Optimising Cheese Brining Times

Steven Psaltis, J. E. F. Green, Troy Farrell, B. Lawson, J. L. Simpson


In this article we detail the work conducted during MISG2014 on the brining of Gouda cheese for the Fonterra Cooperative Group. We consider three different mathematical models that aim to predict the salt content of cheese post-brining. The first is a diffusion model that accounts for the interstitial volume that is available for salt and water transport within the cheese. It predicts moisture content that agrees closely with data provided by Fonterra, and we show how modifications to the salt diffusivity and partial molar volume can improve the accuracy of the salt content predictions. The second model considers the moisture in the cheese to be in two phases---free moisture that contributes to the porosity of the cheese and is accessible to salt diffusion, and water that is bound by the cheese protein. The third model, referred to here as the salt-uptake model, is a reaction-diffusion model that considers salt being bound to the cheese matrix as it diffuses through the cheese. More work is required on this model to be able to draw conclusions regarding the cheese brining process.

  • P. W. Atkins. Physical Chemistry. Oxford University Press, 4th edition, 1990.
  • G. Aylward and T. Findlay. SI Chemical data. John Wiley and Sons, 1974.
  • D. A. G. Bruggeman. Calculation of the various physical constants of heterogeneous substances. I: Dielectric constants and conductivities of mixtures of isotropic substances. Annalen der Physik, 25:636–664, 1935. doi:10.1002/andp.19354160705.
  • G. Carey, N. Fowkes, A. Staelens, , and A. Pardhanani. A class of coupled nonlinear reaction diffusion models exhibiting fingering. Journal of Computational and Applied Mathematics, 166(1), 2004. doi:10.1016/j.cam.2003.09.037.
  • R. Datta and S. A. Vilekar. The continuum mechanical theory of multicomponent diffusion in fluid mixtures. Chemical Engineering Science, 65:5976–5989, 2010. doi:10.1016/j.ces.2010.08.022.
  • C. J. D. Fell and H. Hutchison. Diffusion coefficients for sodium and potassium chlorides in water at elevated temperatures. Journal of Chemical and Engineering Data, 16:427–429, 1971. doi:10.1021/je60051a005.
  • Fonterra Co-Operative Group. Personal communication. 2014.
  • T. J. Geurts, P. Walstra, , and H. Mulder. Transport of salt and water during salting of cheese. 1: Analysis of the processes involved. Netherlands Milk and Dairy Journal, 28:102–129, 1974.
  • T. P. Guinee. Salting and the role of salt in cheese. International Journal of Dairy Technology, 57(2):99–109, 2004. doi:10.1017/S0022112003005512.
  • T. P. Guinee and P. Fox. Sodium chloride and moisture changes in romano–type cheese during salting. Journal of Dairy Research, 50:511–518, 1983. doi:10.1017/S002202990003274X.
  • J. A. Luna and M. S. Chavez. Mathematical model for water diffusion during brining of hard and semi–hard cheese. Journal of Food Science, 57:55–58, 1992. doi:10.1111/j.1365-2621.1992.tb05423.x.
  • K. Mandl, R. W. Hartel, and W. Wendorff. Effects of moisture and salt migration on cheese firmness in cheese–in–sausage products. Journal of Food Engineering, 91:164–172, 2009. doi:10.1016/j.jfoodeng.2008.08.022.
  • MATLAB. version 8.1 (R2013a). The MathWorks Inc., Natick, Massachusetts, 2013.
  • W. Messens, K. Dewettinck, and A. Huyghebaert. Transport of sodium chloride and water in gouda cheese as affected by high–pressure brining. International Dairy Journal, 9:569–576, 1999. doi:10.1016/S0958-6946(99)00126-0.
  • M. R. Payne and K. R. Morison. A multi–component approach to salt and water diffusion in cheese. International Dairy Journal, 9:887–894, 1999. doi:10.1016/S0958-6946(99)00157-0.
  • M. Turhan and G. Kaletunc. Modeling of salt diffusion in white cheese during long–term brining. Journal of Food Science, 57:1082–1085, 1992. doi:10.1111/j.1365-2621.1992.tb11269.x.
  • H. Weingartner. Self–diffusion in liquid water. A reassessment. Zeitschrift fur Physikalische Chemie, 132:129–149, 1982. doi:10.1524/zpch.1982.132.2.129.


cheese; brining; Gouda; mathematical modelling

Full Text:


DOI: http://dx.doi.org/10.21914/anziamj.v56i0.9430

Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.