Prediction of free-ion activities and ionic equilibria in bovine milk

The electrolytes in milk are essential as nutrients and for osmotic balance and have been well characterised at normal milk concentrations. When milk is concentrated by evaporation or reverse osmosis, the concentration of ions can easily exceed solubility limits. The main objective of this work was to be able to accurately predict ions association, activity and solubility in concentrated bovine milk. The Mean Spherical Approximation (MSA) method was used to calculate free-ion activity coefficients as it contained terms that enhanced accuracy at higher concentrations. This approach led to a system of over 80 non-linear equations for equilibria, electroneutrality and conservation, that was solved using Newton’s method. Significant problems were encountered due to incomplete definitions of variables and units in chemical literature. The Gibbs–Duhem relationship was used with numerical integration to determine water activities from free-ion activities, thus enabling some validation using data for binary systems. The predicted pH was also used for validation. The results were considered satisfactory given the impossibility of obtaining accurate data for even the simplest multi-components systems