Abstract
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 m2·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.
Abstract
1 ∼ 5.3 × 10−10 m2·s−1 (10 ∼ 15 °C) (i) (ii)
Résumé
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 m2·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 diffusion effectifs ont été obtenus à l’aide de la méthode classique dite « des profils de concentration », méthode macroscopique présentant l’inconvénient d’être destructive. D’autres techniques, telles que la résonance magnétique nucléaire, l’imagerie par résonance magnétique ou la redistribution de fluorescence après photo-blanchiment sont actuellement développées pour mesurer des propriétés de transfert de matière de solutés à une échelle microscopique. Cependant, elles sont encore difficilement applicables aux matrices complexes comme le fromage. Les perspectives en matière de recherche dans ce domaine sont donc les suivantes : (i) le développement de nouvelles techniques expérimentales pour modéliser à l’échelle microscopique les propriétés de transfert de solutés dans des milieux complexes comme le fromage; (ii) la détermination des propriétés de transfert des métabolites impliqués dans les réactions enzymatiques pendant l’affinage du fromage.
Similar content being viewed by others
References
Aguilera J.M., Why food microstructure? J. Food Eng. 67 (2005) 3–11.
Aldarf M., Fourcade F., Amrane A., Prigent Y., Diffusion of lactate and ammonium in relation to growth of Geotrichum candidum at the surface of solid media, Biotechnol. Bioeng. 87 (2004) 69–80.
Aldarf M., Fourcade F., Amrane A., Prigent Y., Substrate and metabolite diffusion within model medium for soft cheese in relation to growth of Penicillium camembertii, J. Ind. Microbiol. Biotechnol. 33 (2006) 685–692.
Amrane A., Aldarf M., Fourcade F., Prigent Y., Substrate and metabolite diffusion within solid medium in relation to growth of Geotrichum candidum, in: FOODSIM 2006, 4th International Conference Simulation Modelling in the Food and Bio Industry, Naples, Italy, June 15–17, 2006, pp. 179–186.
Axelrod D., Koppel D.E., Schlessinger J., Elson E., Webb W., Mobility measurement by analysis of fluorescence photobleaching recovery kinetics, Biophys. J. 16 (1976) 1055–1069.
Bailey J.E., Diffusion of grouped multicomponent mixtures in uniform and nonuniform media, Aiche J. 21 (1975) 192–194.
Baroni A.F., Menezes M.R., Adell E.A.A., Ribeiro E.P., Modeling of Prato cheese salting: fickian and neural network approaches, in: Welti-Chanes J., Velez-Ruiz J.F., Barbosa-Canovas G.V. (Eds.), Transport Phenomena in Food Processing, CRC Press, Boca Raton, USA, 2003, pp. 192–212.
Bona E., Borsato D., da Silva R.S.S.F., Silva L.H.M., Multicomponent diffusion during simultaneous brining of Prato Brazilian cheese, Cienc. Tecnol. Aliment. 25 (2005) 394–400.
Bona E., Carneiro R.L., Borsato D., da Silva R.S.S.F., Fidelis D.A.S., Silva L.H.M., Simulation of NaCl and KCl mass transfer during salting of Prato cheese in brine with agitation: a numerical solution, Braz. J. Chem. Eng. 24 (2007) 337–349.
Bona E., da Silva R.S.S.F., Borsato D., Silva L.H.M., Fidelis D.A.D., Multicomponent diffusion modeling and simulation in prato cheese salting using brine at rest: the finite element method approach, J. Food Eng. 79 (2007) 771–778.
Bressan J.A., Carroad P.A., Merson R.L., Dunkley W.L., Modelling of isothermal diffusion of whey components from small curd cottage cheese during washing, J. Food Sci. 47 (1982) 84–88.
Broyart B., Boudhrioua N., Bonazzi C., Daudin J.-D., Modelling of moisture and salt transport in gelatine gels during drying at constant temperature, J. Food Eng. 81 (2007) 657–671.
Callaghan P.T., Jolley K.W., Humphrey R.S., Diffusion of fat and water in cheese as studied by pulsed field gradient nuclear magnetic resonance, J. Colloid Interface Sci. 93 (1983) 521–529.
Carreroa G., McDonald D., Crawford E., de Vries G., Hendzel M.J., Using FRAP and mathematical modelling to determine the in vivo kinetics of nuclear proteins, Methods 29 (2003) 14–28.
Cayot N., Dury-Brun C., Karbowiak T., Savary G., Voilley A., Measurement of transport phenomena of volatile compounds: a review, Food Res. Int. 41 (2008) 349–362.
Colsenet R., Soderman O., Mariette F., Effect of casein concentration in suspensions and gels on poly(ethylene glycol)s NMR self-diffusion measurements, Macromolecules 38 (2005) 9171–9179.
Crank J., The Mathematics of Diffusion, Oxford University Press, Oxford, UK, 1975.
Crank J., Park G.S., Methods of measurement, in: Crank J., Park G.S. (Eds.), Diffusion in Polymers, Academic Press, Inc., London, UK, 1968, pp. 1–39.
Cussler E.W., Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge, UK, 1976.
Djelveh G., Gros J.B., Bories B., An improvement of the cell diffusion method for the rapid determination of diffusion constants in gels or foods, J. Food Sci. 54 (1989) 166–169.
Doulia D., Tzia K., Gekas V., A knowledge base for the apparent mass diffusion coefficient (D-eff) of foods, Int. J. Food Prop. 3 (2000) 1–14.
Feunteun S., Mariette F., Impact of casein gel microstructure on self-diffusion coefficient of molecular probes measured by 1H PFG-NMR, J. Agric. Food Chem. 55 (2007) 10764–10772.
Floury J., Rouaud O., le Poullennec M., Famelart M.H., Reducing salt level in food. Part 2: Modelling salt diffusion in model cheese systems with regards to their composition, LWT-Food Sci. Technol. 42 (2009) 1621–1628.
Frias J.M., Foucat L., Bimbenet J.J., Bonazzi C., Modeling of moisture profiles in paddy rice during drying mapped with magnetic resonance imaging, Chem. Eng. J. 86 (2002) 173–178.
Gerla P.E., Rubiolo A.C., A model for determination of multicomponent diffusion coefficients in foods, J. Food Eng. 56 (2003) 401–410.
Geurts T.G., Oortwijn H., Transport phenomena in butter, its relation to its structure, Neth. Milk Dairy J. 29 (1975) 253–262.
Geurts T., Walstra P., Mulder H., Transport of salt and water during salting of cheese. I. Analysis of the processes involved, Neth. Milk Dairy J. 28 (1974) 102–129.
Gomes A.M.P., Vieira M.M., Malcata F.X., Survival of probiotic microbial strains in a cheese matrix during ripening: simulation of rates of salt diffusion and microorganism survival, J. Food Eng. 36 (1998) 281–301.
Gros J.B., Rüegg M., Determination of the apparent diffusion coefficient of sodium chloride in model foods and cheese, in: Jowitt R. (Ed.), Physical Properties of Foods, Vol. 2, Elsevier Applied Science, London, UK, 1987, pp. 71–108.
Guiheneuf T.M., Gibbs S.J., Hall L.D., Measurement of the inter-diffusion of sodium ions during pork brining by one-dimensional 23Na Magnetic Resonance Imaging (MRI), J. Food Eng. 31 (1997) 457–471.
Guinee T.P., Studies on the movements of sodium chloride and water in cheese and the effects on cheese ripening, Ph.D. Thesis, National University of Ireland, Cork, 1985.
Guinee T.P., Salting and the role of salt in cheese, Int. J. Dairy Technol. 57 (2004) 99–109.
Guinee T.P., Fox P.F., Sodium-chloride and moisture changes in Romano-type cheese during salting, J. Dairy Res. 50 (1983) 511–518.
Guinee T.P., Fox P.F., Influence of cheese geometry on the movement of sodiumchloride and water during brining, Ir. J. Food Sci. Technol. 10 (1986) 73–96.
Guinee T.P., Fox P.F., Influence of cheese geometry on the movement of sodiumchloride and water during ripening, Ir. J. Food Sci. Technol. 10 (1986) 97–118.
Guinee T.P., Fox P.F., Salt in Cheese: Physical, Chemical and Biological Aspects, in: Fox P.F. (Ed.), Cheese: Chemistry, Physics and Microbiology: General Aspects, Vol. 1, Chapman & Hall, London, UK, 1993, pp. 257–302.
Guinee T.P., Fox P.F., Salt in cheese: physical, chemical and biological aspects, in: Fox P.F., McSweeney P.L.H., Cogan T.M., Guinee T.P. (Eds.), Cheese: Chemistry, Physics and Microbiology: General Aspects, Vol. 1, Elsevier Applied Science, London, UK, 2004, pp. 207–259.
Gutenwik J., Nilsson B., Axelsson A., Determination of protein diffusion coefficients in agarose gel with a diffusion cell, Biochem. Eng. J. 19 (2009) 1–7.
Hallström B., Skjöldebrand C., Trägardh C., Heat transfer and food products, in: Handbook of Chemistry and Physics, Elsevier Applied Science, London, UK, 1988, pp. 1–29.
Han J.H., Floros J.D., Potassium sorbate diffusivity in American processed and Mozzarella cheeses, J. Food Sci. 63 (1998) 435–437.
Hardy J., Étude de la diffusion du sel dans les fromages à pâte molle de type camembert. Comparaison du salage à sec et du salage en saumure, Ph.D. Thesis, Université Nancy 1, France, 1976.
Ishida N., Kobayashi T., Kano H., Nagai S., Ogawa H., Na-23-NMR imaging of foods, Agric. Biol. Chem. 55 (1991) 2195–2200.
Karbowiak T., Hervet H., Leger L., Champion D., Debeaufort F., Voilley A., Effect of plasticizers (water and glycerol) on the diffusion of a small molecule in iota-carrageenan biopolymer films for edible coating application, Biomacromolecules 7 (2006) 2011–2019.
Kovaleski J.M., Wirth M.J., Applications of fluorescence recovery after photobleaching, Anal. Chem. 69 (1997) 600–605.
Kuo M.I., Anderson M., Gunasekaran S., Determining effects of freezing on pasta filata and non-pasta filata Mozzarella cheeses by nuclear magnetic resonance imaging, J. Dairy Sci. 86 (2003) 2525–2536.
Lauverjat C., Compréhension des mécanismes impliqués dans la mobilité et la libération du sel et des composés d’arôme et leur rôle dans la perception. Cas de matrices fromagères modèles, Ph.D. Thesis, AgroParisTech, France, 2009.
Lauverjat C., de Loubens C., Déléris I., Tréléa I.C., Souchon I., Rapid determination of partition and diffusion properties for salt and aroma compounds in complex food matrices, J. Food Eng. 4 (2009) 407–415.
Lawrence R.C., Gilles J., Factors that determine the pH of young Cheddar cheese, N. Z. J. Dairy Sci. Technol. 17 (1982) 1–14.
Lebrun L., Junter G.A., Diffusion of sucrose and dextran through agar-gel membranes, Enzym. Microb. Technol. 15 (1993) 1057–1062.
Lucas T., Bohuon Ph., Model-free estimation of mass-fluxes based on concentration profiles. I. Presentation of the method and of a sensitivity analysis, J. Food Eng. 70 (2005) 129–137.
Luna J.A., Bressan J.A., Mass-transfer during brining of Cuartirolo Argentino cheese, J. Food Sci. 51 (1986) 829–831.
Luna J.A., Bressan J.A., Mass-transfer during ripening of Cuartirolo Argentino cheese, J. Food Sci. 52 (1987) 308–311.
Luna J.A., Chavez M.S., Mathematical-model for water diffusion during brining of hard and semi-hard cheese, J. Food Sci. 57 (1992) 55–58.
Mammarella E.J., Rubiolo A.C., Predicting the packed-bed reactor performance with immobilized microbial lactase, Process Biochem. 41 (2006) 1627–1636.
Mariette F., Topgaard D., Jonsson B., Soderman O., 1H NMR diffusometry study of water in casein dispersions and gels, J. Agric. Food Chem. 50 (2002) 4295–4302.
Metais A., Cambert M., Riaublanc A., Mariette F., Effects of casein and fat content on water self-diffusion coefficients in casein systems: a pulsed field gradient nuclear magnetic resonance study, J. Agric. Food Chem. 52 (2004) 3988–3995.
Meyvis T.K.L., De Smedt S.C., Van Oostveldt P., Demeester J., Fluorescence recovery after photobleaching: a versatile tool for mobility and interaction measurements in pharmaceutical research, Pharm. Res. 16 (1999) 1153–1162.
Moraine R.A., Rogovin P., Kinetics of polysaccharide B-1459 fermentation, Biotechnol. Bioeng. 8 (1996) 511–524.
Nagata T., Chuda Y., Yan X., Suzuki M., Kawasaki K., The state analysis of NaCl in snow crab (Chionoecetes japonicus) meat examined by 23Na and 35Cl nuclear magnetic resonance (NMR) spectroscopy, J. Sci. Food Agric. 80 (2000) 1151–1154.
Pajonk A.S., Saurel R., Andrieu J., Experimental study and modelling of effective NaCl diffusion coefficients values during Emmental cheese brining, J. Food Eng. 60 (2003) 307–313.
Payne M.R., Morison K.R., A multi-component approach to salt and water diffusion in cheese, Int. Dairy J. 9 (1999) 887–894.
Ramos-Cabrer P., Van Duynhoven J.P.M., Timmer H., Nicolay K., Monitoring of moisture redistribution in multicomponent food systems by use of magnetic resonance imaging, J. Agric. Food Chem. 54 (2006) 672–677.
Renou J.-P., Benderbous S., Bielicki G., Foucat L., Donnat J.-P., 23Na magnetic resonance imaging: distribution of brine in muscle, MRI 12 (1994) 131–137.
Resmini P., Volonterio G., Annibaldi S., Ferri G., Study of salt diffusion in Parmigiano-Reggiano cheese using Na36Cl, Sci. Tec. Latt.-Casearia 25 (1974) 149–166.
Ruiz-Cabrera M.A., Gou P., Foucat L., Renou J.P., Daudin J.D., Water transfer analysis in pork meat supported by NMR imaging, Meat Sci. 67 (2005) 169–178.
Schwartzberg H.G., Chao R.Y., Solute diffusivities in leaching processes, Food Technol. 36 (1982) 73–86.
Seiffert S., Oppermann W., Systematic evaluation of FRAP experiments performed in a confocal laser scanning microscope, J. Microsc. Oxford 220 (2005) 20–30.
Sherwood T.G., Pigford R.L., Wilke C.R., Mass transfer, in: Clark B.J., Maisel J.W. (Eds.), McGraw-Hill Inc., New York, USA, 1975, pp. 39–43.
Simal S., Sanchez E.S., Berna A., Mulet A., Simulation of counter-diffusional mass transfer, Chem. Eng. Commun. 189 (2002) 173–183.
Simal S., Sanchez E.S., Bon J., Femenia A., Rossello C., Water and salt diffusion during cheese ripening: effect of the external and internal resistances to mass transfer, J. Food Eng. 48 (2001) 269–275.
Stephan J., Couriol C., Fourcade F., Amrane A., Prigent Y., Diffusion of glutamic acid in relation to growth of Geotrichum candidum and Penicillium camembertii at the surface of a solid medium, J. Chem. Technol. Biotechnol. 79 (2004) 234–239.
Takeuchi S., Maeda M., Gomi Y., Fukuoka M., Watanabe H., The change of moisture distribution in a rice grain during boiling as observed by NMR imaging, J. Food Eng. 33 (2008) 281–297.
Taylor R., Krishna R., Multicomponent Mass Transfer, Wiley, New York, USA, 1993.
Turhan M., Modelling of salt transfer in white cheese during short initial brining, Neth. Milk Dairy J. 50 (1996) 541–550.
Turhan M., Gunasekaran S., Analysis of moisture transfer in White cheese during brining, Milchwissenschaft 54 (1999) 446–450.
Turhan M., Kaletunc G., Modelling of salt diffusion in white cheese during long-term brining, J. Food Sci. 57 (1992) 1082–1085.
Varzakas T.H., Leach G.C., Israilides C.J., Arapoglou D., Theoretical and experimental approaches towards the determination of solute effective diffusivities in foods, Enzym. Microb. Technol. 37 (2005) 29–41.
Vestergaard C., Andersen B.L., Adler-Nissen J., Sodium diffusion in cured pork determined by 22Na radiology, Meat Sci. 76 (2007) 258–265.
Vestergaard C., Risum J., Adler-Nissen J., Na-MRI quantification of sodium and water mobility in pork during brine curing, Meat Sci. 69 (2005) 663–672.
Voilley A., Souchon I., Flavour retention and release from the food matrix: an overview, in: Voilley A., Etievant P. (Eds.), Flavour in Food, Woodhead Publishing Limited, Cambridge, UK, 2006, pp. 117–132.
Warin F., Gekas V., Voirin A., Dejmek P., Sugar diffusivity in agar gel/milk bilayer systems, J. Food Sci. 62 (1997) 454–456.
Welti-Chanes J., Mujica-Paz H., Valdez-Fragoso A., Leon-Cruz R., Fundamentals of Mass Transport, in: Welti-Chanes J., Vélez-Ruiz J.F., Barbosa-Cánovas G.V. (Eds.), Transport Phenomena in Food Processing, CRC Press, Boca Raton, USA, 2003, pp. 11–65.
Wesselingh J.A., Krishna R., Mass Transfer in Multicomponent Mixtures, Delft University Press, Delft, Netherlands, 2000.
Wesselingh J.A., Vonk P., Kraaijeveld G., Exploring the Maxwell-Stefan description of ion-exchange, Chem. Eng. J. Biochem. Eng. J. 57 (1995) 75–89.
Wilde J., Baumgartner C., Fertsch B., Hinrichs J., Matrix effects on the kinetics of lactose hydrolysis in fermented and acidified milk products, Chem. Biochem. Eng. 15 (2001) 143–147.
Wiles P.G., Baldwin A.J., Dry salting of cheese, part I: Diffusion, Food Bioprod. Process. 74 (C3) (1996) 127–132.
Yanniotis S., Anifantakis E., Diffusion of salt in dry-salted Feta cheese, in: Jowitt R., Escher F., Hallstrom B., Meffert H.F.T., Spiess W.E.L., Vos G. (Eds.), Physical Properties of Foods, Applied Science Publishers, London, UK, 1983.
Zorrilla S.E., Rubiolo A.C., A model for using the diffusion cell in the determination of multicomponent diffusion-coefficients in gels or foods, Chem. Eng. Sci. 49 (1994) 2123–2128.
Zorrilla S.E., Rubiolo A.C., Fynbo cheese NaCl and KCl changes during ripening, J. Food Sci. 59 (1994) 972–975.
Zorrilla S.E., Rubiolo A.C., Modeling NaCl and KCl movement in Fynbo cheese during salting, J. Food Sci. 59 (1994) 976–980.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Floury, J., Jeanson, S., Aly, S. et al. Determination of the diffusion coefficients of small solutes in cheese: A review. Dairy Sci. Technol. 90, 477–508 (2010). https://doi.org/10.1051/dst/2010011
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1051/dst/2010011