Development of a computational framework for the prediction of free–ion activities, ionic equilibria and solubility in dairy liquids. (2018)
Type of ContentTheses / Dissertations
Thesis DisciplineChemical Engineering
Degree NameDoctor of Philosophy
PublisherUniversity of Canterbury
AuthorsNoeparvar, Pariyashow all
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. Hence, it seems necessary to deeply understand the ion partitioning in milk and milk–like solutions at various concentrations either at equilibrium or in a dynamic state.
An ion speciation model was proposed to comprehensively consider principal milk components such as calcium, magnesium, sodium, potassium, and hydrogen as the main cations, and citrate, phosphate, carbonate, sulphate, chloride, phosphate esters, carboxylate, and hydroxide as the main anions in serum milk. The dissociable side groups of amino acids in αs1–, αs2–, β–, and κ–casein were incorporated into the model as well as the calcium phosphate nanoclusters (CPN) and phosphoserine residues in the bovine casein. The saturation of potential solid salts such as calcium phosphate in different phases and calcium citrate were obtained. The Mean Spherical Approximation (MSA) method was used to calculate free–ion activity coefficients as it contained terms that enhanced accuracy at higher concentrations. Further, it allows the addition of non–electrolyte components such as lactose. This approach led to a system of over 180 non–linear equations for equilibria, electroneutrality and conservation, that were scaled and then solved using Newton’s method.
The dynamic calculation of ion speciation was also implemented using Euler’s method to solve differential equations for precipitation kinetics. This enabled the monitoring of pH, saturation, and the concentration of calcium salts formed over time. The model was first applied to the binary solutions of calcium chloride, sodium chloride, buffer solutions of citrate and phosphate with and without lactose, calcium carbonate, calcium phosphate, and calcium citrate solid phases, and milk serum both at equilibrium and dynamically. Moreover, the model was applied to milk as the main system including serum and casein proteins with and without CPN, for which net charge of the molecule was calculated as the means of validation. The model could satisfactorily predict pH and saturation of calcium solid salts in concentrated milk up to four times its normal concentration.
The calcium phosphate precipitation was studied experimentally at various concentrations under varied and controlled pH values. The experiments were carried out at 23 ˚C with various concentrations of calcium and phosphate solutions without and with 9.5%w/w lactose. pH was a key factor to determine the amount of calcium phosphate precipitation. Zetasizer analysis showed that lactose strongly influenced the calcium phosphate solution by forming nanoparticles with a size of about 1 nm. The role of lactose in enabling the formation of nanoparticles was previously unknown but is likely to be an important property of milk.