sticas do queijo prato (1989), Tese de Mestrado. Universidade Estadual de Londrina, PR 106p
31. Sastry S.K., Beelman R.B., and Speroni J.J. A three-dimensional finite element model for thermally induced changes in foods: application to degradation of agaritine in canned mushrooms. Journal of Food Science 50 (1985) 1293-1299
32. Schwartzberg H.G., and Chao R.Y. Solute diffusivities in leaching processes. Food Technology 36 2 (1982) 73-86
33. Silva R.S.F., Borsato D., and Silva L.H.M. Difusão do cloreto de sódio no processo de salga de queijos: modelagem matemática com o emprego do método de elementos finitos. Ciência e Tecnologia de Alimentos 18 1 (1998) 87-92
34. Silva L.H.M., Silva R.S.S.F., and Borsato D. Finite element analysis of diffusion problem during cheese salting: combined influence of space and time discretization. Acta Scientiarum 21 4 (1999) 873-879
35. Singh R.P. Numerical techniques. In: Saguy I. (Ed). Computer-aided techniques in food technology (1983), Marcel Dekker, New York 23-47
36. Sperandio D., Mendes J.T., and Silva L.H.M. Cálculo numérico: Caracteri{dotless}́sticas matemáticas e computacionais dos métodos numéricos (2003), Prentice Hall, São Paulo 354p
37. Walters F.H., Morgan S.L., Parker L.R., and Deming S.N. Sequential simplex optimization (1999), Licensed eletronic reprint by Multisimplex AB, Karskrona, Sweden 403p
38. Wang G.L., and Sun D. Recent developments in numerical modelling of heating or cooling processes in the food industry - a review. Trends in Food Science and Technology 14 (2003) 408-423
39. Zorrilla S.E., and Rubiolo A.C. A model for using the diffusion cell in the determination of multicomponent diffusion coefficients in gels or food. Chemical Engineering Science 49 13 (1994) 2123-2128
40. Zorrilla S.E., and Rubiolo A.C. Modelling average concentrations of salt and salt substitute in partial or total volumes of semihard cylindrical cheeses. International Journal of Food Science and Technology 33 (1998) 501-508