Kinetics of milk coagulation: III. Mathematical modeling of the kinetics of curd formation following enzymatic hydrolysis of κ‐casein—parameter estimation

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Abstract
A step function model of milk micelle agglomeration is proposed to explain the observed kinetics of milk clotting following rennet addition. The model ties together the primary and secondary phases of coagulation. The basis of the model is that no micelle flocculation takes place until ca. 75% of the κ‐casein in the milk is hydrolyzed, at which time flocculation occurs rapidly and the rate limiting step for the clotting process shifts to the κ‐casein hydrolysis reaction. Using such a model, it is possible to explain the clotting kinetics for both rapidly denaturing enzymes and stable enzyme systems. The average rate of the flocculation reaction can be obtained from clotting time‐versus‐reciprocal‐enzyme‐concentration data by extrapolating the data to infinite enzyme concentration. The critical conversion required for imminent flocculation can be found by extrapolating the enzyme concentration to zero. This approach indicates that the critical conversion necessary for gelation is temperature dependent changing from a limiting value of essentially 100% hydrolysis at temperatures below 15°C to only 60% conversion at temperatures above 30°C.