Experimental study and modeling of effective NaCl diffusion coefficients values during Emmental cheese brining

Abstract

Experimental data concerning NaCl concentration profiles for industrially processed Emmental cheese were determined with cylindrical samples ensuring semi-infinite unidirectional mass transfer with saturated brining aqueous solutions for different temperature conditions in the range between 4 and 18 °C. Considering a binary diffusion system constituted by the cheese water and the NaCl solute, the NaCl diffusion kinetics were analyzed at each investigated temperature by three different approaches: firstly, using the second Fick’s law with a constant NaCl diffusivity, which gave a poor interpretation of the experimental data; secondly, using the Boltzmann’s method with a concentration dependent NaCl diffusion coefficient and thirdly, by numerical identification from the diffusion equation with an empirical variation of the NaCl diffusivity with the salt concentration (2nd order polynomial) and a boundary condition expressing the mass flux continuity at the interface. As a whole, the derived diffusivity values were found to be in good agreement with the previous published data concerning different cheese types. These two last analyses clearly indicated a decrease of the NaCl effective diffusivity with the salt concentration and, secondly, an increase of this diffusivity with the temperature. Finally, the last modelling, based on a quadratic reduction in the salt diffusivity with the salt concentration and on a Dirichlet (type II) limit condition lead to the best fitting between the measured and the predicted NaCl concentration profiles.